XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-22-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:27
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 3 23 12.49 13.00 112,432 MAX VALUE 22,531.20 2.51 0.20 2.34

Relational linkage 0.12 0.52 0.35 0.36 351.40 0.00 -1,062.90 0.06 0.18 1.84

Tightness 0.46 0.54 0.50 0.50 90.05 0.00 -124.78 0.02 0.04 3.66

Tuples 285 335 312.31 313.00 56,216 MAX VALUE 1,033.80 11.35 0.04 3.66

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

Value table constraints 5 13 9.00 9.00 360 4.17e+37 86.62 2.12 0.24 2.06

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	3	23	12.49	13.00	112,432	MAX VALUE	22,531.20	2.51	0.20	2.34
Relational linkage	0.12	0.52	0.35	0.36	351.40	0.00	-1,062.90	0.06	0.18	1.84
Tightness	0.46	0.54	0.50	0.50	90.05	0.00	-124.78	0.02	0.04	3.66
Tuples	285	335	312.31	313.00	56,216	MAX VALUE	1,033.80	11.35	0.04	3.66
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	5	13	9.00	9.00	360	4.17e+37	86.62	2.12	0.24	2.06
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: 3
CIR: 0.07
Independent Cluster Pairs: 12
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/Tree1.json

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

Cluster constraints 5 54 20.05 17.00 401 1.77e+24 55.83 13.30 0.66 2.72

Variables per cluster 6 21 11.10 10.00 222 1.86e+20 46.67 4.36 0.39 2.35

Separator constraints 0 40 11.05 8.00 221 0 None 10.80 0.98 2.51

Separator variables 0 18 9.10 9.00 182 0 None 4.26 0.47 2.35

Clusters per var 1 12 5.55 5.50 222 3.20e+23 54.12 3.83 0.69 2.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	54	20.05	17.00	401	1.77e+24	55.83	13.30	0.66	2.72
Variables per cluster	6	21	11.10	10.00	222	1.86e+20	46.67	4.36	0.39	2.35
Separator constraints	0	40	11.05	8.00	221	0	None	10.80	0.98	2.51
Separator variables	0	18	9.10	9.00	182	0	None	4.26	0.47	2.35
Clusters per var	1	12	5.55	5.50	222	3.20e+23	54.12	3.83	0.69	2.09

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 140
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/DualTree1.json

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

Cluster constraints 20 332 119.87 100.50 4,555 MAX VALUE 174.53 73.53 0.61 3.46

Variables per cluster 9 83 28.68 21.50 1,090 MAX VALUE 121.52 17.81 0.62 3.16

Separator constraints 0 177 79.61 71.50 3,025 0 None 43.35 0.54 3.53

Separator variables 0 60 23.95 20.00 910 0 None 13.46 0.56 3.06

Clusters per variable 1 11 6.06 7.00 1,090 MAX VALUE 295.33 2.63 0.43 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	20	332	119.87	100.50	4,555	MAX VALUE	174.53	73.53	0.61	3.46
Variables per cluster	9	83	28.68	21.50	1,090	MAX VALUE	121.52	17.81	0.62	3.16
Separator constraints	0	177	79.61	71.50	3,025	0	None	43.35	0.54	3.53
Separator variables	0	60	23.95	20.00	910	0	None	13.46	0.56	3.06
Clusters per variable	1	11	6.06	7.00	1,090	MAX VALUE	295.33	2.63	0.43	2.15

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 145
Triangles: 102
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/Primal1.json

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

Clustering coefficient 0.00 0.33 0.19 0.20 7.74 0.00 None 0.08 0.39 3.28

Degree 5 13 9.00 9.00 360 4.17e+37 86.62 2.12 0.24 2.06

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.37 3.00 488 MAX VALUE 174.55 0.48 0.14 0.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.19	0.20	7.74	0.00	None	0.08	0.39	3.28
Degree	5	13	9.00	9.00	360	4.17e+37	86.62	2.12	0.24	2.06
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.37	3.00	488	MAX VALUE	174.55	0.48	0.14	0.66

Triangulated primal graph

Density: 50.26%
MCB compute time (ms): 6
MCB cycles: 404
Triangles: 2,249

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

Clustering coefficient 0.65 1.00 0.83 0.81 33.28 0.00 -7.81 0.13 0.15 2.93

Degree 5 31 19.60 24.50 784 MAX VALUE 112.44 9.41 0.48 2.76

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,212 MAX VALUE 443.84 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.65	1.00	0.83	0.81	33.28	0.00	-7.81	0.13	0.15	2.93
Degree	5	31	19.60	24.50	784	MAX VALUE	112.44	9.41	0.48	2.76
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,212	MAX VALUE	443.84	0.00	0.00	0.00

Dual graph

Density: 9.50%
MCB compute time (ms): 387
MCB cycles: 1,535
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/Dual1.json

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

Clustering coefficient 0.43 0.61 0.50 0.49 89.49 0.00 -126.02 0.03 0.05 4.02

Degree 8 23 17.00 17.00 3,060 MAX VALUE 507.39 2.72 0.16 2.36

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.16 3.00 4,845 MAX VALUE 1,754.83 0.38 0.12 0.45

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.61	0.50	0.49	89.49	0.00	-126.02	0.03	0.05	4.02
Degree	8	23	17.00	17.00	3,060	MAX VALUE	507.39	2.72	0.16	2.36
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.16	3.00	4,845	MAX VALUE	1,754.83	0.38	0.12	0.45

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 66
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 6 3.56 3.00 640 MAX VALUE 224.27 0.75 0.21 1.12

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.86 7.00 967 MAX VALUE 269.96 0.98 0.14 1.37

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	6	3.56	3.00	640	MAX VALUE	224.27	0.75	0.21	1.12
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.86	7.00	967	MAX VALUE	269.96	0.98	0.14	1.37

Triangulated dual graph

Density: 44.87%
Triangles: 182,062

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

Clustering coefficient 0.67 1.00 0.83 0.81 148.90 0.00 -35.23 0.09 0.11 4.56

Degree 8 131 80.32 92.00 14,458 MAX VALUE 754.26 39.69 0.49 3.98

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	0.67	1.00	0.83	0.81	148.90	0.00	-35.23	0.09	0.11	4.56
Degree	8	131	80.32	92.00	14,458	MAX VALUE	754.26	39.69	0.49	3.98
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.49%

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

Clustering coefficient 0.52 1.00 0.80 0.75 144.20 0.00 -42.86 0.15 0.18 3.33

Degree 2 68 22.36 7.00 4,024 MAX VALUE 430.06 24.29 1.09 3.13

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	0.52	1.00	0.80	0.75	144.20	0.00	-42.86	0.15	0.18	3.33
Degree	2	68	22.36	7.00	4,024	MAX VALUE	430.06	24.29	1.09	3.13
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 43
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-22-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 13 3.27 2.00 720 MAX VALUE 211.39 2.85 0.87 0.85

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.71 6.00 946 MAX VALUE 267.02 0.96 0.14 0.65

XCSP 2.1 Benchmarks