XCSP 2.1 Benchmark Database

Instance: normalized-bqwh-18-141-92-ext
Number of variables: 141
Number of constraints: 966
Satisfiable: True
Timestamp: 2025-07-27 21:34:25
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 141
Number of constraints: 966

General features

Coarse blocks: 7,495
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 3.39 3.00 25,424 MAX VALUE 8,804.09 0.99 0.29 1.40

Relational linkage 0.50 0.83 0.65 0.67 355.45 0.00 -238.04 0.07 0.11 0.83

Tightness 0.00 0.33 0.13 0.12 120.78 0.00 None 0.06 0.45 2.64

Tuples 3 32 13.16 13.00 12,712 MAX VALUE 2,422.51 4.91 0.37 2.83

Values 2 6 3.87 4.00 546 MAX VALUE 186.07 1.00 0.26 1.39

Value table constraints 12 14 13.70 14.00 1,932 MAX VALUE 368.97 0.52 0.04 0.67

Value table partitions 2 6 3.87 4.00 546 MAX VALUE 186.07 1.00 0.26 1.39

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	3.39	3.00	25,424	MAX VALUE	8,804.09	0.99	0.29	1.40
Relational linkage	0.50	0.83	0.65	0.67	355.45	0.00	-238.04	0.07	0.11	0.83
Tightness	0.00	0.33	0.13	0.12	120.78	0.00	None	0.06	0.45	2.64
Tuples	3	32	13.16	13.00	12,712	MAX VALUE	2,422.51	4.91	0.37	2.83
Values	2	6	3.87	4.00	546	MAX VALUE	186.07	1.00	0.26	1.39
Value table constraints	12	14	13.70	14.00	1,932	MAX VALUE	368.97	0.52	0.04	0.67
Value table partitions	2	6	3.87	4.00	546	MAX VALUE	186.07	1.00	0.26	1.39

Tree decomposition

Number of clusters: 54
Number of leaves: 26
Tree depth: 7
CIR: 0.17
Independent Cluster Pairs: 240
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-ext/Tree1.json

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

Cluster constraints 23 284 68.54 48.50 3,701 MAX VALUE 217.96 50.74 0.74 3.59

Variables per cluster 10 78 23.67 16.50 1,278 MAX VALUE 161.15 15.87 0.67 3.05

Separator constraints 0 189 51.98 36.00 2,807 0 None 39.39 0.76 3.55

Separator variables 0 64 21.06 14.50 1,137 0 None 13.82 0.66 3.09

Clusters per var 1 20 9.06 11.00 1,278 MAX VALUE 262.31 5.30 0.58 2.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	23	284	68.54	48.50	3,701	MAX VALUE	217.96	50.74	0.74	3.59
Variables per cluster	10	78	23.67	16.50	1,278	MAX VALUE	161.15	15.87	0.67	3.05
Separator constraints	0	189	51.98	36.00	2,807	0	None	39.39	0.76	3.55
Separator variables	0	64	21.06	14.50	1,137	0	None	13.82	0.66	3.09
Clusters per var	1	20	9.06	11.00	1,278	MAX VALUE	262.31	5.30	0.58	2.61

Dual tree decomposition

Number of clusters: 139
Number of leaves: 69
Tree depth: 7
CIR: 0.51
Independent Cluster Pairs: 4,851
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-ext/DualTree1.json

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

Cluster constraints 75 1,518 285.06 188.00 39,624 MAX VALUE 757.86 234.02 0.82 4.01

Variables per cluster 17 314 51.83 30.00 7,204 MAX VALUE 511.76 51.72 1.00 3.62

Separator constraints 0 940 208.92 162.00 29,040 0 None 149.78 0.72 4.00

Separator variables 0 251 45.40 26.00 6,310 0 None 40.55 0.89 3.53

Clusters per variable 1 14 8.06 9.00 7,204 MAX VALUE 1,685.51 4.00 0.50 2.41

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	75	1,518	285.06	188.00	39,624	MAX VALUE	757.86	234.02	0.82	4.01
Variables per cluster	17	314	51.83	30.00	7,204	MAX VALUE	511.76	51.72	1.00	3.62
Separator constraints	0	940	208.92	162.00	29,040	0	None	149.78	0.72	4.00
Separator variables	0	251	45.40	26.00	6,310	0	None	40.55	0.89	3.53
Clusters per variable	1	14	8.06	9.00	7,204	MAX VALUE	1,685.51	4.00	0.50	2.41

