XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-40-135-650-30-ext
Number of variables: 40
Number of constraints: 135
Satisfiable: True
Timestamp: 2025-07-20 22:09:32
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 2 27 14.06 14.00 151,874 MAX VALUE 28,283.40 3.03 0.22 2.53

Relational linkage 0.05 0.45 0.26 0.25 410.20 0.00 -2,209.39 0.05 0.19 2.09

Tightness 0.62 0.68 0.65 0.65 87.54 0.00 -58.50 0.01 0.02 3.97

Tuples 514 611 562.50 560.00 75,937 MAX VALUE 854.79 19.06 0.03 3.97

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

Value table constraints 2 11 6.75 7.00 270 7.42e+31 73.38 2.32 0.34 2.13

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	2	27	14.06	14.00	151,874	MAX VALUE	28,283.40	3.03	0.22	2.53
Relational linkage	0.05	0.45	0.26	0.25	410.20	0.00	-2,209.39	0.05	0.19	2.09
Tightness	0.62	0.68	0.65	0.65	87.54	0.00	-58.50	0.01	0.02	3.97
Tuples	514	611	562.50	560.00	75,937	MAX VALUE	854.79	19.06	0.03	3.97
Values	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00
Value table constraints	2	11	6.75	7.00	270	7.42e+31	73.38	2.32	0.34	2.13
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: 23
Number of leaves: 11
Tree depth: 4
CIR: 0.24
Independent Cluster Pairs: 56
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/Tree1.json

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

Cluster constraints 2 31 11.22 8.00 258 1.73e+21 48.90 8.28 0.74 2.63

Variables per cluster 3 18 8.52 7.00 196 1.16e+20 46.20 4.41 0.52 2.45

Separator constraints 0 26 5.35 3.00 123 0 None 6.82 1.28 2.10

Separator variables 0 17 6.78 6.00 156 0 None 4.18 0.62 2.51

Clusters per var 1 12 4.90 3.50 196 4.23e+20 47.49 3.75 0.76 2.10

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	31	11.22	8.00	258	1.73e+21	48.90	8.28	0.74	2.63
Variables per cluster	3	18	8.52	7.00	196	1.16e+20	46.20	4.41	0.52	2.45
Separator constraints	0	26	5.35	3.00	123	0	None	6.82	1.28	2.10
Separator variables	0	17	6.78	6.00	156	0	None	4.18	0.62	2.51
Clusters per var	1	12	4.90	3.50	196	4.23e+20	47.49	3.75	0.76	2.10

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.30
Independent Cluster Pairs: 200
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/DualTree1.json

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

Cluster constraints 16 155 62.03 45.50 2,357 MAX VALUE 148.52 39.46 0.64 3.28

Variables per cluster 7 58 20.26 16.00 770 MAX VALUE 108.02 12.71 0.63 2.96

Separator constraints 0 85 38.76 33.50 1,473 0 None 24.11 0.62 3.21

Separator variables 0 43 16.71 13.50 635 0 None 9.78 0.59 2.85

Clusters per variable 1 11 5.70 6.00 770 MAX VALUE 208.35 2.87 0.50 2.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	155	62.03	45.50	2,357	MAX VALUE	148.52	39.46	0.64	3.28
Variables per cluster	7	58	20.26	16.00	770	MAX VALUE	108.02	12.71	0.63	2.96
Separator constraints	0	85	38.76	33.50	1,473	0	None	24.11	0.62	3.21
Separator variables	0	43	16.71	13.50	635	0	None	9.78	0.59	2.85
Clusters per variable	1	11	5.70	6.00	770	MAX VALUE	208.35	2.87	0.50	2.25

Primal graph

Density: 17.31%
MCB compute time (ms): 3
MCB cycles: 97
Triangles: 46
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/Primal1.json

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

Clustering coefficient 0.00 0.50 0.15 0.14 5.82 0.00 None 0.10 0.69 2.60

Degree 2 11 6.75 7.00 270 7.42e+31 73.38 2.32 0.34 2.13

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.57 4.00 346 MAX VALUE 122.19 0.55 0.16 0.81

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.50	0.15	0.14	5.82	0.00	None	0.10	0.69	2.60
Degree	2	11	6.75	7.00	270	7.42e+31	73.38	2.32	0.34	2.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.57	4.00	346	MAX VALUE	122.19	0.55	0.16	0.81

Triangulated primal graph

Density: 39.62%
MCB compute time (ms): 6
MCB cycles: 289
Triangles: 1,468

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

Clustering coefficient 0.61 1.00 0.83 0.81 33.16 0.00 -8.07 0.14 0.17 2.82

Degree 2 28 15.45 15.50 618 MAX VALUE 98.46 9.28 0.60 2.82

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 867 MAX VALUE 317.50 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	0.81	33.16	0.00	-8.07	0.14	0.17	2.82
Degree	2	28	15.45	15.50	618	MAX VALUE	98.46	9.28	0.60	2.82
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	867	MAX VALUE	317.50	0.00	0.00	0.00

Dual graph

Density: 9.77%
MCB compute time (ms): 101
MCB cycles: 892
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/Dual1.json

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

Clustering coefficient 0.43 0.80 0.51 0.49 68.32 0.00 -92.64 0.06 0.11 3.72

Degree 6 19 13.10 14.00 1,768 MAX VALUE 343.44 2.93 0.22 2.40

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.26 3.00 2,904 MAX VALUE 1,043.25 0.52 0.16 0.63

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.80	0.51	0.49	68.32	0.00	-92.64	0.06	0.11	3.72
Degree	6	19	13.10	14.00	1,768	MAX VALUE	343.44	2.93	0.22	2.40
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.26	3.00	2,904	MAX VALUE	1,043.25	0.52	0.16	0.63

Minimal dual graph

Density: 2.54%
MCB compute time (ms): 30
MCB cycles: 96

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.60 0.00 None 0.03 7.40 0.13

Degree 2 5 3.41 3.00 460 MAX VALUE 162.68 0.69 0.20 1.04

Eccentricity None None None None None None None None None None

MCB cycle size 3 10 6.84 7.00 657 MAX VALUE 182.58 1.33 0.19 1.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.60	0.00	None	0.03	7.40	0.13
Degree	2	5	3.41	3.00	460	MAX VALUE	162.68	0.69	0.20	1.04
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	10	6.84	7.00	657	MAX VALUE	182.58	1.33	0.19	1.66

Triangulated dual graph

Density: 40.71%
Triangles: 63,661

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

Clustering coefficient 0.68 1.00 0.82 0.78 110.92 0.00 -27.51 0.10 0.12 4.38

Degree 6 92 54.55 66.00 7,364 MAX VALUE 508.46 29.36 0.54 3.77

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	0.68	1.00	0.82	0.78	110.92	0.00	-27.51	0.10	0.12	4.38
Degree	6	92	54.55	66.00	7,364	MAX VALUE	508.46	29.36	0.54	3.77
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.74%

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

Clustering coefficient 0.50 1.00 0.79 0.71 106.08 0.00 -35.95 0.18 0.22 3.05

Degree 2 49 15.73 7.00 2,124 MAX VALUE 291.69 16.40 1.04 2.96

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	0.79	0.71	106.08	0.00	-35.95	0.18	0.22	3.05
Degree	2	49	15.73	7.00	2,124	MAX VALUE	291.69	16.40	1.04	2.96
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-2-40-40-135-650-30-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-30-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 11 3.09 2.00 540 MAX VALUE 166.96 2.28 0.74 0.96

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.12 8.00 684 MAX VALUE 187.35 1.11 0.16 0.81

XCSP 2.1 Benchmarks