From b8217a59eed9c64a46eff43726d81c20524d9192 Mon Sep 17 00:00:00 2001
From: Maria Hartmann <lm.hartmann@gmx.de>
Date: Mon, 3 May 2021 17:18:12 +0200
Subject: [PATCH] included slim heaps in experiments; modified plot appearance

---
 data/dijkstra-comps.csv               |   22 +
 data/dijkstra-links.csv               |   22 +
 data/sorting-loc-new-comps.csv        |   64 +-
 data/sorting-loc-new-links.csv        |   64 +-
 data/sorting-sep-new-comps-test.csv   |   19 +
 data/sorting-sep-new-links-test.csv   |   19 +
 data/sorting-subseq-new-comps.csv     |   42 +-
 data/sorting-subseq-new-links.csv     |   42 +-
 data/sorting-uniform-new-comps.csv    |   38 +-
 data/sorting-uniform-new-links.csv    |   38 +-
 pairing_heap.py                       |    8 +-
 plots/paper-dijkstra-new.svg          | 1215 +++++++++------
 plots/paper-dijkstra2-new.svg         | 1556 ++++++++-----------
 plots/paper-permutation-localized.svg | 1509 ++++++++----------
 plots/paper-permutation-separable.svg | 1509 ++++++++----------
 plots/paper-permutation-subseq.svg    | 1509 ++++++++----------
 plots/paper-permutation-uniform.svg   | 1294 ++++++++--------
 plots/paper-sorting-loc-new.svg       | 2035 +++++++++++--------------
 plots/paper-sorting-sep-new-test.svg  | 1217 +++++++++++++++
 plots/paper-sorting-subseq-new.svg    | 1373 ++++++++---------
 plots/paper-sorting-uniform-new.svg   | 1084 ++++++++-----
 scripts/paper-dijkstra-test.py        |   20 +-
 scripts/paper-dijkstra-test2.py       |   22 +-
 scripts/paper-permutations.py         |   23 +-
 scripts/paper-sorting-loc.py          |   24 +-
 scripts/paper-sorting-sep.py          |   24 +-
 scripts/paper-sorting-subseq.py       |   24 +-
 scripts/paper-sorting-uniform.py      |   22 +-
 slim_heap.py                          |  330 ++++
 slim_heap_l.py                        |  196 +++
 30 files changed, 8220 insertions(+), 7144 deletions(-)
 create mode 100644 data/dijkstra-comps.csv
 create mode 100644 data/dijkstra-links.csv
 create mode 100644 data/sorting-sep-new-comps-test.csv
 create mode 100644 data/sorting-sep-new-links-test.csv
 create mode 100644 plots/paper-sorting-sep-new-test.svg
 create mode 100644 slim_heap.py
 create mode 100644 slim_heap_l.py