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-18-141-92-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-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 65.05 0.00 -109.08 0.00 0.00 0.13

Degree 12 14 13.70 14.00 1,932 MAX VALUE 368.97 0.52 0.04 0.67

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	65.05	0.00	-109.08	0.00	0.00	0.13
Degree	12	14	13.70	14.00	1,932	MAX VALUE	368.97	0.52	0.04	0.67
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: 46.62%
MCB compute time (ms): None
MCB cycles: None
Triangles: 92,940

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

Clustering coefficient 0.71 1.00 0.83 0.81 116.79 0.00 -27.43 0.09 0.11 3.53

Degree 12 101 65.26 77.00 9,202 MAX VALUE 563.69 31.25 0.48 2.96

Eccentricity 2 3 2.36 2.00 333 MAX VALUE 118.41 0.48 0.20 0.65

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	0.71	1.00	0.83	0.81	116.79	0.00	-27.43	0.09	0.11	3.53
Degree	12	101	65.26	77.00	9,202	MAX VALUE	563.69	31.25	0.48	2.96
Eccentricity	2	3	2.36	2.00	333	MAX VALUE	118.41	0.48	0.20	0.65
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 2.64%
MCB compute time (ms): 161,341
MCB cycles: 13,630
Triangles: 49,986
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-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 -672.24 0.00 0.00 0.99

Degree 22 26 25.44 26.00 24,578 MAX VALUE 3,125.83 0.86 0.03 1.00

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 3.18 3.00 43,395 MAX VALUE 15,688.70 0.40 0.13 0.50

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	-672.24	0.00	0.00	0.99
Degree	22	26	25.44	26.00	24,578	MAX VALUE	3,125.83	0.86	0.03	1.00
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	3.18	3.00	43,395	MAX VALUE	15,688.70	0.40	0.13	0.50

Minimal dual graph

Density: 0.38%
MCB compute time (ms): 19,550
MCB cycles: 840

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.02 18.62 0.02

Degree 2 6 3.71 4.00 3,582 MAX VALUE 1,244.15 0.82 0.22 1.13

Eccentricity 8 12 9.84 10.00 9,508 MAX VALUE 2,206.48 0.71 0.07 1.07

MCB cycle size 3 12 6.76 7.00 5,680 MAX VALUE 1,577.64 1.69 0.25 1.89

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.02	18.62	0.02
Degree	2	6	3.71	4.00	3,582	MAX VALUE	1,244.15	0.82	0.22	1.13
Eccentricity	8	12	9.84	10.00	9,508	MAX VALUE	2,206.48	0.71	0.07	1.07
MCB cycle size	3	12	6.76	7.00	5,680	MAX VALUE	1,577.64	1.69	0.25	1.89

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: 6.29%

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

Clustering coefficient 0.47 1.00 0.83 0.80 797.38 0.00 -201.05 0.15 0.18 4.09

Degree 2 257 60.73 8.00 58,666 MAX VALUE 2,650.34 90.93 1.50 3.70

Eccentricity 3 6 4.49 5.00 4,342 MAX VALUE 1,443.21 0.59 0.13 0.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.83	0.80	797.38	0.00	-201.05	0.15	0.18	4.09
Degree	2	257	60.73	8.00	58,666	MAX VALUE	2,650.34	90.93	1.50	3.70
Eccentricity	3	6	4.49	5.00	4,342	MAX VALUE	1,443.21	0.59	0.13	0.88

Incidence graph

Density: 0.32%
MCB compute time (ms): 10,019
MCB cycles: 826
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-92-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 1,038.55 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