XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-40-135-650-79-ext
Number of variables: 40
Number of constraints: 135
Satisfiable: True
Timestamp: 2025-07-20 22:09:36
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 135

General features

Coarse blocks: 10,800
Value tables: 40

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

Arity 2 2 2.00 2.00 270 MAX VALUE 93.57 0.00 0.00 0.00

Coarse blocks size 3 25 14.06 14.00 151,882 MAX VALUE 28,294.30 2.97 0.21 2.51

Relational linkage 0.07 0.45 0.26 0.25 415.95 0.00 -2,188.33 0.05 0.20 2.13

Tightness 0.62 0.68 0.65 0.65 87.54 0.00 -58.50 0.01 0.02 3.92

Tuples 513 605 562.53 561.00 75,941 MAX VALUE 854.81 17.50 0.03 3.92

Values 40 40 40.00 40.00 1,600 MAX VALUE 147.56 0.00 0.00 0.00

Value table constraints 2 12 6.75 7.00 270 4.10e+31 72.79 2.54 0.38 2.22

Value table partitions 40 40 40.00 40.00 1,600 MAX VALUE 147.56 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	270	MAX VALUE	93.57	0.00	0.00	0.00
Coarse blocks size	3	25	14.06	14.00	151,882	MAX VALUE	28,294.30	2.97	0.21	2.51
Relational linkage	0.07	0.45	0.26	0.25	415.95	0.00	-2,188.33	0.05	0.20	2.13
Tightness	0.62	0.68	0.65	0.65	87.54	0.00	-58.50	0.01	0.02	3.92
Tuples	513	605	562.53	561.00	75,941	MAX VALUE	854.81	17.50	0.03	3.92
Values	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00
Value table constraints	2	12	6.75	7.00	270	4.10e+31	72.79	2.54	0.38	2.22
Value table partitions	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00

Tree decomposition

Number of clusters: 24
Number of leaves: 14
Tree depth: 4
CIR: 0.26
Independent Cluster Pairs: 65
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/Tree1.json

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

Cluster constraints 3 30 9.96 7.00 239 1.76e+21 48.92 7.54 0.76 2.47

Variables per cluster 3 17 7.83 6.50 188 1.25e+20 46.27 4.09 0.52 2.38

Separator constraints 0 23 4.33 2.00 104 0 None 5.56 1.28 2.22

Separator variables 0 15 6.17 5.00 148 0 None 3.84 0.62 2.38

Clusters per var 1 14 4.70 3.00 188 2.50e+19 44.67 3.91 0.83 2.10

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	30	9.96	7.00	239	1.76e+21	48.92	7.54	0.76	2.47
Variables per cluster	3	17	7.83	6.50	188	1.25e+20	46.27	4.09	0.52	2.38
Separator constraints	0	23	4.33	2.00	104	0	None	5.56	1.28	2.22
Separator variables	0	15	6.17	5.00	148	0	None	3.84	0.62	2.38
Clusters per var	1	14	4.70	3.00	188	2.50e+19	44.67	3.91	0.83	2.10

Dual tree decomposition

Number of clusters: 38
Number of leaves: 14
Tree depth: 5
CIR: 0.27
Independent Cluster Pairs: 177
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/DualTree1.json

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

Cluster constraints 10 177 66.45 55.50 2,525 MAX VALUE 151.40 41.88 0.63 3.46

Variables per cluster 7 57 20.61 17.00 783 MAX VALUE 108.83 12.89 0.63 2.93

Separator constraints 0 97 42.63 36.50 1,620 0 None 25.23 0.59 3.35

Separator variables 0 45 17.05 14.50 648 0 None 9.85 0.58 3.03

Clusters per variable 1 11 5.80 7.00 783 MAX VALUE 210.88 2.89 0.50 2.29

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	10	177	66.45	55.50	2,525	MAX VALUE	151.40	41.88	0.63	3.46
Variables per cluster	7	57	20.61	17.00	783	MAX VALUE	108.83	12.89	0.63	2.93
Separator constraints	0	97	42.63	36.50	1,620	0	None	25.23	0.59	3.35
Separator variables	0	45	17.05	14.50	648	0	None	9.85	0.58	3.03
Clusters per variable	1	11	5.80	7.00	783	MAX VALUE	210.88	2.89	0.50	2.29

