XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-35-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 22 12.45 12.00 112,076 MAX VALUE 22,508.40 2.48 0.20 2.33

Relational linkage 0.12 0.52 0.36 0.36 355.84 0.00 -1,049.13 0.06 0.17 1.83

Tightness 0.45 0.55 0.50 0.50 90.34 0.00 -124.23 0.02 0.04 3.71

Tuples 280 344 311.32 312.00 56,038 MAX VALUE 1,033.20 12.49 0.04 3.71

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 4.09e+37 86.61 2.20 0.24 2.11

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	22	12.45	12.00	112,076	MAX VALUE	22,508.40	2.48	0.20	2.33
Relational linkage	0.12	0.52	0.36	0.36	355.84	0.00	-1,049.13	0.06	0.17	1.83
Tightness	0.45	0.55	0.50	0.50	90.34	0.00	-124.23	0.02	0.04	3.71
Tuples	280	344	311.32	312.00	56,038	MAX VALUE	1,033.20	12.49	0.04	3.71
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	4.09e+37	86.61	2.20	0.24	2.11
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: 12
Tree depth: 4
CIR: 0.11
Independent Cluster Pairs: 18
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/Tree1.json

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

Cluster constraints 8 55 23.30 17.50 466 3.57e+25 58.84 15.02 0.64 2.62

Variables per cluster 6 21 11.45 9.50 229 2.31e+20 46.89 5.06 0.44 2.39

Separator constraints 0 43 14.30 7.50 286 0 None 13.55 0.95 2.76

Separator variables 0 19 9.45 7.50 189 0 None 5.05 0.53 2.39

Clusters per var 1 11 5.72 7.00 229 1.13e+24 55.38 3.71 0.65 2.10

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	8	55	23.30	17.50	466	3.57e+25	58.84	15.02	0.64	2.62
Variables per cluster	6	21	11.45	9.50	229	2.31e+20	46.89	5.06	0.44	2.39
Separator constraints	0	43	14.30	7.50	286	0	None	13.55	0.95	2.76
Separator variables	0	19	9.45	7.50	189	0	None	5.05	0.53	2.39
Clusters per var	1	11	5.72	7.00	229	1.13e+24	55.38	3.71	0.65	2.10

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.23
Independent Cluster Pairs: 151
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/DualTree1.json

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

Cluster constraints 38 315 120.82 93.00 4,591 MAX VALUE 175.92 72.90 0.60 3.53

Variables per cluster 12 81 28.76 23.00 1,093 MAX VALUE 121.87 17.62 0.61 3.12

Separator constraints 0 182 80.37 70.50 3,054 0 None 42.93 0.53 3.56

Separator variables 0 59 24.03 20.50 913 0 None 13.35 0.56 3.21

Clusters per variable 1 10 6.07 7.00 1,093 MAX VALUE 294.21 2.74 0.45 2.18

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	38	315	120.82	93.00	4,591	MAX VALUE	175.92	72.90	0.60	3.53
Variables per cluster	12	81	28.76	23.00	1,093	MAX VALUE	121.87	17.62	0.61	3.12
Separator constraints	0	182	80.37	70.50	3,054	0	None	42.93	0.53	3.56
Separator variables	0	59	24.03	20.50	913	0	None	13.35	0.56	3.21
Clusters per variable	1	10	6.07	7.00	1,093	MAX VALUE	294.21	2.74	0.45	2.18

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 147
Triangles: 130
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/Primal1.json

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

Clustering coefficient 0.13 0.40 0.26 0.25 10.40 0.00 -55.03 0.06 0.24 2.98

Degree 5 13 9.00 9.00 360 4.09e+37 86.61 2.20 0.24 2.11

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.23 3.00 475 MAX VALUE 171.28 0.42 0.13 0.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.13	0.40	0.26	0.25	10.40	0.00	-55.03	0.06	0.24	2.98
Degree	5	13	9.00	9.00	360	4.09e+37	86.61	2.20	0.24	2.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.23	3.00	475	MAX VALUE	171.28	0.42	0.13	0.54

Triangulated primal graph

Density: 51.15%
MCB compute time (ms): 9
MCB cycles: 378
Triangles: 2,384

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

Clustering coefficient 0.68 1.00 0.84 0.78 33.57 0.00 -7.38 0.11 0.14 2.91

Degree 5 30 19.95 26.00 798 MAX VALUE 112.83 9.52 0.48 2.58

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,134 MAX VALUE 415.27 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.68	1.00	0.84	0.78	33.57	0.00	-7.38	0.11	0.14	2.91
Degree	5	30	19.95	26.00	798	MAX VALUE	112.83	9.52	0.48	2.58
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,134	MAX VALUE	415.27	0.00	0.00	0.00

Dual graph

Density: 9.54%
MCB compute time (ms): 238
MCB cycles: 1,736
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/Dual1.json

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

Clustering coefficient 0.45 0.62 0.50 0.50 90.66 0.00 -123.69 0.03 0.05 3.99

Degree 11 24 17.08 17.00 3,074 MAX VALUE 508.12 2.90 0.17 2.44

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.25 3.00 5,641 MAX VALUE 2,029.05 0.49 0.15 0.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.62	0.50	0.50	90.66	0.00	-123.69	0.03	0.05	3.99
Degree	11	24	17.08	17.00	3,074	MAX VALUE	508.12	2.90	0.17	2.44
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.25	3.00	5,641	MAX VALUE	2,029.05	0.49	0.15	0.61

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 6 3.56 3.00 640 MAX VALUE 224.48 0.74 0.21 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.68 7.00 942 MAX VALUE 265.44 1.16 0.17 1.53

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	224.48	0.74	0.21	1.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.68	7.00	942	MAX VALUE	265.44	1.16	0.17	1.53

Triangulated dual graph

Density: 44.56%
Triangles: 179,171

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

Clustering coefficient 0.69 1.00 0.83 0.81 148.85 0.00 -35.35 0.09 0.11 4.54

Degree 11 126 79.76 97.50 14,356 MAX VALUE 753.17 39.51 0.50 3.83

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	0.69	1.00	0.83	0.81	148.85	0.00	-35.35	0.09	0.11	4.54
Degree	11	126	79.76	97.50	14,356	MAX VALUE	753.17	39.51	0.50	3.83
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.73%

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

Clustering coefficient 0.50 1.00 0.80 0.75 144.37 0.00 -43.21 0.16 0.20 3.19

Degree 2 67 21.00 7.00 3,780 MAX VALUE 421.93 23.14 1.10 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	0.50	1.00	0.80	0.75	144.37	0.00	-43.21	0.16	0.20	3.19
Degree	2	67	21.00	7.00	3,780	MAX VALUE	421.93	23.14	1.10	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-2-40-25-180-500-35-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-35-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 211.37 2.86 0.87 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.40 6.00 902 MAX VALUE 260.69 0.80 0.12 0.50

XCSP 2.1 Benchmarks