diff --git a/data/dijkstra-comps.csv b/data/dijkstra-comps.csv
new file mode 100644
index 0000000..e391419
--- /dev/null
+++ b/data/dijkstra-comps.csv
@@ -0,0 +1,22 @@
+randomness parameter value;Pairing;Smooth;Slim
+randomness parameter value;21;22;23
+0.05;11.295882352941176;13.954901960784314;14.419999999999998
+0.1;12.4409900990099;15.918217821782179;16.585049504950497
+0.15000000000000002;13.17291390728477;16.937483443708608;17.81165562913907
+0.2;13.344228855721392;18.057064676616914;19.06452736318408
+0.25;14.197968127490043;18.27940239043825;19.3001593625498
+0.30000000000000004;14.620564784053155;18.740531561461797;19.889568106312293
+0.35000000000000003;14.793931623931623;19.161538461538463;20.429116809116813
+0.4;14.86875311720698;19.73922693266833;21.09344139650873
+0.45;14.973281596452328;20.13133037694013;21.526341463414635
+0.5;15.278443113772456;20.33125748502994;21.79740518962076
+0.55;15.462232304900184;20.587277676950997;22.080925589836664
+0.6000000000000001;15.659317803660567;20.716805324459234;22.29154742096506
+0.65;15.801643625192014;20.967019969278034;22.59758832565284
+0.7000000000000001;15.792710413694719;21.266162624821686;22.9316119828816
+0.75;15.977483355525965;21.410026631158456;23.131118508655124
+0.8;16.029737827715355;21.599438202247192;23.351098626716606
+0.8500000000000001;16.176839012925967;21.704183313748533;23.534324324324327
+0.9;16.44336293007769;21.73238623751387;23.58506104328524
+0.9500000000000001;16.198611987381707;22.20273396424816;24.07757097791798
+1.0;16.352507492507492;22.283306693306695;24.203316683316682
diff --git a/data/dijkstra-links.csv b/data/dijkstra-links.csv
new file mode 100644
index 0000000..a78e5da
--- /dev/null
+++ b/data/dijkstra-links.csv
@@ -0,0 +1,22 @@
+randomness parameter value;Pairing;Smooth;Slim
+randomness parameter value;21;22;23
+0.05;11.295882352941176;9.018431372549019;9.774705882352942
+0.1;12.4409900990099;10.034554455445546;11.043267326732675
+0.15000000000000002;13.17291390728477;10.625629139072847;11.82185430463576
+0.2;13.344228855721392;11.026268656716418;12.359104477611941
+0.25;14.197968127490043;11.36972111553785;12.744541832669324
+0.30000000000000004;14.620564784053155;11.64970099667774;13.143023255813956
+0.35000000000000003;14.793931623931623;11.838404558404559;13.419287749287752
+0.4;14.86875311720698;12.030573566084788;13.6901246882793
+0.45;14.973281596452328;12.200576496674056;13.90419068736142
+0.5;15.278443113772456;12.346467065868264;14.113612774451097
+0.55;15.462232304900184;12.477531760435571;14.283157894736842
+0.6000000000000001;15.659317803660567;12.599217970049915;14.466988352745421
+0.65;15.801643625192014;12.71179723502304;14.61820276497696
+0.7000000000000001;15.792710413694719;12.810756062767476;14.758630527817404
+0.75;15.977483355525965;12.918588548601864;14.898814913448732
+0.8;16.029737827715355;12.99980024968789;15.011123595505616
+0.8500000000000001;16.176839012925967;13.07427732079906;15.142702702702705
+0.9;16.44336293007769;13.164228634850167;15.25294117647059
+0.9500000000000001;16.198611987381707;13.242754994742377;15.364563617245006
+1.0;16.352507492507492;13.307212787212787;15.458991008991006
diff --git a/data/sorting-loc-new-comps.csv b/data/sorting-loc-new-comps.csv
index e5f6e07..7a9a967 100644
--- a/data/sorting-loc-new-comps.csv
+++ b/data/sorting-loc-new-comps.csv
@@ -1,32 +1,32 @@
-randomness parameter value;Pairing;Smooth
-randomness parameter value;0;12
-1e-05;3.3110000000000004;0.9997999999999998
-0.01001;9.695700000000002;10.025450000000001
-0.02001;10.85029;11.63291
-0.03001;11.54132;12.58502
-0.040010000000000004;12.00077;13.229379999999999
-0.050010000000000006;12.386989999999999;13.76429
-0.06001;12.68024;14.18097
-0.07001;12.901870000000002;14.504279999999998
-0.08001;13.10722;14.776249999999997
-0.09000999999999999;13.286290000000001;15.04036
-0.10001;13.454849999999999;15.25796
-0.11001;13.583470000000002;15.44508
-0.12000999999999999;13.70061;15.617080000000001
-0.13001000000000001;13.79743;15.745219999999998
-0.14001000000000002;13.926459999999999;15.91376
-0.15001;14.00538;16.05316
-0.16001;14.084409999999998;16.14607
-0.17001000000000002;14.157020000000001;16.25582
-0.18001;14.223750000000003;16.3467
-0.19001;14.300799999999999;16.46123
-0.20001000000000002;14.33816;16.52597
-0.21001;14.4027;16.58205
-0.22001;14.437909999999999;16.66046
-0.23001000000000002;14.500430000000001;16.726419999999997
-0.24001;14.531600000000001;16.78245
-0.25001;14.58332;16.8614
-0.26001;14.613059999999997;16.90503
-0.27001000000000003;14.6482;16.94697
-0.28001000000000004;14.68594;17.00532
-0.29001;14.715880000000002;17.047040000000003
+randomness parameter value;Pairing;Smooth;Slim
+randomness parameter value;0;12;24
+1e-05;3.3110000000000004;0.9997999999999998;0.9997999999999998
+0.01001;9.67775;10.0012;10.721779999999999
+0.02001;10.85817;11.643739999999998;12.760180000000002
+0.03001;11.539510000000002;12.58643;13.9607
+0.040010000000000004;12.00396;13.256720000000001;14.792639999999999
+0.050010000000000006;12.37384;13.74697;15.44101
+0.06001;12.659740000000001;14.16565;15.96928
+0.07001;12.90557;14.48692;16.405980000000003
+0.08001;13.09812;14.7944;16.75909
+0.09000999999999999;13.29203;15.05026;17.09758
+0.10001;13.429640000000001;15.2323;17.33226
+0.11001;13.585540000000002;15.445480000000002;17.60907
+0.12000999999999999;13.69317;15.58945;17.822210000000002
+0.13001000000000001;13.803190000000003;15.759569999999998;18.00556
+0.14001000000000002;13.908909999999999;15.88996;18.16571
+0.15001;13.99105;16.02691;18.32263
+0.16001;14.083679999999998;16.16697;18.51621
+0.17001000000000002;14.14457;16.251450000000002;18.6329
+0.18001;14.22918;16.34441;18.73009
+0.19001;14.30017;16.453380000000003;18.874979999999997
+0.20001000000000002;14.337049999999998;16.515639999999998;18.9681
+0.21001;14.392430000000001;16.58045;19.067680000000003
+0.22001;14.45719;16.66163;19.15207
+0.23001000000000002;14.49798;16.72156;19.23429
+0.24001;14.543500000000002;16.78512;19.295849999999998
+0.25001;14.575109999999999;16.84369;19.384130000000003
+0.26001;14.62004;16.90114;19.449379999999998
+0.27001000000000003;14.668430000000003;16.96322;19.532780000000002
+0.28001000000000004;14.67765;17.003639999999997;19.57112
+0.29001;14.714970000000001;17.041320000000002;19.62939
diff --git a/data/sorting-loc-new-links.csv b/data/sorting-loc-new-links.csv
index ce73ae8..51d77df 100644
--- a/data/sorting-loc-new-links.csv
+++ b/data/sorting-loc-new-links.csv
@@ -1,32 +1,32 @@
-randomness parameter value;Pairing;Smooth
-randomness parameter value;0;12
-1e-05;3.3110000000000004;0.9997999999999998
-0.01001;9.695700000000002;6.3199499999999995
-0.02001;10.85029;7.162200000000001
-0.03001;11.54132;7.654059999999999
-0.040010000000000004;12.00077;7.984989999999999
-0.050010000000000006;12.386989999999999;8.26281
-0.06001;12.68024;8.46781
-0.07001;12.901870000000002;8.63679
-0.08001;13.10722;8.77514
-0.09000999999999999;13.286290000000001;8.90821
-0.10001;13.454849999999999;9.01913
-0.11001;13.583470000000002;9.11216
-0.12000999999999999;13.70061;9.2018
-0.13001000000000001;13.79743;9.27063
-0.14001000000000002;13.926459999999999;9.354729999999998
-0.15001;14.00538;9.421119999999998
-0.16001;14.084409999999998;9.46995
-0.17001000000000002;14.157020000000001;9.527839999999998
-0.18001;14.223750000000003;9.57139
-0.19001;14.300799999999999;9.629190000000001
-0.20001000000000002;14.33816;9.65897
-0.21001;14.4027;9.688220000000001
-0.22001;14.437909999999999;9.73125
-0.23001000000000002;14.500430000000001;9.761690000000002
-0.24001;14.531600000000001;9.79034
-0.25001;14.58332;9.8314
-0.26001;14.613059999999997;9.85144
-0.27001000000000003;14.6482;9.87486
-0.28001000000000004;14.68594;9.90154
-0.29001;14.715880000000002;9.924119999999998
+randomness parameter value;Pairing;Smooth;Slim
+randomness parameter value;0;12;24
+1e-05;3.3110000000000004;0.9997999999999998;0.9997999999999998
+0.01001;9.67775;6.3042300000000004;7.19188
+0.02001;10.85817;7.168280000000001;8.42992
+0.03001;11.539510000000002;7.655379999999999;9.160339999999998
+0.040010000000000004;12.00396;7.999249999999999;9.654850000000001
+0.050010000000000006;12.37384;8.252419999999999;10.041140000000002
+0.06001;12.659740000000001;8.46188;10.357009999999999
+0.07001;12.90557;8.62622;10.61492
+0.08001;13.09812;8.78675;10.82337
+0.09000999999999999;13.29203;8.91469;11.027660000000001
+0.10001;13.429640000000001;9.00646;11.164819999999999
+0.11001;13.585540000000002;9.11176;11.332920000000001
+0.12000999999999999;13.69317;9.18681;11.460630000000002
+0.13001000000000001;13.803190000000003;9.272210000000001;11.56523
+0.14001000000000002;13.908909999999999;9.341800000000001;11.65909
+0.15001;13.99105;9.411700000000002;11.754840000000003
+0.16001;14.083679999999998;9.47869;11.869200000000001
+0.17001000000000002;14.14457;9.52315;11.935640000000001
+0.18001;14.22918;9.56991;12.0
+0.19001;14.30017;9.62381;12.08285
+0.20001000000000002;14.337049999999998;9.657720000000001;12.13275
+0.21001;14.392430000000001;9.69139;12.19594
+0.22001;14.45719;9.72949;12.243250000000003
+0.23001000000000002;14.49798;9.76287;12.287560000000001
+0.24001;14.543500000000002;9.79236;12.32669
+0.25001;14.575109999999999;9.822109999999999;12.378240000000002
+0.26001;14.62004;9.85026;12.42158
+0.27001000000000003;14.668430000000003;9.88027;12.464500000000001
+0.28001000000000004;14.67765;9.89911;12.489040000000001
+0.29001;14.714970000000001;9.92091;12.52088
diff --git a/data/sorting-sep-new-comps-test.csv b/data/sorting-sep-new-comps-test.csv
new file mode 100644
index 0000000..dc4195d
--- /dev/null
+++ b/data/sorting-sep-new-comps-test.csv
@@ -0,0 +1,19 @@
+randomness parameter value;Pairing;Smooth;Slim