Primal graph

Density: 17.31%
MCB compute time (ms): 3
MCB cycles: 106
Triangles: 53
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 0.21 0.17 8.25 0.00 None 0.20 0.98 2.95

Degree 2 12 6.75 7.00 270 4.10e+31 72.79 2.54 0.38 2.22

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.55 4.00 376 MAX VALUE 132.94 0.55 0.16 0.80

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	0.21	0.17	8.25	0.00	None	0.20	0.98	2.95
Degree	2	12	6.75	7.00	270	4.10e+31	72.79	2.54	0.38	2.22
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.55	4.00	376	MAX VALUE	132.94	0.55	0.16	0.80

Triangulated primal graph

Density: 36.41%
MCB compute time (ms): 7
MCB cycles: 245
Triangles: 1,239

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

Clustering coefficient 0.52 1.00 0.83 0.82 33.05 0.00 -8.38 0.16 0.19 2.64

Degree 2 29 14.20 14.00 568 MAX VALUE 94.19 9.09 0.64 2.87

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 735 MAX VALUE 269.16 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.52	1.00	0.83	0.82	33.05	0.00	-8.38	0.16	0.19	2.64
Degree	2	29	14.20	14.00	568	MAX VALUE	94.19	9.09	0.64	2.87
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	735	MAX VALUE	269.16	0.00	0.00	0.00

Dual graph

Density: 10.01%
MCB compute time (ms): 125
MCB cycles: 831
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/Dual1.json

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

Clustering coefficient 0.43 0.85 0.52 0.50 70.07 0.00 -89.59 0.07 0.14 3.92

Degree 6 21 13.41 14.00 1,810 MAX VALUE 346.98 2.88 0.21 2.45

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.14 3.00 2,607 MAX VALUE 944.97 0.38 0.12 0.42

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.85	0.52	0.50	70.07	0.00	-89.59	0.07	0.14	3.92
Degree	6	21	13.41	14.00	1,810	MAX VALUE	346.98	2.88	0.21	2.45
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.14	3.00	2,607	MAX VALUE	944.97	0.38	0.12	0.42

Minimal dual graph

Density: 2.54%
MCB compute time (ms): 31
MCB cycles: 96

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 3.41 3.00 460 MAX VALUE 162.57 0.69 0.20 1.05

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.88 7.00 660 MAX VALUE 183.82 1.05 0.15 1.43

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	3.41	3.00	460	MAX VALUE	162.57	0.69	0.20	1.05
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.88	7.00	660	MAX VALUE	183.82	1.05	0.15	1.43

Triangulated dual graph

Density: 41.88%
Triangles: 67,238

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

Clustering coefficient 0.64 1.00 0.82 0.81 111.35 0.00 -26.96 0.10 0.12 4.49

Degree 6 99 56.12 70.00 7,576 MAX VALUE 513.37 29.58 0.53 3.91

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	0.64	1.00	0.82	0.81	111.35	0.00	-26.96	0.10	0.12	4.49
Degree	6	99	56.12	70.00	7,576	MAX VALUE	513.37	29.58	0.53	3.91
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.95%

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

Clustering coefficient 0.44 1.00 0.78 0.72 105.34 0.00 -36.76 0.17 0.22 3.08

Degree 2 49 16.01 6.00 2,162 MAX VALUE 294.97 16.61 1.04 3.02

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	0.44	1.00	0.78	0.72	105.34	0.00	-36.76	0.17	0.22	3.08
Degree	2	49	16.01	6.00	2,162	MAX VALUE	294.97	16.61	1.04	3.02
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.77%
MCB compute time (ms): 22
MCB cycles: 96
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-79-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 12 3.09 2.00 540 MAX VALUE 166.37 2.33 0.76 0.98

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 6.96 6.00 668 MAX VALUE 185.18 1.04 0.15 0.74

XCSP 2.1 Benchmarks