XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-72-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:31
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 21 12.55 13.00 112,938 MAX VALUE 22,571.70 2.52 0.20 2.34

Relational linkage 0.12 0.56 0.36 0.36 355.84 0.00 -1,050.70 0.06 0.18 1.87

Tightness 0.45 0.56 0.50 0.50 89.65 0.00 -125.61 0.02 0.04 3.71

Tuples 275 344 313.72 315.00 56,469 MAX VALUE 1,034.58 12.47 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 3 14 9.00 9.00 360 1.87e+37 85.82 2.69 0.30 2.34

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	21	12.55	13.00	112,938	MAX VALUE	22,571.70	2.52	0.20	2.34
Relational linkage	0.12	0.56	0.36	0.36	355.84	0.00	-1,050.70	0.06	0.18	1.87
Tightness	0.45	0.56	0.50	0.50	89.65	0.00	-125.61	0.02	0.04	3.71
Tuples	275	344	313.72	315.00	56,469	MAX VALUE	1,034.58	12.47	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	3	14	9.00	9.00	360	1.87e+37	85.82	2.69	0.30	2.34
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: 22
Number of leaves: 14
Tree depth: 4
CIR: 0.08
Independent Cluster Pairs: 17
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/Tree1.json

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

Cluster constraints 3 49 21.77 14.00 479 9.66e+26 62.13 14.94 0.69 2.71

Variables per cluster 4 19 10.68 8.50 235 4.72e+21 49.91 4.79 0.45 2.32

Separator constraints 0 44 13.59 6.50 299 0 None 14.07 1.04 2.69

Separator variables 0 18 8.86 7.00 195 0 None 4.84 0.55 2.41

Clusters per var 1 14 5.88 6.00 235 1.22e+23 53.16 4.40 0.75 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	49	21.77	14.00	479	9.66e+26	62.13	14.94	0.69	2.71
Variables per cluster	4	19	10.68	8.50	235	4.72e+21	49.91	4.79	0.45	2.32
Separator constraints	0	44	13.59	6.50	299	0	None	14.07	1.04	2.69
Separator variables	0	18	8.86	7.00	195	0	None	4.84	0.55	2.41
Clusters per var	1	14	5.88	6.00	235	1.22e+23	53.16	4.40	0.75	2.17

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 142
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/DualTree1.json

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

Cluster constraints 38 328 121.66 104.50 4,623 MAX VALUE 175.72 73.56 0.60 3.53

Variables per cluster 11 80 28.32 22.00 1,076 MAX VALUE 121.08 17.45 0.62 3.12

Separator constraints 0 166 79.95 74.00 3,038 0 None 43.04 0.54 3.53

Separator variables 0 57 23.58 20.00 896 0 None 13.19 0.56 3.02

Clusters per variable 1 10 5.98 7.00 1,076 MAX VALUE 291.39 2.70 0.45 2.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	38	328	121.66	104.50	4,623	MAX VALUE	175.72	73.56	0.60	3.53
Variables per cluster	11	80	28.32	22.00	1,076	MAX VALUE	121.08	17.45	0.62	3.12
Separator constraints	0	166	79.95	74.00	3,038	0	None	43.04	0.54	3.53
Separator variables	0	57	23.58	20.00	896	0	None	13.19	0.56	3.02
Clusters per variable	1	10	5.98	7.00	1,076	MAX VALUE	291.39	2.70	0.45	2.16

Primal graph

Density: 23.08%
MCB compute time (ms): 6
MCB cycles: 143
Triangles: 130
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/Primal1.json

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

Clustering coefficient 0.00 0.47 0.25 0.24 10.12 0.00 None 0.08 0.33 3.21

Degree 3 14 9.00 9.00 360 1.87e+37 85.82 2.69 0.30 2.34

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.21 3.00 459 MAX VALUE 165.73 0.41 0.13 0.51

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.47	0.25	0.24	10.12	0.00	None	0.08	0.33	3.21
Degree	3	14	9.00	9.00	360	1.87e+37	85.82	2.69	0.30	2.34
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.21	3.00	459	MAX VALUE	165.73	0.41	0.13	0.51

Triangulated primal graph

Density: 46.92%
MCB compute time (ms): 10
MCB cycles: 329
Triangles: 1,993

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

Clustering coefficient 0.61 1.00 0.83 0.78 33.35 0.00 -7.80 0.13 0.16 2.77

Degree 3 31 18.30 23.00 732 MAX VALUE 108.25 9.56 0.52 2.86

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 987 MAX VALUE 361.44 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.61	1.00	0.83	0.78	33.35	0.00	-7.80	0.13	0.16	2.77
Degree	3	31	18.30	23.00	732	MAX VALUE	108.25	9.56	0.52	2.86
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	987	MAX VALUE	361.44	0.00	0.00	0.00

Dual graph

Density: 9.84%
MCB compute time (ms): 365
MCB cycles: 1,504
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/Dual1.json

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

Clustering coefficient 0.46 0.67 0.51 0.50 92.31 0.00 -120.65 0.04 0.07 4.31

Degree 10 25 17.61 18.00 3,170 MAX VALUE 512.80 3.40 0.19 2.59

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.08 3.00 4,630 MAX VALUE 1,686.13 0.27 0.09 0.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.67	0.51	0.50	92.31	0.00	-120.65	0.04	0.07	4.31
Degree	10	25	17.61	18.00	3,170	MAX VALUE	512.80	3.40	0.19	2.59
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.08	3.00	4,630	MAX VALUE	1,686.13	0.27	0.09	0.28

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 73
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 223.89 0.79 0.22 1.16

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.66 7.00 939 MAX VALUE 265.14 1.12 0.17 1.50

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	223.89	0.79	0.22	1.16
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.66	7.00	939	MAX VALUE	265.14	1.12	0.17	1.50

Triangulated dual graph

Density: 43.85%
Triangles: 172,793

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

Clustering coefficient 0.66 1.00 0.82 0.80 148.37 0.00 -35.98 0.10 0.12 4.59

Degree 10 130 78.50 91.00 14,130 MAX VALUE 749.87 39.05 0.50 3.99

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	0.66	1.00	0.82	0.80	148.37	0.00	-35.98	0.10	0.12	4.59
Degree	10	130	78.50	91.00	14,130	MAX VALUE	749.87	39.05	0.50	3.99
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.94%

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

Clustering coefficient 0.48 1.00 0.80 0.74 143.60 0.00 -43.96 0.15 0.19 3.35

Degree 2 65 21.37 7.00 3,846 MAX VALUE 424.51 23.34 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	0.48	1.00	0.80	0.74	143.60	0.00	-43.96	0.15	0.19	3.35
Degree	2	65	21.37	7.00	3,846	MAX VALUE	424.51	23.34	1.09	3.13
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 46
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-72-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 210.59 2.93 0.90 0.90

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