+randomness parameter value;0;12;24
+2;0.0;0.0;0.0
+4;0.6249999999999999;0.5625000000000001;0.5625000000000001
+8;1.2312500000000002;1.2250000000000003;1.2250000000000003
+16;1.8062500000000001;1.734375;1.746875
+32;2.2093749999999996;2.1828125000000003;2.1906250000000003
+64;2.5601562499999995;2.5015625000000004;2.51171875
+128;2.8164062500000004;2.7449218750000006;2.7507812499999997
+256;2.9751953124999995;2.931640625;2.94296875
+512;3.1471679687500003;3.08076171875;3.085546875
+1024;3.2168457031249997;3.1895507812499995;3.1858886718750004
+2048;3.3531005859374994;3.2681640625;3.2591552734375
+4096;3.3708862304687504;3.30394287109375;3.29910888671875
+8192;3.427282714843751;3.34471435546875;3.335760498046875
+16384;3.4669952392578125;3.366510009765625;3.3556823730468754
+32768;3.473672485351563;3.385777282714844;3.373991394042969
+65536;3.4976760864257814;3.396915435791016;3.3844589233398437
+131072;3.500126647949218;3.405287933349609;3.3921943664550787
diff --git a/data/sorting-sep-new-links-test.csv b/data/sorting-sep-new-links-test.csv
new file mode 100644
index 0000000..8a02af8
--- /dev/null
+++ b/data/sorting-sep-new-links-test.csv
@@ -0,0 +1,19 @@
+randomness parameter value;Pairing;Smooth;Slim
+randomness parameter value;0;12;24
+2;0.0;0.0;0.0
+4;0.6249999999999999;0.5500000000000002;0.5500000000000002
+8;1.2312500000000002;0.9750000000000003;0.9750000000000003
+16;1.8062500000000001;1.3281250000000002;1.3218750000000001
+32;2.2093749999999996;1.6078125;1.5953125
+64;2.5601562499999995;1.76484375;1.7375000000000003
+128;2.8164062500000004;1.9191406249999998;1.8773437499999996
+256;2.9751953124999995;2.009765625;1.9525390625
+512;3.1471679687500003;2.0896484375;2.02109375
+1024;3.2168457031249997;2.1350585937499997;2.0554687499999997
+2048;3.3531005859374994;2.17060546875;2.0829833984375
+4096;3.3708862304687504;2.1817749023437503;2.094384765625
+8192;3.427282714843751;2.1978515625000004;2.1041320800781254
+16384;3.4669952392578125;2.206170654296875;2.1098266601562496
+32768;3.473672485351563;2.211837768554687;2.114335632324219
+65536;3.4976760864257814;2.216072845458984;2.1168922424316405
+131072;3.500126647949218;2.2179931640625;2.118241882324219
diff --git a/data/sorting-subseq-new-comps.csv b/data/sorting-subseq-new-comps.csv
index c9f3891..603ae1f 100644
--- a/data/sorting-subseq-new-comps.csv
+++ b/data/sorting-subseq-new-comps.csv
@@ -1,21 +1,21 @@
-randomness parameter value;Pairing;Smooth
-randomness parameter value;0;12
-1900;7.140770000000002;6.0651
-1800;7.261944999999999;6.198515
-1700;7.313929999999999;6.256444999999999
-1600;7.462670000000001;6.48028
-1500;7.5541849999999995;6.535635000000001
-1400;7.711180000000001;6.737559999999998
-1300;7.786554999999999;6.852745
-1200;7.948655000000001;7.065579999999999
-1100;8.04499;7.18305
-1000;8.25514;7.484164999999999
-900;8.48538;7.764014999999999
-800;8.644215;7.9804650000000015
-700;8.897675;8.31422
-600;9.121414999999999;8.6109
-500;9.441964999999998;9.036955
-400;9.87564;9.61485
-300;10.334719999999999;10.22929
-200;10.993725;11.170739999999999
-100;12.144270000000002;12.770485
+randomness parameter value;Pairing;Smooth;Slim
+randomness parameter value;0;12;24
+1900;7.153065;6.05814;6.10638
+1800;7.220275;6.125749999999999;6.184085
+1700;7.257635;6.1938;6.236489999999999
+1600;7.391990000000002;6.326405;6.41053
+1500;7.509505000000001;6.47197;6.5726700000000005
+1400;7.581990000000001;6.570784999999998;6.651484999999999
+1300;7.837345000000001;6.931944999999999;7.048145
+1200;7.924210000000001;7.0518550000000015;7.172499999999999
+1100;8.034790000000001;7.172065;7.318725
+1000;8.206145;7.39088;7.56936
+900;8.479135000000001;7.776070000000001;7.976265
+800;8.662115;7.995735;8.261940000000001
+700;8.863864999999999;8.280320000000001;8.56643
+600;9.13595;8.625425;8.981399999999999
+500;9.422649999999999;9.01364;9.44304
+400;9.834005000000001;9.57885;10.134455
+300;10.352394999999998;10.286950000000001;11.004845
+200;11.020954999999999;11.196654999999998;12.148670000000001
+100;12.138380000000002;12.756085;14.14317
diff --git a/data/sorting-subseq-new-links.csv b/data/sorting-subseq-new-links.csv
index a9d195f..9f93878 100644
--- a/data/sorting-subseq-new-links.csv
+++ b/data/sorting-subseq-new-links.csv
@@ -1,21 +1,21 @@
-randomness parameter value;Pairing;Smooth
-randomness parameter value;0;12
-1900;7.140770000000002;4.111149999999999
-1800;7.261944999999999;4.206099999999998
-1700;7.313929999999999;4.23051
-1600;7.462670000000001;4.356905000000001
-1500;7.5541849999999995;4.397234999999999
-1400;7.711180000000001;4.501015000000001
-1300;7.786554999999999;4.575859999999999
-1200;7.948655000000001;4.6985
-1100;8.04499;4.7659400000000005
-1000;8.25514;4.933224999999999
-900;8.48538;5.093285
-800;8.644215;5.216295
-700;8.897675;5.39767
-600;9.121414999999999;5.562875000000001
-500;9.441964999999998;5.790405
-400;9.87564;6.099679999999998
-300;10.334719999999999;6.429255
-200;10.993725;6.9218
-100;12.144270000000002;7.751835000000001
+randomness parameter value;Pairing;Smooth;Slim
+randomness parameter value;0;12;24
+1900;7.153065;4.109310000000001;4.242609999999999
+1800;7.220275;4.152085;4.294115
+1700;7.257635;4.198955;4.33525
+1600;7.391990000000002;4.272915;4.447325
+1500;7.509505000000001;4.3566650000000005;4.54668
+1400;7.581990000000001;4.411449999999999;4.59764
+1300;7.837345000000001;4.6216;4.855535000000001
+1200;7.924210000000001;4.686185;4.930525000000001
+1100;8.034790000000001;4.7547749999999995;5.025485000000001
+1000;8.206145;4.88674;5.19118
+900;8.479135000000001;5.094884999999999;5.4413800000000005
+800;8.662115;5.22276;5.627315
+700;8.863864999999999;5.378835;5.821145
+600;9.13595;5.568364999999999;6.07888
+500;9.422649999999999;5.77793;6.364665
+400;9.834005000000001;6.082489999999999;6.7924750000000005
+300;10.352394999999998;6.457979999999999;7.324980000000001
+200;11.020954999999999;6.935074999999998;8.020215
+100;12.138380000000002;7.746515;9.222365000000002
diff --git a/data/sorting-uniform-new-comps.csv b/data/sorting-uniform-new-comps.csv
index 351c717..a5cf751 100644
--- a/data/sorting-uniform-new-comps.csv
+++ b/data/sorting-uniform-new-comps.csv
@@ -1,19 +1,19 @@
-randomness parameter value;Pairing;Smooth
-randomness parameter value;0;12
-2;0.0;0.0
-4;0.7000000000000001;0.6000000000000001
-8;1.6749999999999998;1.6500000000000001
-16;2.9875;3.025
-32;4.05625;4.14375
-64;5.71875;5.665625
-128;7.171875;7.395312499999999
-256;8.4984375;8.960156249999999
-512;9.845703125;10.61015625
-1024;11.176171875;12.24921875
-2048;12.404296875000002;13.93369140625
-4096;13.6794921875;15.63544921875
-8192;14.9508056640625;17.39541015625
-16384;16.2085693359375;19.12520751953125
-32768;17.44716796875;20.857037353515626
-65536;18.6917236328125;22.592379760742183
-131072;19.929542541503906;24.330378723144527
+randomness parameter value;Pairing;Smooth;Slim
+randomness parameter value;0;12;24
+2;0.0;0.0;0.0
+4;0.65;0.7;0.7
+8;1.6500000000000001;1.75;1.775
+16;3.0125;3.0;3.05
+32;4.36875;4.28125;4.2875
+64;5.65;5.784375;6.0125
+128;7.096875000000001;7.293749999999999;7.6953125
+256;8.50234375;9.017187499999999;9.42421875
+512;9.79140625;10.534374999999999;11.40546875
+1024;11.1201171875;12.249414062500001;13.541015625
+2048;12.4150390625;13.990625;15.75517578125
+4096;13.6927734375;15.6712890625;17.820849609375
+8192;14.946044921875002;17.400000000000002;20.0787353515625
+16384;16.199816894531253;19.117529296875;22.252026367187497
+32768;17.454876708984376;20.84237060546875;24.40491943359375
+65536;18.695001220703126;22.5908935546875;26.56299743652344
+131072;19.936421203613282;24.33431549072266;28.716687011718747
diff --git a/data/sorting-uniform-new-links.csv b/data/sorting-uniform-new-links.csv
index 72aaf46..6514c73 100644
--- a/data/sorting-uniform-new-links.csv
+++ b/data/sorting-uniform-new-links.csv
@@ -1,19 +1,19 @@
-randomness parameter value;Pairing;Smooth
-randomness parameter value;0;12
-2;0.0;0.0
-4;0.7000000000000001;0.55
-8;1.6749999999999998;1.25
-16;2.9875;2.1624999999999996
-32;4.05625;2.8999999999999995
-64;5.71875;3.8562499999999997
-128;7.171875;4.846875
-256;8.4984375;5.70703125
-512;9.845703125;6.605078125
-1024;11.176171875;7.468554687500001
-2048;12.404296875000002;8.33544921875
-4096;13.6794921875;9.20283203125
-8192;14.9508056640625;10.0988037109375
-16384;16.2085693359375;10.96561279296875
-32768;17.44716796875;11.841461181640625
-65536;18.6917236328125;12.714126586914062
-131072;19.929542541503906;13.582135009765626
+randomness parameter value;Pairing;Smooth;Slim
+randomness parameter value;0;12;24
+2;0.0;0.0;0.0
+4;0.65;0.65;0.65
+8;1.6500000000000001;1.35;1.375
+16;3.0125;2.2125;2.25
+32;4.36875;3.0625;3.05
+64;5.65;3.884375;4.196875
+128;7.096875000000001;4.7671875;5.2859375
+256;8.50234375;5.71640625;6.362500000000001
+512;9.79140625;6.567187499999999;7.5972656249999995
+1024;11.1201171875;7.4564453125;8.886328125
+2048;12.4150390625;8.36669921875;10.220214843749998
+4096;13.6927734375;9.22490234375;11.449951171875
+8192;14.946044921875002;10.1025146484375;12.78759765625
+16384;16.199816894531253;10.967944335937501;14.073291015625003
+32768;17.454876708984376;11.833294677734376;15.348345947265624
+65536;18.695001220703126;12.709674072265624;16.62651672363281
+131072;19.936421203613282;13.584622192382811;17.89972839355469
diff --git a/pairing_heap.py b/pairing_heap.py
index be23a3b..96e95be 100644
--- a/pairing_heap.py
+++ b/pairing_heap.py
@@ -8,6 +8,8 @@ from pairing_heap_standard import PairingHeapStandard
 from smooth_heap import SmoothHeap
 from pairing_heap_l import PairingHeapL
 from smooth_heap_l import SmoothHeapL
+from slim_heap_l import SlimHeapL
+from slim_heap import SlimHeap
 
