XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-20-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:24
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 180

General features

Coarse blocks: 9,000
Value tables: 40

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Coarse blocks size 4 21 12.53 13.00 112,810 MAX VALUE 22,564.00 2.51 0.20 2.34

Relational linkage 0.16 0.56 0.36 0.36 355.92 0.00 -1,049.23 0.06 0.18 1.86

Tightness 0.46 0.55 0.50 0.50 89.75 0.00 -125.38 0.02 0.04 3.62

Tuples 284 340 313.36 314.50 56,405 MAX VALUE 1,034.41 11.02 0.04 3.62

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 4 14 9.00 9.00 360 3.42e+37 86.43 2.36 0.26 2.10

Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	360	MAX VALUE	124.77	0.00	0.00	0.00
Coarse blocks size	4	21	12.53	13.00	112,810	MAX VALUE	22,564.00	2.51	0.20	2.34
Relational linkage	0.16	0.56	0.36	0.36	355.92	0.00	-1,049.23	0.06	0.18	1.86
Tightness	0.46	0.55	0.50	0.50	89.75	0.00	-125.38	0.02	0.04	3.62
Tuples	284	340	313.36	314.50	56,405	MAX VALUE	1,034.41	11.02	0.04	3.62
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	14	9.00	9.00	360	3.42e+37	86.43	2.36	0.26	2.10
Value table partitions	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 20
Number of leaves: 11
Tree depth: 4
CIR: 0.08
Independent Cluster Pairs: 13
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Tree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 5 60 22.20 14.50 444 8.94e+24 57.45 15.95 0.72 2.65

Variables per cluster 5 21 11.25 9.50 225 1.79e+20 46.64 4.89 0.43 2.29

Separator constraints 0 53 13.20 6.00 264 0 None 13.91 1.05 2.48

Separator variables 0 20 9.25 7.50 185 0 None 4.84 0.52 2.36

Clusters per var 1 13 5.62 5.50 225 4.18e+23 54.39 3.96 0.70 2.32

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	60	22.20	14.50	444	8.94e+24	57.45	15.95	0.72	2.65
Variables per cluster	5	21	11.25	9.50	225	1.79e+20	46.64	4.89	0.43	2.29
Separator constraints	0	53	13.20	6.00	264	0	None	13.91	1.05	2.48
Separator variables	0	20	9.25	7.50	185	0	None	4.84	0.52	2.36
Clusters per var	1	13	5.62	5.50	225	4.18e+23	54.39	3.96	0.70	2.32

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 137
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/DualTree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 31 370 124.39 90.50 4,727 MAX VALUE 175.10 86.51 0.70 3.51

Variables per cluster 11 86 29.00 22.00 1,102 MAX VALUE 121.63 18.59 0.64 3.21

Separator constraints 0 223 83.58 67.50 3,176 0 None 53.72 0.64 3.60

Separator variables 0 62 24.26 20.00 922 0 None 14.18 0.58 3.14

Clusters per variable 1 10 6.12 7.00 1,102 MAX VALUE 296.54 2.71 0.44 2.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	31	370	124.39	90.50	4,727	MAX VALUE	175.10	86.51	0.70	3.51
Variables per cluster	11	86	29.00	22.00	1,102	MAX VALUE	121.63	18.59	0.64	3.21
Separator constraints	0	223	83.58	67.50	3,176	0	None	53.72	0.64	3.60
Separator variables	0	62	24.26	20.00	922	0	None	14.18	0.58	3.14
Clusters per variable	1	10	6.12	7.00	1,102	MAX VALUE	296.54	2.71	0.44	2.16

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 160
Triangles: 111
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Primal1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.11 0.40 0.22 0.22 8.86 0.00 -61.96 0.06 0.29 3.12

Degree 4 14 9.00 9.00 360 3.42e+37 86.43 2.36 0.26 2.10

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.34 3.00 535 MAX VALUE 191.60 0.47 0.14 0.64

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.11	0.40	0.22	0.22	8.86	0.00	-61.96	0.06	0.29	3.12
Degree	4	14	9.00	9.00	360	3.42e+37	86.43	2.36	0.26	2.10
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.34	3.00	535	MAX VALUE	191.60	0.47	0.14	0.64

Triangulated primal graph

Density: 50.64%
MCB compute time (ms): 9
MCB cycles: 361
Triangles: 2,327

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.62 1.00 0.84 0.82 33.58 0.00 -7.43 0.12 0.15 3.03

Degree 4 32 19.75 24.50 790 MAX VALUE 112.42 9.60 0.49 2.73

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,083 MAX VALUE 396.60 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.62	1.00	0.84	0.82	33.58	0.00	-7.43	0.12	0.15	3.03
Degree	4	32	19.75	24.50	790	MAX VALUE	112.42	9.60	0.49	2.73
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,083	MAX VALUE	396.60	0.00	0.00	0.00

Dual graph

Density: 9.63%
MCB compute time (ms): 557
MCB cycles: 1,423
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Dual1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.46 0.67 0.50 0.49 90.64 0.00 -123.81 0.03 0.06 4.15

Degree 10 25 17.23 17.00 3,102 MAX VALUE 509.31 3.15 0.18 2.50

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.06 3.00 4,351 MAX VALUE 1,586.92 0.23 0.08 0.22

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.67	0.50	0.49	90.64	0.00	-123.81	0.03	0.06	4.15
Degree	10	25	17.23	17.00	3,102	MAX VALUE	509.31	3.15	0.18	2.50
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.06	3.00	4,351	MAX VALUE	1,586.92	0.23	0.08	0.22

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 78
MCB cycles: 141

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 5 3.56 3.00 640 MAX VALUE 224.40 0.74 0.21 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.77 7.00 955 MAX VALUE 267.43 1.16 0.17 1.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.00	0.00	0.00	0.00	0.00	None	0.00	None	0.00
Degree	2	5	3.56	3.00	640	MAX VALUE	224.40	0.74	0.21	1.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.77	7.00	955	MAX VALUE	267.43	1.16	0.17	1.49

Triangulated dual graph

Density: 46.24%
Triangles: 195,301

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.71 1.00 0.83 0.81 149.90 0.00 -33.92 0.09 0.11 4.68

Degree 10 131 82.77 95.50 14,898 MAX VALUE 758.97 40.64 0.49 4.08

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.71	1.00	0.83	0.81	149.90	0.00	-33.92	0.09	0.11	4.68
Degree	10	131	82.77	95.50	14,898	MAX VALUE	758.97	40.64	0.49	4.08
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.25%

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.46 1.00 0.80 0.77 143.43 0.00 -44.62 0.16 0.20 3.16

Degree 2 65 20.13 6.00 3,624 MAX VALUE 414.39 22.35 1.11 3.05

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	1.00	0.80	0.77	143.43	0.00	-44.62	0.16	0.20	3.16
Degree	2	65	20.13	6.00	3,624	MAX VALUE	414.39	22.35	1.11	3.05
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 42
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-20-ext/Incidence1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 14 3.27 2.00 720 MAX VALUE 211.19 2.88 0.88 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.51 6.00 918 MAX VALUE 263.00 0.87 0.13 0.57

XCSP 2.1 Benchmarks