XCSP 2.1 Benchmark Database

Instance: normalized-bqwh-18-141-43-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: 7,649
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 3.46 3.00 26,480 MAX VALUE 9,129.20 0.98 0.28 1.40

Relational linkage 0.50 0.80 0.66 0.67 361.38 0.00 -232.45 0.08 0.12 0.98

Tightness 0.00 0.33 0.13 0.12 122.26 0.00 None 0.05 0.42 2.66

Tuples 2 32 13.71 13.00 13,240 MAX VALUE 2,455.87 4.92 0.36 2.87

Values 1 6 3.96 4.00 558 MAX VALUE 188.59 0.99 0.25 1.39

Value table constraints 12 14 13.70 14.00 1,932 MAX VALUE 368.96 0.53 0.04 0.68

Value table partitions 1 6 3.96 4.00 558 MAX VALUE 188.59 0.99 0.25 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	3.46	3.00	26,480	MAX VALUE	9,129.20	0.98	0.28	1.40
Relational linkage	0.50	0.80	0.66	0.67	361.38	0.00	-232.45	0.08	0.12	0.98
Tightness	0.00	0.33	0.13	0.12	122.26	0.00	None	0.05	0.42	2.66
Tuples	2	32	13.71	13.00	13,240	MAX VALUE	2,455.87	4.92	0.36	2.87
Values	1	6	3.96	4.00	558	MAX VALUE	188.59	0.99	0.25	1.39
Value table constraints	12	14	13.70	14.00	1,932	MAX VALUE	368.96	0.53	0.04	0.68
Value table partitions	1	6	3.96	4.00	558	MAX VALUE	188.59	0.99	0.25	1.39

Tree decomposition

Number of clusters: 47
Number of leaves: 24
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 215
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-ext/Tree1.json

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

Cluster constraints 7 225 66.91 49.00 3,145 MAX VALUE 188.97 43.20 0.65 3.25

Variables per cluster 5 71 22.23 15.00 1,045 MAX VALUE 137.78 14.45 0.65 2.94

Separator constraints 0 122 47.34 36.00 2,225 0 None 28.91 0.61 3.33

Separator variables 0 52 19.23 14.00 904 0 None 11.73 0.61 2.90

Clusters per var 1 15 7.41 9.00 1,045 MAX VALUE 243.14 4.03 0.54 2.45

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	225	66.91	49.00	3,145	MAX VALUE	188.97	43.20	0.65	3.25
Variables per cluster	5	71	22.23	15.00	1,045	MAX VALUE	137.78	14.45	0.65	2.94
Separator constraints	0	122	47.34	36.00	2,225	0	None	28.91	0.61	3.33
Separator variables	0	52	19.23	14.00	904	0	None	11.73	0.61	2.90
Clusters per var	1	15	7.41	9.00	1,045	MAX VALUE	243.14	4.03	0.54	2.45

Dual tree decomposition

Number of clusters: 139
Number of leaves: 69
Tree depth: 7
CIR: 0.51
Independent Cluster Pairs: 4,818
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-ext/DualTree1.json

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

Cluster constraints 74 1,629 304.18 188.00 42,281 MAX VALUE 767.55 246.37 0.81 3.72

Variables per cluster 15 324 53.32 27.00 7,411 MAX VALUE 516.21 52.45 0.98 3.28

Separator constraints 0 974 223.37 162.00 31,049 0 None 155.27 0.70 3.66

Separator variables 0 250 46.70 26.00 6,491 0 None 40.96 0.88 3.25

Clusters per variable 1 14 8.06 9.00 7,411 MAX VALUE 1,738.39 3.97 0.49 2.34

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	74	1,629	304.18	188.00	42,281	MAX VALUE	767.55	246.37	0.81	3.72
Variables per cluster	15	324	53.32	27.00	7,411	MAX VALUE	516.21	52.45	0.98	3.28
Separator constraints	0	974	223.37	162.00	31,049	0	None	155.27	0.70	3.66
Separator variables	0	250	46.70	26.00	6,491	0	None	40.96	0.88	3.25
Clusters per variable	1	14	8.06	9.00	7,411	MAX VALUE	1,738.39	3.97	0.49	2.34