 COUNT_TYPE_LINKS=-1
 COUNT_TYPE_COMPS=-2
@@ -15,7 +17,7 @@ COUNT_TYPE_BOTH=0
 
 
 class PairingHeap(PairingHeapInterface):
-	MODES = {21: "Pairing_L", 22: "Smooth_L"}
+	MODES = {21: "Pairing_L", 22: "Smooth_L", 23: "Slim_L", 24: "Slim"}
 	mode = 0
 	countType = COUNT_TYPE_COMPS
 	heap = None
@@ -33,6 +35,10 @@ class PairingHeap(PairingHeapInterface):
 			self.heap = PairingHeapL()
 		elif self.mode == 22:  # root list version, everything lazy, to be used for Dijkstra test in paper
 			self.heap = SmoothHeapL()
+		elif self.mode == 23:
+			self.heap = SlimHeapL()  # root list version, everything lazy, to be used for Dijkstra test in paper
+		elif self.mode == 24:
+			self.heap = SlimHeap()
 		else:
 			raise Exception("Invalid heap ID! No heap of type ID {} is implemented.")
 	
diff --git a/plots/paper-dijkstra-new.svg b/plots/paper-dijkstra-new.svg
index b581527..a27d015 100644
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-    <g id="text_15">
+    <g id="text_16">
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-     <defs>
-      <path d="M 19.671875 64.796875 
+     <g transform="translate(643.836875 760.759682)scale(0.3 -0.3)">
+      <defs>
+       <path d="M 19.671875 64.796875 
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+       <path d="M 48.78125 52.59375 
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 Q 44.96875 46.296875 41.140625 47.34375 
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       <use xlink:href="#DejaVuSans-80"/>
       <use x="55.802734" xlink:href="#DejaVuSans-97"/>
       <use x="117.082031" xlink:href="#DejaVuSans-105"/>
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+    <g id="line2d_35">
+     <path d="M 559.836875 794.294057 
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+    <g id="line2d_36">
      <g>
-      <use style="fill:#fe0002;stroke:#000000;" x="617.474687" xlink:href="#mafb4c47c91" y="890.886562"/>
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     </g>
-    <g id="text_16">
+    <g id="text_17">
      <!-- Pairing links -->
-     <defs>
-      <path d="M 9.421875 75.984375 
+     <g transform="translate(643.836875 804.794057)scale(0.3 -0.3)">
+      <defs>
+       <path d="M 9.421875 75.984375 
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-      <path d="M 9.078125 75.984375 
+       <path d="M 9.078125 75.984375 
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       <use x="55.802734" xlink:href="#DejaVuSans-97"/>
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-L 643.474687 929.049688 
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+    <g id="line2d_37">
+     <path d="M 559.836875 838.328432 
+L 619.836875 838.328432 
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+    <g id="line2d_38">
      <g>
-      <use style="fill:#15b01a;stroke:#000000;stroke-linejoin:miter;" x="617.474687" xlink:href="#m19b99d2f82" y="929.049688"/>
+      <use style="fill:#53fca1;stroke:#000000;stroke-linejoin:miter;" x="589.836875" xlink:href="#m2ede362ce6" y="838.328432"/>
      </g>
     </g>
-    <g id="text_17">
+    <g id="text_18">
      <!-- Smooth comparisons -->
-     <defs>
-      <path d="M 53.515625 70.515625 
+     <g transform="translate(643.836875 848.828432)scale(0.3 -0.3)">
+      <defs>
+       <path d="M 53.515625 70.515625 
 L 53.515625 60.890625 
 Q 47.90625 63.578125 42.921875 64.890625 
 Q 37.9375 66.21875 33.296875 66.21875 
@@ -1392,7 +1627,7 @@ Q 37.3125 74.21875 42.625 73.28125
 Q 47.953125 72.359375 53.515625 70.515625 
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-      <path d="M 54.890625 33.015625 
+       <path d="M 54.890625 33.015625 
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 L 45.90625 0 
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@@ -1411,8 +1646,7 @@ Q 45.21875 56 50.046875 50.171875
 Q 54.890625 44.34375 54.890625 33.015625 
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-     </defs>
-     <g transform="translate(664.274687 938.149688)scale(0.26 -0.26)">
+      </defs>
       <use xlink:href="#DejaVuSans-83"/>
       <use x="63.476562" xlink:href="#DejaVuSans-109"/>
       <use x="160.888672" xlink:href="#DejaVuSans-111"/>
@@ -1433,19 +1667,19 @@ z
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-L 643.474687 967.212813 
-" style="fill:none;stroke:#15b01a;stroke-dasharray:5.55,2.4;stroke-dashoffset:0;stroke-width:1.5;"/>
+    <g id="line2d_39">
+     <path d="M 559.836875 882.362807 
+L 619.836875 882.362807 
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     </g>
-    <g id="line2d_36">
+    <g id="line2d_40">
      <g>
-      <use style="fill:#15b01a;stroke:#000000;stroke-linejoin:miter;" x="617.474687" xlink:href="#m10060ec369" y="967.212813"/>
+      <use style="fill:#53fca1;stroke:#000000;stroke-linejoin:miter;" x="589.836875" xlink:href="#mef6c664eca" y="882.362807"/>
      </g>
     </g>
-    <g id="text_18">
+    <g id="text_19">
      <!-- Smooth links -->
-     <g transform="translate(664.274687 976.312813)scale(0.26 -0.26)">
+     <g transform="translate(643.836875 892.862807)scale(0.3 -0.3)">
       <use xlink:href="#DejaVuSans-83"/>
       <use x="63.476562" xlink:href="#DejaVuSans-109"/>
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+    <g id="line2d_41">
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+L 619.836875 926.397182 
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+    <g id="line2d_42">
+     <g>
+      <use style="fill:#0652ff;stroke:#000000;stroke-linejoin:miter;" x="589.836875" xlink:href="#m4ef76ed219" y="926.397182"/>
+     </g>
+    </g>
+    <g id="text_20">
+     <!-- Slim comparisons -->
+     <g transform="translate(643.836875 936.897182)scale(0.3 -0.3)">
+      <use xlink:href="#DejaVuSans-83"/>
+      <use x="63.476562" xlink:href="#DejaVuSans-108"/>
+      <use x="91.259766" xlink:href="#DejaVuSans-105"/>
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+      <use x="832.128906" xlink:href="#DejaVuSans-115"/>
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+    <g id="line2d_44">
+     <g>
+      <use style="fill:#0652ff;stroke:#000000;stroke-linejoin:miter;" x="589.836875" xlink:href="#m871af77189" y="970.431557"/>
+     </g>
+    </g>
+    <g id="text_21">
+     <!-- Slim links -->
+     <g transform="translate(643.836875 980.931557)scale(0.3 -0.3)">
+      <use xlink:href="#DejaVuSans-83"/>
+      <use x="63.476562" xlink:href="#DejaVuSans-108"/>
+      <use x="91.259766" xlink:href="#DejaVuSans-105"/>
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+      <use x="276.025391" xlink:href="#DejaVuSans-105"/>
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+      <use x="425.097656" xlink:href="#DejaVuSans-115"/>
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-   <rect height="997.92" width="892.8" x="68.813125" y="7.2"/>
+  <clipPath id="pe07d4745fc">
+   <rect height="997.92" width="892.8" x="94.119688" y="16.250619"/>
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 </svg>
diff --git a/scripts/paper-dijkstra-test.py b/scripts/paper-dijkstra-test.py
index aeaeada..0972009 100755
--- a/scripts/paper-dijkstra-test.py
+++ b/scripts/paper-dijkstra-test.py
@@ -23,12 +23,12 @@ COUNT_TYPE_BOTH = 0
 COUNT_TYPE_LINKS = -1
 COUNT_TYPE_COMPS = -2
 
-TYPES = {21: "Pairing", 22: "Smooth"} 
+TYPES = {21: "Pairing", 22: "Smooth", 23: "Slim"} 
 MAX_TYPE_KEY = max(TYPES.keys())
 FIG_LABELS = ["comparisons", "links"]
 
-COLOURS = {21:'xkcd:fire engine red', 22:'xkcd:sea green'}
-SHADE_COLOURS = {21: '#fe4d4e', 22: '#58ab8e'}
+COLOURS = {21:'xkcd:fire engine red', 22:'xkcd:sea green', 23:'xkcd:electric blue'}
+SHADE_COLOURS = {21:'xkcd:fire engine red', 22:'xkcd:sea green', 23:'xkcd:electric blue'}
 
 NUMBER_TESTS = 10  # number of tests to run
 TEST_SIZE = 500
@@ -39,8 +39,8 @@ WEIGHT_RANGE = 10000
 def plot_avg_counts(avgCounts):
     """generates and saves plot of results"""
     # colours from https://xkcd.com/color/rgb/
-    MARKERS_COMP = {21:"o", 12:"d", 22:"^"}#https://matplotlib.org/3.1.1/api/markers_api.html
-    MARKERS_LINK = {21:"o", 12:"D", 22:"D"}
+    MARKERS_COMP = {21:"o", 12:"d", 22:"^", 23:"p"}#https://matplotlib.org/3.1.1/api/markers_api.html
+    MARKERS_LINK = {21:"o", 12:"D", 22:"D", 23: "X"}
     plt.figure('avg number of operations in Dijkstra\'s algorithm')
     deviations = [factor * EDGE_PROBABILITY for factor in range(1, 21, 1)]
     for k in TYPES.keys():
@@ -55,11 +55,11 @@ def plot_avg_counts(avgCounts):
         plt.plot(deviations, avgLinks, color=COLOURS[k], linestyle="--", marker=MARKERS_LINK[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " links")
         plt.fill_between(deviations, minLinks, maxLinks, color=SHADE_COLOURS[k], alpha=.3)
 
-    plt.xlabel('Edge probability', fontsize=26)
-    plt.ylabel('Avg. number of operations / size', fontsize=26)
-    plt.xticks(fontsize=20)
-    plt.yticks(fontsize=20)
-    plt.rc('legend',fontsize=26)  # using a size in points
+    plt.xlabel('Edge probability', fontsize=39)
+    plt.ylabel('Avg. number of operations / size', fontsize=39)
+    plt.xticks(fontsize=30)
+    plt.yticks(fontsize=30)
+    plt.rc('legend',fontsize=30)  # using a size in points
     plt.legend()
     plt.grid(True)
     figure = plt.gcf()  # get current figure
diff --git a/scripts/paper-dijkstra-test2.py b/scripts/paper-dijkstra-test2.py
index 20793e1..34cc71b 100755
--- a/scripts/paper-dijkstra-test2.py
+++ b/scripts/paper-dijkstra-test2.py
@@ -21,13 +21,13 @@ COUNT_TYPE_BOTH = 0
 COUNT_TYPE_LINKS = -1
 COUNT_TYPE_COMPS = -2
 
-TYPES = {21: "Pairing", 22: "Smooth"} 
+TYPES = {21: "Pairing", 22: "Smooth", 23: "Slim"} 
 MAX_TYPE_KEY = max(TYPES.keys())
 FIG_LABELS = ["comparisons", "links"]
 
