XCSP 2.1 Benchmark Database

Instance: normalized-bqwh-18-141-75-ext
Number of variables: 141
Number of constraints: 966
Satisfiable: True
Timestamp: 2025-07-27 21:34:26
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 141
Number of constraints: 966

General features

Coarse blocks: 7,216
Value tables: 141

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

Arity 2 2 2.00 2.00 1,932 MAX VALUE 669.58 0.00 0.00 0.00

Coarse blocks size 1 6 3.28 3.00 23,668 MAX VALUE 8,171.06 1.01 0.31 1.43

Relational linkage 0.50 1.00 0.63 0.67 325.10 0.00 -245.38 0.09 0.14 0.98

Tightness 0.00 0.50 0.12 0.12 118.68 0.00 None 0.06 0.51 2.63

Tuples 1 32 12.25 11.00 11,834 MAX VALUE 2,338.13 4.82 0.39 2.85

Values 1 6 3.73 4.00 526 MAX VALUE 179.68 1.02 0.27 1.44

Value table constraints 12 14 13.70 14.00 1,932 MAX VALUE 368.96 0.54 0.04 0.68

Value table partitions 1 6 3.73 4.00 526 MAX VALUE 179.68 1.02 0.27 1.44

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	1,932	MAX VALUE	669.58	0.00	0.00	0.00
Coarse blocks size	1	6	3.28	3.00	23,668	MAX VALUE	8,171.06	1.01	0.31	1.43
Relational linkage	0.50	1.00	0.63	0.67	325.10	0.00	-245.38	0.09	0.14	0.98
Tightness	0.00	0.50	0.12	0.12	118.68	0.00	None	0.06	0.51	2.63
Tuples	1	32	12.25	11.00	11,834	MAX VALUE	2,338.13	4.82	0.39	2.85
Values	1	6	3.73	4.00	526	MAX VALUE	179.68	1.02	0.27	1.44
Value table constraints	12	14	13.70	14.00	1,932	MAX VALUE	368.96	0.54	0.04	0.68
Value table partitions	1	6	3.73	4.00	526	MAX VALUE	179.68	1.02	0.27	1.44

Tree decomposition

Number of clusters: 54
Number of leaves: 24
Tree depth: 7
CIR: 0.22
Independent Cluster Pairs: 305
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/Tree1.json

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

Cluster constraints 19 227 63.74 46.00 3,442 MAX VALUE 213.60 46.26 0.73 3.52

Variables per cluster 9 69 22.37 16.00 1,208 MAX VALUE 158.08 15.11 0.68 3.08

Separator constraints 0 153 47.33 34.00 2,556 0 None 36.09 0.76 3.47

Separator variables 0 58 19.76 14.50 1,067 0 None 13.07 0.66 3.10

Clusters per var 1 18 8.57 9.00 1,208 MAX VALUE 254.81 5.21 0.61 2.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	19	227	63.74	46.00	3,442	MAX VALUE	213.60	46.26	0.73	3.52
Variables per cluster	9	69	22.37	16.00	1,208	MAX VALUE	158.08	15.11	0.68	3.08
Separator constraints	0	153	47.33	34.00	2,556	0	None	36.09	0.76	3.47
Separator variables	0	58	19.76	14.50	1,067	0	None	13.07	0.66	3.10
Clusters per var	1	18	8.57	9.00	1,208	MAX VALUE	254.81	5.21	0.61	2.67

Dual tree decomposition

Number of clusters: 139
Number of leaves: 67
Tree depth: 7
CIR: 0.51
Independent Cluster Pairs: 4,868
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/DualTree1.json

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

Cluster constraints 66 1,435 276.74 188.00 38,467 MAX VALUE 754.48 219.90 0.79 4.10

Variables per cluster 16 303 51.00 31.00 7,089 MAX VALUE 510.25 49.92 0.98 3.68

Separator constraints 0 881 201.80 162.00 28,050 0 None 138.93 0.69 4.01

Separator variables 0 239 44.63 26.00 6,203 0 None 39.00 0.87 3.64

Clusters per variable 1 14 8.00 9.00 7,089 MAX VALUE 1,665.82 3.98 0.50 2.45

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	66	1,435	276.74	188.00	38,467	MAX VALUE	754.48	219.90	0.79	4.10
Variables per cluster	16	303	51.00	31.00	7,089	MAX VALUE	510.25	49.92	0.98	3.68
Separator constraints	0	881	201.80	162.00	28,050	0	None	138.93	0.69	4.01
Separator variables	0	239	44.63	26.00	6,203	0	None	39.00	0.87	3.64
Clusters per variable	1	14	8.00	9.00	7,089	MAX VALUE	1,665.82	3.98	0.50	2.45

Primal graph

Density: 9.79%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,890
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/Primal1.json