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-18-141-43-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-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 65.04 0.00 -109.10 0.00 0.00 0.15

Degree 12 14 13.70 14.00 1,932 MAX VALUE 368.96 0.53 0.04 0.68

Eccentricity 3 4 3.03 3.00 427 MAX VALUE 156.06 0.17 0.05 0.13

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	65.04	0.00	-109.10	0.00	0.00	0.15
Degree	12	14	13.70	14.00	1,932	MAX VALUE	368.96	0.53	0.04	0.68
Eccentricity	3	4	3.03	3.00	427	MAX VALUE	156.06	0.17	0.05	0.13
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 45.42%
MCB compute time (ms): None
MCB cycles: None
Triangles: 87,394

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

Clustering coefficient 0.69 1.00 0.82 0.78 116.20 0.00 -28.24 0.10 0.12 3.37

Degree 12 100 63.59 76.00 8,966 MAX VALUE 560.36 30.64 0.48 2.88

Eccentricity 2 3 2.33 2.00 328 MAX VALUE 116.39 0.47 0.20 0.63

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	0.69	1.00	0.82	0.78	116.20	0.00	-28.24	0.10	0.12	3.37
Degree	12	100	63.59	76.00	8,966	MAX VALUE	560.36	30.64	0.48	2.88
Eccentricity	2	3	2.33	2.00	328	MAX VALUE	116.39	0.47	0.20	0.63
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 2.64%
MCB compute time (ms): 159,621
MCB cycles: 14,003
Triangles: 49,998
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-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 25.45 26.00 24,580 MAX VALUE 3,125.87 0.88 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 3.21 3.00 44,982 MAX VALUE 16,226.90 0.44 0.14 0.55

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	25.45	26.00	24,580	MAX VALUE	3,125.87	0.88	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	3.21	3.00	44,982	MAX VALUE	16,226.90	0.44	0.14	0.55

Minimal dual graph

Density: 0.38%
MCB compute time (ms): 20,400
MCB cycles: 832

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

Clustering coefficient 0.00 0.33 0.00 0.00 1.67 0.00 None 0.02 13.15 0.04

Degree 2 6 3.71 4.00 3,582 MAX VALUE 1,243.29 0.83 0.22 1.15

Eccentricity 8 12 9.91 10.00 9,573 MAX VALUE 2,213.26 0.68 0.07 1.03

MCB cycle size 3 11 6.70 7.00 5,575 MAX VALUE 1,557.06 1.60 0.24 1.83

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	1.67	0.00	None	0.02	13.15	0.04
Degree	2	6	3.71	4.00	3,582	MAX VALUE	1,243.29	0.83	0.22	1.15
Eccentricity	8	12	9.91	10.00	9,573	MAX VALUE	2,213.26	0.68	0.07	1.03
MCB cycle size	3	11	6.70	7.00	5,575	MAX VALUE	1,557.06	1.60	0.24	1.83

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: 6.41%

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

Clustering coefficient 0.49 1.00 0.83 0.80 797.04 0.00 -201.34 0.15 0.18 4.13

Degree 2 260 61.89 8.00 59,790 MAX VALUE 2,657.33 92.18 1.49 3.67

Eccentricity 3 6 4.72 5.00 4,557 MAX VALUE 1,491.56 0.56 0.12 0.83

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	1.00	0.83	0.80	797.04	0.00	-201.34	0.15	0.18	4.13
Degree	2	260	61.89	8.00	59,790	MAX VALUE	2,657.33	92.18	1.49	3.67
Eccentricity	3	6	4.72	5.00	4,557	MAX VALUE	1,491.56	0.56	0.12	0.83

Incidence graph

Density: 0.32%
MCB compute time (ms): 9,408
MCB cycles: 826
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-43-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 7.88 8.00 8,719 MAX VALUE 2,283.65 0.33 0.04 0.37

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