 # colours from https://xkcd.com/color/rgb/
-COLOURS = {21:'xkcd:fire engine red', 22:'xkcd:sea green'}
-SHADE_COLOURS = {21: '#fe4d4e', 22: '#58ab8e'}
+COLOURS = {21:'xkcd:fire engine red', 22:'xkcd:sea green', 23:'xkcd:electric blue'}
+SHADE_COLOURS = {21:'xkcd:fire engine red', 22:'xkcd:sea green', 23:'xkcd:electric blue'}
 
 NUMBER_TESTS = 10  # number of tests to run
 TEST_SIZE = 500
@@ -36,8 +36,8 @@ WEIGHT_RANGE = 10000
 
 
 def plot_avg_counts(avgCounts):
-    MARKERS_COMP = {21:"o", 12:"d", 22:"^"}#https://matplotlib.org/3.1.1/api/markers_api.html
-    MARKERS_LINK = {21:"o", 12:"D", 22:"D"}
+    MARKERS_COMP = {21:"o", 12:"d", 22:"^", 23:"p"}#https://matplotlib.org/3.1.1/api/markers_api.html
+    MARKERS_LINK = {21:"o", 12:"D", 22:"D", 23: "X"}
     plt.figure('avg number of operations in Dijkstra\'s algorithm')
     deviations = [ 10+round(TEST_SIZE*20*factor * EDGE_PROBABILITY) for factor in range(1, 21, 1)]
     for k in TYPES.keys():
@@ -52,12 +52,12 @@ def plot_avg_counts(avgCounts):
         plt.plot(deviations, avgLinks, color=COLOURS[k], linestyle="--", marker=MARKERS_LINK[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " links")
         plt.fill_between(deviations, minLinks, maxLinks, color=SHADE_COLOURS[k], alpha=.3)
 
-    plt.xlabel('Graph size', fontsize=26)
-    plt.ylabel('Avg. number of operations / size', fontsize=26)
-    plt.xticks(fontsize=20)
-    plt.yticks(fontsize=20)
-    plt.rc('legend', fontsize=26)  # using a size in points
-    plt.legend()
+    plt.xlabel('Graph size', fontsize=39)
+    #plt.ylabel('Avg. number of operations / size', fontsize=39)
+    plt.xticks(fontsize=30)
+    plt.yticks(fontsize=30)
+    #plt.rc('legend', fontsize=39)  # using a size in points
+    #plt.legend()
     plt.grid(True)
     figure = plt.gcf()  # get current figure
     figure.set_size_inches(16, 18)  # set figure's size manually to full screen
diff --git a/scripts/paper-permutations.py b/scripts/paper-permutations.py
index 5d8b956..32e00bd 100755
--- a/scripts/paper-permutations.py
+++ b/scripts/paper-permutations.py
@@ -8,7 +8,7 @@ import numpy as np
 """This file generates visualizations of the different random permutation classes.
 Resulting plots are stored in ../plots"""
 
-def plot_permutation(permutation, title, filename):
+def plot_permutation(permutation, title, filename, show_legend=True):
     # visualizing given permutation as element index in permutation over element index in sorted list
     # colours from https://xkcd.com/color/rgb/
     plt.figure(title)
@@ -17,12 +17,15 @@ def plot_permutation(permutation, title, filename):
     indices = [i for i in range(len(sortedList))]
     pindices = [permutation.index(x) for x in sortedList]
     plt.plot(indices, pindices, color='xkcd:charcoal', marker='o', linestyle="", label="(sorted index, permuted index)")
-    plt.xlabel('Index in sorted list', fontsize=26)
-    plt.ylabel('Index in permutation', fontsize=26)
-    plt.xticks(fontsize=20)
-    plt.yticks(fontsize=20)
-    plt.rc('legend',fontsize=26) # using a size in points
-    plt.legend()
+    plt.xlabel('Index in sorted list', fontsize=39)
+    plt.xticks(fontsize=30)
+    if show_legend:
+        plt.ylabel('Index in permutation', fontsize=39)
+        plt.yticks(fontsize=30)
+        plt.rc('legend',fontsize=30) # using a size in points
+        plt.legend()
+    else:
+        plt.gca().axes.yaxis.set_ticklabels([])
     plt.grid(True)
     figure = plt.gcf()  # get current figure
     figure.set_size_inches(16, 18)  # set figure's size manually to full screen
@@ -82,11 +85,11 @@ random.shuffle(randomPermutation)
 plot_permutation(randomPermutation, "Uniformly Random Permutation", "uniform")
 #  generating random separable permutation
 separablePermutation = separablePermutation(512)
-plot_permutation(separablePermutation, "Random Separable Permutation", "separable")
+plot_permutation(separablePermutation, "Random Separable Permutation", "separable", False)
 #  generating random localized permutation
 localizedPermutation = localizedShuffleByIndex(sortedList, 0.15)
-plot_permutation(localizedPermutation, "Random Localized Permutation", "localized")
+plot_permutation(localizedPermutation, "Random Localized Permutation", "localized", False)
 #  generating random permutation with continuous sorted subsequences
 subseqPermutation = generateContSortedSubseq(sortedList, 30)
-plot_permutation(subseqPermutation, "Random Subsequence Permutation", "subseq")
+plot_permutation(subseqPermutation, "Random Subsequence Permutation", "subseq", False)
 
diff --git a/scripts/paper-sorting-loc.py b/scripts/paper-sorting-loc.py
index d7c5b34..fce1cd6 100644
--- a/scripts/paper-sorting-loc.py
+++ b/scripts/paper-sorting-loc.py
@@ -23,10 +23,10 @@ COUNT_TYPE_LINKS = -1
 COUNT_TYPE_COMPS = -2
 NUMBER_TESTS = 10  # number of tests to run
 INCREMENT_LOC = 0.01
-TYPES = {0: "Pairing", 12: "Smooth"}
+TYPES = {0: "Pairing", 12: "Smooth", 24:"Slim"}
 MAX_TYPE_KEY = max(TYPES.keys())
-COLOURS = {0: 'xkcd:fire engine red', 12: 'xkcd:green'}
-SHADE_COLOURS = {0: '#fe4d4e', 12: '#58ab8e'}
+COLOURS = {0: 'xkcd:fire engine red', 12:'xkcd:sea green', 24:'xkcd:electric blue'}
+SHADE_COLOURS = {0: 'xkcd:fire engine red', 12:'xkcd:sea green', 24:'xkcd:electric blue'}
 
 
 def isSorted(list0):
@@ -46,8 +46,8 @@ def localizedShuffleByIndex(llist, sdev):
 
 def plot_avg_counts(avgCounts):
 	# colours from https://xkcd.com/color/rgb/
-	MARKERS_COMP = {0:"o", 12:"^"}#https://matplotlib.org/3.1.1/api/markers_api.html
-	MARKERS_LINK = {0:"o", 12:"D"}
+	MARKERS_COMP = {0:"o", 12:"^", 24:"p"}#https://matplotlib.org/3.1.1/api/markers_api.html
+	MARKERS_LINK = {0:"o", 12:"D", 24:"X"}
 
 	plt.figure('avg number of operations by heap type')
 	deviations = [fac * INCREMENT_LOC for fac in range(0, math.ceil(0.3 / INCREMENT_LOC), 1)]
@@ -63,12 +63,12 @@ def plot_avg_counts(avgCounts):
 		plt.plot(deviations, avgLinks, color=COLOURS[k], linestyle="--", marker=MARKERS_LINK[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " links")
 		plt.fill_between(deviations, minLinks, maxLinks, color=SHADE_COLOURS[k], alpha=.3)
 
-	plt.xlabel('Locality parameter', fontsize=26)
-	plt.ylabel('Avg. number of operations / size', fontsize=26)
-	plt.xticks(fontsize=20)
-	plt.yticks(fontsize=20)
-	plt.rc('legend', fontsize=26)  # using a size in points
-	plt.legend()
+	plt.xlabel('Locality parameter', fontsize=39)
+	#plt.ylabel('Avg. number of operations / size', fontsize=39)
+	plt.xticks(fontsize=30)
+	plt.yticks(fontsize=30)
+	#plt.rc('legend', fontsize=39)  # using a size in points
+	#plt.legend()
 	plt.grid(True)
 	figure = plt.gcf()  # get current figure
 	figure.set_size_inches(16, 18)  # set figure's size manually to your full screen (32x18)
@@ -78,7 +78,7 @@ def plot_avg_counts(avgCounts):
 
 
 