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

Clustering coefficient 0.45 0.46 0.46 0.46 65.03 0.00 -109.11 0.00 0.00 0.18

Degree 12 14 13.70 14.00 1,932 MAX VALUE 368.96 0.54 0.04 0.68

Eccentricity 3 3 3.00 3.00 423 MAX VALUE 154.90 0.00 0.00 0.00

MCB cycle size 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	0.45	0.46	0.46	0.46	65.03	0.00	-109.11	0.00	0.00	0.18
Degree	12	14	13.70	14.00	1,932	MAX VALUE	368.96	0.54	0.04	0.68
Eccentricity	3	3	3.00	3.00	423	MAX VALUE	154.90	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 44.28%
MCB compute time (ms): None
MCB cycles: None
Triangles: 81,320

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

Clustering coefficient 0.64 1.00 0.82 0.80 115.64 0.00 -29.12 0.11 0.13 3.38

Degree 12 105 61.99 71.00 8,740 MAX VALUE 557.91 29.45 0.48 3.01

Eccentricity 2 3 2.38 2.00 335 MAX VALUE 119.22 0.48 0.20 0.66

MCB cycle size 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	0.80	115.64	0.00	-29.12	0.11	0.13	3.38
Degree	12	105	61.99	71.00	8,740	MAX VALUE	557.91	29.45	0.48	3.01
Eccentricity	2	3	2.38	2.00	335	MAX VALUE	119.22	0.48	0.20	0.66
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 2.64%
MCB compute time (ms): 147,561
MCB cycles: 13,330
Triangles: 50,010
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/Dual1.json

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

Clustering coefficient 0.50 0.50 0.50 0.50 481.67 0.00 -672.25 0.00 0.00 0.98

Degree 22 26 25.45 26.00 24,582 MAX VALUE 3,125.91 0.92 0.04 0.99

Eccentricity 4 4 4.00 4.00 3,864 MAX VALUE 1,339.16 0.00 0.00 0.00

MCB cycle size 3 5 3.16 3.00 42,166 MAX VALUE 15,266.20 0.38 0.12 0.46

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	0.50	0.50	0.50	481.67	0.00	-672.25	0.00	0.00	0.98
Degree	22	26	25.45	26.00	24,582	MAX VALUE	3,125.91	0.92	0.04	0.99
Eccentricity	4	4	4.00	4.00	3,864	MAX VALUE	1,339.16	0.00	0.00	0.00
MCB cycle size	3	5	3.16	3.00	42,166	MAX VALUE	15,266.20	0.38	0.12	0.46

Minimal dual graph

Density: 0.38%
MCB compute time (ms): 20,686
MCB cycles: 835

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

Clustering coefficient 0.00 1.00 0.00 0.00 2.33 0.00 None 0.04 15.67 0.04

Degree 2 6 3.71 4.00 3,582 MAX VALUE 1,243.43 0.83 0.22 1.14

Eccentricity 8 11 9.77 10.00 9,440 MAX VALUE 2,199.79 0.66 0.07 1.00

MCB cycle size 3 11 6.72 7.00 5,609 MAX VALUE 1,563.60 1.64 0.24 1.87

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	0.00	0.00	2.33	0.00	None	0.04	15.67	0.04
Degree	2	6	3.71	4.00	3,582	MAX VALUE	1,243.43	0.83	0.22	1.14
Eccentricity	8	11	9.77	10.00	9,440	MAX VALUE	2,199.79	0.66	0.07	1.00
MCB cycle size	3	11	6.72	7.00	5,609	MAX VALUE	1,563.60	1.64	0.24	1.87

Triangulated dual graph

Density: None%
Triangles: None

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

Clustering coefficient None None None None None None None None None None

Degree None None None None None None None None None None

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	None	None	None	None	None	None	None	None	None	None
Degree	None	None	None	None	None	None	None	None	None	None
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 6.42%

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

Clustering coefficient 0.48 1.00 0.83 0.80 799.83 0.00 -198.04 0.15 0.18 4.10

Degree 2 258 61.93 8.00 59,822 MAX VALUE 2,650.98 93.02 1.50 3.63

Eccentricity 3 5 3.98 4.00 3,843 MAX VALUE 1,323.12 0.58 0.15 0.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	1.00	0.83	0.80	799.83	0.00	-198.04	0.15	0.18	4.10
Degree	2	258	61.93	8.00	59,822	MAX VALUE	2,650.98	93.02	1.50	3.63
Eccentricity	3	5	3.98	4.00	3,843	MAX VALUE	1,323.12	0.58	0.15	0.88

Incidence graph

Density: 0.32%
MCB compute time (ms): 8,953
MCB cycles: 826
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-75-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 3.49 2.00 3,864 MAX VALUE 1,038.54 3.91 1.12 0.47

Eccentricity 7 8 7.87 8.00 8,715 MAX VALUE 2,283.11 0.33 0.04 0.38

MCB cycle size 6 8 6.26 6.00 5,168 MAX VALUE 1,510.49 0.67 0.11 0.38

XCSP 2.1 Benchmarks