-def export_results(params, results, countType, heapTypes, filename="dijkstra"):
+def export_results(params, results, countType, heapTypes, filename="sorting-loc"):
 	#  exports results of simulation as separate .csv files, one for links and one for comparisons, into ../data directory
 	#  each row contains randomness parameter value; plus one column containing the number of operations for each heap type
 	if countType == COUNT_TYPE_BOTH:
diff --git a/scripts/paper-sorting-sep.py b/scripts/paper-sorting-sep.py
index 533b79c..da2994f 100644
--- a/scripts/paper-sorting-sep.py
+++ b/scripts/paper-sorting-sep.py
@@ -28,10 +28,10 @@ TEST_SIZE = 10000  # number of elements in test list
 STEP_SIZE = 100
 INCREMENT_LOC = 0.005
 INCREMENT_SUBSEQS = 100
-TYPES = {0: "Pairing", 12: "Smooth"}
+TYPES = {0: "Pairing", 12: "Smooth", 24: "Slim"}
 MAX_TYPE_KEY = max(TYPES.keys())
-COLOURS = {0:'xkcd:fire engine red', 12:'xkcd:green'}
-SHADE_COLOURS = {0:'#fe4d4e', 12:'#58ab8e'}
+COLOURS = {0: 'xkcd:fire engine red', 12:'xkcd:sea green', 24:'xkcd:electric blue'}
+SHADE_COLOURS = {0: 'xkcd:fire engine red', 12:'xkcd:sea green', 24:'xkcd:electric blue'}
 
 
 def isSorted(list0):
@@ -40,8 +40,8 @@ def isSorted(list0):
 
 def plot_avg_counts(avgCounts):
 	# colours from https://xkcd.com/color/rgb/
-	MARKERS_COMP = {0:"o", 12:"^"}#https://matplotlib.org/3.1.1/api/markers_api.html
-	MARKERS_LINK = {0:"o", 12:"D"}
+	MARKERS_COMP = {0:"o", 12:"^", 24: "p"}#https://matplotlib.org/3.1.1/api/markers_api.html
+	MARKERS_LINK = {0:"o", 12:"D", 24: "X"}
 
 	plt.figure('avg number of operations by heap type')
 	for k in TYPES.keys():
@@ -57,12 +57,12 @@ def plot_avg_counts(avgCounts):
 		plt.plot([2**p for p in range(4, MAXSIZE)], avgLinks[3:MAXSIZE-1], color=COLOURS[k], linestyle="--", marker=MARKERS_LINK[k], markerfacecolor=COLOURS[k], markersize=9, markeredgewidth=1, markeredgecolor='black', label=TYPES[k] + " links")
 		plt.fill_between([2**p for p in range(4, MAXSIZE)], minLinks[3:MAXSIZE-1], maxLinks[3:MAXSIZE-1], color=SHADE_COLOURS[k], alpha=.3)
 
-	plt.xlabel('Input size', fontsize=26)
-	plt.ylabel('Avg. number of operations / size', fontsize=26)
-	plt.xticks(fontsize=20)
-	plt.yticks(fontsize=20)
-	plt.rc('legend', fontsize=26)  # using a size in points
-	plt.legend()
+	plt.xlabel('Input size', fontsize=39)
+	#plt.ylabel('Avg. number of operations / size', fontsize=39)
+	plt.xticks(fontsize=30)
+	plt.yticks(fontsize=30)
+	#plt.rc('legend', fontsize=39)  # using a size in points
+	#plt.legend()
 	plt.grid(True)
 	figure = plt.gcf()  # get current figure
 	figure.set_size_inches(16, 18)  # set figure's size manually to full screen
@@ -71,7 +71,7 @@ def plot_avg_counts(avgCounts):
 	plt.show()
 
 
-def export_results(params, results, countType, heapTypes, filename="dijkstra"):
+def export_results(params, results, countType, heapTypes, filename="sorting-sep"):
 	#  exports results of simulation as separate .csv files, one for links and one for comparisons, into ../data directory
 	#  each row contains randomness parameter value; plus one column containing the number of operations for each heap type
 	if countType == COUNT_TYPE_BOTH:
diff --git a/scripts/paper-sorting-subseq.py b/scripts/paper-sorting-subseq.py
index 6c8e24d..8194b7f 100644
--- a/scripts/paper-sorting-subseq.py
+++ b/scripts/paper-sorting-subseq.py
@@ -27,10 +27,10 @@ NUMBER_TESTS = 20  # number of tests to run
 LIST_LEN = 10000  # number of elements in test list
 TEST_SIZE = 10000  # number of elements in test list
 INCREMENT_SUBSEQS = 100
-TYPES = {0: "Pairing", 12: "Smooth"} 
+TYPES = {0: "Pairing", 12: "Smooth", 24: "Slim"} 
 MAX_TYPE_KEY = max(TYPES.keys())
-COLOURS = {0:'xkcd:fire engine red', 12:'xkcd:green'}
-SHADE_COLOURS = {0:'#fe4d4e', 12:'#58ab8e'}
+COLOURS = {0: 'xkcd:fire engine red', 12:'xkcd:sea green', 24:'xkcd:electric blue'}
+SHADE_COLOURS = {0: 'xkcd:fire engine red', 12:'xkcd:sea green', 24:'xkcd:electric blue'}
 
 
 def isSorted(list0):
@@ -53,8 +53,8 @@ def generateContSortedSubseq(llist, sublen):
 
 def plot_avg_counts(avgCounts):
 	# colours from https://xkcd.com/color/rgb/
-	MARKERS_COMP = {0:"o", 12:"^"}#https://matplotlib.org/3.1.1/api/markers_api.html
-	MARKERS_LINK = {0:"o", 12:"D"}
+	MARKERS_COMP = {0:"o", 12:"^", 24: "p"}#https://matplotlib.org/3.1.1/api/markers_api.html
+	MARKERS_LINK = {0:"o", 12:"D", 24:"X"}
 	plt.figure('avg number of operations by heap type')
 	deviations = [fac*INCREMENT_SUBSEQS/200 for fac in range(1, math.ceil((TEST_SIZE/5)/INCREMENT_SUBSEQS), 1)]
 	deviations.reverse()
@@ -72,12 +72,12 @@ def plot_avg_counts(avgCounts):
 		plt.fill_between(deviations, minLinks, maxLinks, color=SHADE_COLOURS[k], alpha=.3)
 
 
-	plt.xlabel('Avg. length of sorted blocks, % of size', fontsize=26)
-	plt.ylabel('Avg. number of operations / size', fontsize=26)
-	plt.xticks(fontsize=20)
-	plt.yticks(fontsize=20)
-	plt.rc('legend', fontsize=26)  # using a size in points
-	plt.legend()
+	plt.xlabel('Avg. length of sorted blocks, % of size', fontsize=39)
+	#plt.ylabel('Avg. number of operations / size', fontsize=39)
+	plt.xticks(fontsize=30)
+	plt.yticks(fontsize=30)
+	#plt.rc('legend', fontsize=39)  # using a size in points
+	#plt.legend()
 	plt.grid(True)
 	plt.gca().invert_xaxis()
 	figure = plt.gcf()  # get current figure
@@ -87,7 +87,7 @@ def plot_avg_counts(avgCounts):
 	plt.show()
 
 
-def export_results(params, results, countType, heapTypes, filename="dijkstra"):
+def export_results(params, results, countType, heapTypes, filename="sorting-subseq"):
 	#  exports results of simulation as separate .csv files, one for links and one for comparisons, into ../data directory
 	#  each row contains randomness parameter value; plus one column containing the number of operations for each heap type
 	if countType == COUNT_TYPE_BOTH:
diff --git a/scripts/paper-sorting-uniform.py b/scripts/paper-sorting-uniform.py
index 5e445d0..d5280e3 100644
--- a/scripts/paper-sorting-uniform.py
+++ b/scripts/paper-sorting-uniform.py
@@ -23,10 +23,10 @@ COUNT_TYPE_LINKS = -1
 COUNT_TYPE_COMPS = -2
 MAXSIZE = 18
 NUMBER_TESTS = 5  # number of tests to run
-TYPES = {0: "Pairing", 12: "Smooth"}
+TYPES = {0: "Pairing", 12: "Smooth", 24:"Slim"}
 MAX_TYPE_KEY = max(TYPES.keys())
-COLOURS = {0: 'xkcd:fire engine red', 12: 'xkcd:green'}
-SHADE_COLOURS = {0: '#fe4d4e', 12: '#58ab8e'}
+COLOURS = {0: 'xkcd:fire engine red', 12:'xkcd:sea green', 24:'xkcd:electric blue'}
+SHADE_COLOURS = {0: 'xkcd:fire engine red', 12:'xkcd:sea green', 24:'xkcd:electric blue'}
 
 
 def isSorted(list0):
@@ -35,8 +35,8 @@ def isSorted(list0):
 
 def plot_avg_counts_uni(avgCounts):
     # colours from https://xkcd.com/color/rgb/
-    MARKERS_COMP = {0: "o", 12: "^"}  # https://matplotlib.org/3.1.1/api/markers_api.html
-    MARKERS_LINK = {0: "o", 12: "D"}
+    MARKERS_COMP = {0: "o", 12: "^", 24:"p"}  # https://matplotlib.org/3.1.1/api/markers_api.html
+    MARKERS_LINK = {0: "o", 12: "D", 24:"X"}
     plt.figure('avg number of operations by heap type')
     for k in TYPES.keys():
         avgComps = [acounts[k] for acounts in avgCounts[0]]
@@ -57,11 +57,11 @@ def plot_avg_counts_uni(avgCounts):
                          color=SHADE_COLOURS[k], alpha=.3)
 
     # plt.title('Sorting random permutations', fontsize=25)
-    plt.xlabel('Input size', fontsize=26)
-    plt.ylabel('Avg. number of operations / size', fontsize=26)
-    plt.xticks(fontsize=20)
-    plt.yticks(fontsize=20)
-    plt.rc('legend', fontsize=26)  # using a size in points
+    plt.xlabel('Input size', fontsize=39)
+    plt.ylabel('Avg. number of operations / size', fontsize=39)
+    plt.xticks(fontsize=30)
+    plt.yticks(fontsize=30)
+    plt.rc('legend', fontsize=30)  # using a size in points
     plt.legend()
     plt.grid(True)
     figure = plt.gcf()  # get current figure
@@ -71,7 +71,7 @@ def plot_avg_counts_uni(avgCounts):
     plt.show()
 
 
-def export_results(params, results, countType, heapTypes, filename="dijkstra"):
+def export_results(params, results, countType, heapTypes, filename="sorting-uniform"):
     # parse data as randomness parameter; counts per heap type
     if countType == COUNT_TYPE_BOTH:
         with open("../data/" + filename + '-comps.csv', 'w', newline='') as csvfile:
diff --git a/slim_heap.py b/slim_heap.py
new file mode 100644
index 0000000..f611de6
--- /dev/null
+++ b/slim_heap.py
@@ -0,0 +1,330 @@
+#!/usr/bin/python3
+from node import Node
+import math
+from pairing_heap_interface import PairingHeapInterface
+
+
+class SlimHeap(PairingHeapInterface):
+    forest = []  # list storing roots of all top-level trees not in buffer
+    buffer = []  # decrease buffer
+    minNode = None
+    size = 0
+
+    def __init__(self, root=None):
+        self.forest = []
+        self.buffer = []
+        if root is not None:
+            root.parent = None
+            root.nextSibling = root
+            self.minNode = root
+            self.forest += [root]
+
+
+    def make_heap(self):
+        # this is equivalent to init
+        pass
+
+    def find_min(self):
+        return self.minNode
+
+    def listPreOrderHelper(self, root):
+        res = []
+        if root.rightChild is None:
+            return [root.key]
+        else:
+            current = root.rightChild
+            res += [root.key, self.listPreOrderHelper(current)]
+            while current.nextSibling != root.rightChild:
+                current = current.nextSibling
+                res += [self.listPreOrderHelper(current)]
+            return [res]
+
+    def listPreOrder(self):
+        res = []
+        buf = []
+        for item in self.forest:
+            res += self.listPreOrderHelper(item)
+        print(res)
+        for elem in self.buffer:
+            buf += self.listPreOrderHelper(elem)
+        print("buffer: {}".format(buf))
+        
+    def link(self, parent, child):
+    	"""child becomes leftmost child of parent"""
+    	if parent.rightChild is None:
+    		parent.rightChild = child
+    		child.nextSibling = child
+    	else:
+    		child.nextSibling = parent.rightChild.nextSibling
+    		parent.rightChild.nextSibling = child
+    	child.parent = parent
+
+    def stable_link_left(self, left, right):
+        """left node becomes parent of right node"""
+        if left.rightChild is not None:
+            right.nextSibling = left.rightChild.nextSibling
+            left.rightChild.nextSibling = right
+        else:
+            right.nextSibling = right
+        left.rightChild = right
+        right.parent = left
+
+    def stable_link_right(self, left, right):
+        """right node becomes parent of left node"""
+        if right.rightChild is None:
+            right.rightChild = left
+            left.nextSibling = left
+        else:
+            left.nextSibling = right.rightChild.nextSibling
+            right.rightChild.nextSibling = left
+        left.parent = right
+
+    def insert(self, node):
+        """concatenates node to list of roots in forest list"""
+        if node is None:
+            return (0, 0)  # no comparisons, no links
+        node.nextSibling = node
+        node.parent = None
+        self.forest += [node]
+        self.size += 1
+        if self.minNode is None or node.key <= self.minNode.key:
+            self.minNode = node
+        return (1, 0)  # 1 comparison, no links
+
+    def merge(self, heap2):
+        """cleans buffer of smaller heap, then concatenates forest lists
+        returns number of comparisons and link operations"""
+        if heap2 is None:
+            return (0, 0)
+        compCount = 0
+        linkCount = 0
+        if len(self.forest) + len(self.buffer) > len(heap2.forest) + len(heap2.buffer):
+            # first heap larger than second
+            (cc, lc) = heap2.clean_buffer()
+            linkCount += lc
+            compCount += cc + 1  # accounting for minNode comparison (at the end) as well
+            self.forest += heap2.forest
+        else:
+            (cc, lc) = self.clean_buffer()
+            linkCount += lc
+            compCount += cc + 1  # accounting for minNode comparison (at the end) as well
+            self.forest = heap2.forest + self.forest
+            self.buffer = heap2.buffer
+        self.size += heap2.size
+        if (self.minNode.key >= heap2.minNode.key):
+            self.minNode = heap2.minNode
+        return (compCount, linkCount)
+
+    def delete_min(self):
+        """consolidates and empties buffer, replaces minimum by its children in root list,
+        then consolidates root list.
+        Returns minNode, number of comparisons, number of link operations"""
+        (compCount, linkCount) = self.clean_buffer()
+        if self.minNode is None or len(self.forest) + len(self.buffer) == 0:  # this should be the same
+            return (None, 0, 0)
+        minKeyNode = self.minNode
+        minNodeChildren = []
+
+        if self.minNode.rightChild is not None:
+            minNodeChildren += [self.minNode.rightChild]
+            self.minNode.rightChild.parent = None
+            current = self.minNode.rightChild.nextSibling
+            self.minNode.rightChild.nextSibling = self.minNode.rightChild
+
+            while current != self.minNode.rightChild:
+                minNodeChildren += [current]
+                tempNode = current
+                current = current.nextSibling
+                tempNode.nextSibling = tempNode
+                tempNode.parent = None
+        idx = self.forest.index(self.minNode)
+        self.forest = self.forest[:idx] + minNodeChildren + self.forest[idx + 1:]  # replace minNode with its children
+        self.size -= 1
+        (cc, lc) = self.treapify()
+        return (minKeyNode, compCount + cc, linkCount + lc)
+
+    def treapify(self):
+        """links roots in pool (forest) into treap
+        (this uses the pseudocode of delete-min from https://arxiv.org/abs/1802.05471)
+        returns number of links/comparisons
+        """
+        linkCount = 0  # counts only number of links
+        compCount = 0  # counts only number of comparisons
+        if len(self.forest) == 0:  # pool is empty
+            self.minNode = None
+            return (compCount, linkCount)
+
+        elif len(self.forest) == 1:
+            self.minNode = self.forest[0]
+            return (compCount, linkCount)
+
+        else:
+            i = 0
+            curr_forest = self.forest
+            while i < len(curr_forest) - 1:
+                compCount += 1  # first if-else comparison
+                if curr_forest[i].key < curr_forest[i + 1].key:
+                    i = i + 1
+                else:
+                    skip = False
+                    while i > 0:
+                        compCount += 1
+                        linkCount += 1
+                        if curr_forest[i - 1].key > curr_forest[i + 1].key:
+                            # link predecessor as parent of current node
+                            self.link(curr_forest[i - 1], curr_forest[i])
+                            #self.stable_link_left(curr_forest[i - 1], curr_forest[i])
+                            # remove node at index i from top-list
+                            curr_forest = curr_forest[:i] + curr_forest[i + 1:]
+                            i = i - 1
+                        else:
+                            # link successor as parent of current node
+                            self.link(curr_forest[i + 1], curr_forest[i])
+                            #self.stable_link_right(curr_forest[i], curr_forest[i + 1])
+                            # remove node at index i from top-list
+                            curr_forest = curr_forest[:i] + curr_forest[i + 1:]
+                            # i=i+1
+                            skip = True
+                            break
+                    if not skip:  # i==0
+                        # link current as leftmost child of successor
+                        self.link(curr_forest[i + 1], curr_forest[i])
+                        #self.stable_link_right(curr_forest[i], curr_forest[i + 1])
+                        # remove node from top-list
+                        curr_forest = curr_forest[i + 1:]
+                        linkCount += 1
+
+            while i > 0:
+                # link predecessor as parent of current node
+                self.link(curr_forest[i - 1], curr_forest[i])
+                #self.stable_link_left(curr_forest[i - 1], curr_forest[i])
+                curr_forest = curr_forest[:i]
+                linkCount += 1
+                i = i - 1
+            self.forest = curr_forest
+            assert len(self.forest) == 1
+            self.minNode = self.forest[0]
+        return (compCount, linkCount)
+
+    def mergesort(self, llist):
+        # standard mergesort, implemented to count comparisons properly
+        if len(llist) < 2:
+            return 0, llist
+        split_idx = int(math.floor(len(llist) / 2))
+        compsleft, lleft = self.mergesort(llist[:split_idx])
+        compsright, lright = self.mergesort(llist[split_idx:])
+        l = 0
+        r = 0
+        comps = compsleft + compsright
+        sorted = []
+        while l + r < len(llist):
+            if r == len(lright) or (l < len(lleft) and lleft[l].key <= lright[r].key):
+                sorted += [lleft[l]]
+                l += 1
+            else:
+                sorted += [lright[r]]
+                r += 1
+            comps += 1
+        return comps, sorted
+
+    def clean_buffer(self):
+        if len(self.buffer) == 0:  # buffer is empty
+            return (0, 0)
+        comps, self.buffer = self.mergesort(self.buffer)
+        self.buffer.reverse()
+        n = len(self.buffer)
+
+        while len(self.buffer) > 1:
+            self.stable_link_right(self.buffer[0], self.buffer[1])
+            self.buffer = self.buffer[1:]
+
+        treapified = self.buffer[0]
+        self.buffer = []
+        (compCount, linkCount) = self.merge(SlimHeap(treapified))
+
+        return (compCount + comps, linkCount + n - 1)  # (n-1)links while consolidating
+
+    def decrease_key(self, node, diff):
+        """cut out node from current location, leaving leftmost child;
+        decrease key; place node with remaining subtree in buffer.
+        Returns number of comparisons, links"""
+        assert node is not None
+        linkCount = 0
+        compCount = 0
+        node.key = node.key - diff
+
+        if node.parent is None and node.rightChild is None:  # node is root and has no children
+            # could just leave this in place alternatively
+            if node in self.forest:
+                idx = self.forest.index(node)
+                self.forest = self.forest[:idx] + self.forest[idx + 1:]
+                self.buffer += [node]
+            elif node in self.buffer:
+                pass
+            else:
+                self.listPreOrder()
+                raise Exception("node with key {} is not in heap".format(node.key))
+
+        elif node.parent is None:  # node is a root and has children
+            leftChild = node.rightChild.nextSibling
+            if leftChild.nextSibling != leftChild:
+                node.rightChild.nextSibling = leftChild.nextSibling  # cut out leftmost child
+            else:
+                node.rightChild = None
+            leftChild.nextSibling = leftChild
+            leftChild.parent = None
+            if node in self.forest:
+                idx = self.forest.index(node)  # remove node from pool and replace with leftChild
+                self.forest = self.forest[:idx] + [leftChild] + self.forest[idx + 1:]
+                self.buffer += [node]
+            elif node in self.buffer:
+                pass
+            else:
+                self.listPreOrder()
+                raise Exception("node with key {} is not in heap".format(node.key))
+        else:  # node is not a root
+            leftChild = None
+            if node.rightChild is not None:
+                leftChild = node.rightChild.nextSibling
+                leftChild.parent = node.parent
+            current = node.parent.rightChild
+
+            if node.nextSibling == node and leftChild is not None:  # node not a leaf and has no siblings
+                if leftChild.nextSibling != leftChild:
+                    node.rightChild.nextSibling = leftChild.nextSibling  # cut out leftmost child
+                else:
+                    node.rightChild = None
+                leftChild.nextSibling = leftChild
+                node.parent.rightChild = leftChild
+
+            elif leftChild is not None:  # node is not a leaf and has siblings
+                if leftChild.nextSibling != leftChild:
+                    node.rightChild.nextSibling = leftChild.nextSibling  # cut out leftmost child
+                else:
+                    node.rightChild = None
+                while current.nextSibling != node:  # find predecessor of node
+                    current = current.nextSibling
+                current.nextSibling = leftChild
+                leftChild.nextSibling = node.nextSibling
+                if node.parent.rightChild == node:
+                    node.parent.rightChild = leftChild
+
+            elif node.nextSibling != node:  # node is leaf and has siblings
+                while current.nextSibling != node:
+                    current = current.nextSibling
+                current.nextSibling = node.nextSibling
+                if node.parent.rightChild == node:
+                    node.parent.rightChild = current
+
+            else:  # node is leaf and has no siblings
+                node.parent.rightChild = None
+
+            node.parent = None
+            node.nextSibling = node
+            self.buffer += [node]
+
+        if len(self.buffer) > math.ceil(math.log(self.size, 2)):
+            (cc2, lc2) = self.clean_buffer()
+            compCount += cc2
+            linkCount += lc2
+        return (compCount, linkCount)
diff --git a/slim_heap_l.py b/slim_heap_l.py
new file mode 100644
index 0000000..f01bf74
--- /dev/null
+++ b/slim_heap_l.py
@@ -0,0 +1,196 @@
+#!/usr/bin/python3
+from node import Node
+import math
+from pairing_heap_interface import PairingHeapInterface
+
+
+class SlimHeapL(PairingHeapInterface):
+    """lazy implementation of slim heap without buffer"""
+    forest = []  # list storing roots of all top-level trees
+    minNode = None
+
+    def __init__(self, root=None):
+        self.forest = []
+        if root != None:
+            root.parent = None
+            root.nextSibling = root
+            self.minNode = root
+            self.forest += [root]
+
+    def make_heap(self):
+        # this is equivalent to init
+        pass
+
+    def find_min(self):
+        return self.minNode
+
+    def listPreOrderHelper(self, root):
+        res = []
+        if root.rightChild == None:
+            return [root.key]
+        else:
+            current = root.rightChild
+            res += [root.key, self.listPreOrderHelper(current)]
+            while current.nextSibling != root.rightChild:
+                current = current.nextSibling
+                res += [self.listPreOrderHelper(current)]
+            return [res]
+
+    def listPreOrder(self):
+        res = []
+        buf = []
+        for item in self.forest:
+            res += self.listPreOrderHelper(item)
+        print(res)
+        
+    def link(self, parent, child):
+        """child becomes leftmost child of parent"""
+        if parent.rightChild is None:
+            parent.rightChild = child
+            child.nextSibling = child
+        else:
+            child.nextSibling = parent.rightChild.nextSibling
+            parent.rightChild.nextSibling = child
+        child.parent = parent
+                
+
+    def insert(self, node):
+        """concatenates node to list of trees in pool"""
+        if node is None:
+            return (0, 0)  # no comparisons, no links
+        node.nextSibling = node
+        node.parent = None
+        self.forest += [node]
+        return (0, 0)  # 1 comparison, no links
+
+    def merge(self, heap2):
+        """concatenates root lists of heaps"""
+        if heap2 is None:
+            return (0, 0)
+        compCount = 0
+        linkCount = 0
+        if len(self.forest) > len(heap2.forest):
+            # first heap larger than second
+            self.forest += heap2.forest
+        else:
+            self.forest = heap2.forest + self.forest
+        return (compCount, linkCount)
+
+    def delete_min(self):
+        """consolidates into single tree; extracts min node,
+        placing its orphaned children in root list.
+        Returns min node, number comparisons, number links"""
+        if len(self.forest) == 0:
+            return (None, 0, 0)
+        (cc, lc) = self.treapify()
+        assert len(self.forest) == 1
+        minKeyNode = self.minNode
+        minNodeChildren = []
+
+        if self.minNode.rightChild is not None:
+            minNodeChildren += [self.minNode.rightChild]
+            self.minNode.rightChild.parent = None
+            current = self.minNode.rightChild.nextSibling
+            self.minNode.rightChild.nextSibling = self.minNode.rightChild
+
+            while current != self.minNode.rightChild:
+                minNodeChildren += [current]
+                tempNode = current
+                current = current.nextSibling
+                tempNode.nextSibling = tempNode
+                tempNode.parent = None
+        self.forest = minNodeChildren
+        return (minKeyNode, cc, lc)
+
+    def treapify(self):
+        """links roots in pool (forest) into treap and returns number of links/comparisons
+        this uses the pseudocode of delete-min from https://arxiv.org/abs/1802.05471
+        returns number comparisons, number link operations performed"""
+        linkCount = 0  # counts only number of links
+        compCount = 0  # counts only number of comparisons
+        fs = len(self.forest)
+        if len(self.forest) == 0:  # pool is empty
+            self.minNode = None
+            return (compCount, linkCount)
+
+        elif len(self.forest) == 1:
+            self.minNode = self.forest[0]
+            return (compCount, linkCount)
+
+        else:
+            i = 0
+            curr_forest = self.forest
+            while i < len(curr_forest) - 1:
+                compCount += 1  # first if-else comparison
+                if curr_forest[i].key < curr_forest[i + 1].key:
+                    i = i + 1
+                else:
+                    skip = False
+                    while i > 0:
+                        compCount += 1
+                        linkCount += 1
+                        if curr_forest[i - 1].key > curr_forest[i + 1].key:
+                            # link predecessor as parent of current node
+                            self.link(curr_forest[i - 1], curr_forest[i])
+                          	
+                            # remove node at index i from top-list
+                            curr_forest = curr_forest[:i] + curr_forest[i + 1:]
+                            i = i - 1
+                        else:
+                            # link successor as parent of current node
+                            self.link(curr_forest[i + 1], curr_forest[i])
+                            # remove node at index i from top-list
+                            curr_forest = curr_forest[:i] + curr_forest[i + 1:]
+                            # i=i+1
+                            skip = True
+                            break
+                    if not skip:  # i==0
+                        # link current as leftmost child of successor
+                        self.link(curr_forest[i + 1], curr_forest[i])
+                        # remove node from top-list
+                        curr_forest = curr_forest[i + 1:]
+                        linkCount += 1
+
+            while i > 0:
+                # link predecessor as parent of current node
+                self.link(curr_forest[i - 1], curr_forest[i])
+                curr_forest = curr_forest[:i]
+                linkCount += 1
+                i = i - 1
+            self.forest = curr_forest
+            assert len(self.forest) == 1
+            self.minNode = self.forest[0]
+        assert (fs - 1 == linkCount)
+        return (compCount, linkCount)
+
+
+    def decrease_key(self, node, diff):
+        """removes node with subtree from current position;
+        decreases key; places node in root list."""
+        assert node is not None
+        node.key = node.key - diff
+        # concatenates node to list of trees in pool
+
+        if node.parent is None:  # node is a root and has children
+            if node in self.forest:
+                pass  # leave in-place
+            else:
+                self.listPreOrder()
+                raise Exception("node with key {} is not in heap".format(node.key))
+        else:  # node is not a root
+
+            if node.nextSibling == node:  # node has no siblings
+                node.parent.rightChild = None
+
+            else:  # node has siblings
+                current = node.nextSibling
+                while current.nextSibling != node:  # find predecessor of node
+                    current = current.nextSibling
+                current.nextSibling = node.nextSibling
+                if node.parent.rightChild == node:
+                    node.parent.rightChild = current
+
+            node.parent = None
+            node.nextSibling = node
+            self.forest += [node]
+        return (0, 0)
-- 
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