XCSP 2.1 Benchmark Database

Instance: normalized-bqwh-18-141-34-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: 7,240
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 3.29 3.00 23,848 MAX VALUE 8,258.52 0.97 0.30 1.39

Relational linkage 0.50 1.00 0.64 0.67 332.02 0.00 -240.27 0.09 0.14 1.02

Tightness 0.00 0.50 0.13 0.12 120.92 0.00 None 0.06 0.49 2.58

Tuples 1 31 12.34 12.00 11,924 MAX VALUE 2,347.60 4.76 0.39 2.83

Values 1 6 3.74 4.00 528 MAX VALUE 180.65 0.98 0.26 1.39

Value table constraints 12 14 13.70 14.00 1,932 MAX VALUE 368.99 0.47 0.03 0.64

Value table partitions 1 6 3.74 4.00 528 MAX VALUE 180.65 0.98 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	3.29	3.00	23,848	MAX VALUE	8,258.52	0.97	0.30	1.39
Relational linkage	0.50	1.00	0.64	0.67	332.02	0.00	-240.27	0.09	0.14	1.02
Tightness	0.00	0.50	0.13	0.12	120.92	0.00	None	0.06	0.49	2.58
Tuples	1	31	12.34	12.00	11,924	MAX VALUE	2,347.60	4.76	0.39	2.83
Values	1	6	3.74	4.00	528	MAX VALUE	180.65	0.98	0.26	1.39
Value table constraints	12	14	13.70	14.00	1,932	MAX VALUE	368.99	0.47	0.03	0.64
Value table partitions	1	6	3.74	4.00	528	MAX VALUE	180.65	0.98	0.26	1.39

Tree decomposition

Number of clusters: 55
Number of leaves: 25
Tree depth: 7
CIR: 0.21
Independent Cluster Pairs: 300
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-ext/Tree1.json

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

Cluster constraints 16 226 62.75 47.00 3,451 MAX VALUE 216.39 45.09 0.72 3.53

Variables per cluster 8 70 22.42 17.00 1,233 MAX VALUE 161.05 15.02 0.67 3.08

Separator constraints 0 156 46.69 35.00 2,568 0 None 34.74 0.74 3.50

Separator variables 0 59 19.85 14.00 1,092 0 None 13.03 0.66 3.05

Clusters per var 1 19 8.74 10.00 1,233 MAX VALUE 256.99 5.18 0.59 2.62

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	226	62.75	47.00	3,451	MAX VALUE	216.39	45.09	0.72	3.53
Variables per cluster	8	70	22.42	17.00	1,233	MAX VALUE	161.05	15.02	0.67	3.08
Separator constraints	0	156	46.69	35.00	2,568	0	None	34.74	0.74	3.50
Separator variables	0	59	19.85	14.00	1,092	0	None	13.03	0.66	3.05
Clusters per var	1	19	8.74	10.00	1,233	MAX VALUE	256.99	5.18	0.59	2.62

Dual tree decomposition

Number of clusters: 139
Number of leaves: 69
Tree depth: 7
CIR: 0.51
Independent Cluster Pairs: 4,817
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-ext/DualTree1.json

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

Cluster constraints 60 1,454 274.62 188.00 38,172 MAX VALUE 753.47 221.21 0.81 4.01

Variables per cluster 15 316 50.78 27.00 7,058 MAX VALUE 509.38 50.47 0.99 3.58

Separator constraints 0 854 200.27 162.00 27,838 0 None 141.87 0.71 3.95

Separator variables 0 238 44.42 26.00 6,175 0 None 39.50 0.89 3.54

Clusters per variable 1 14 7.99 9.00 7,058 MAX VALUE 1,655.08 4.02 0.50 2.38

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	60	1,454	274.62	188.00	38,172	MAX VALUE	753.47	221.21	0.81	4.01
Variables per cluster	15	316	50.78	27.00	7,058	MAX VALUE	509.38	50.47	0.99	3.58
Separator constraints	0	854	200.27	162.00	27,838	0	None	141.87	0.71	3.95
Separator variables	0	238	44.42	26.00	6,175	0	None	39.50	0.89	3.54
Clusters per variable	1	14	7.99	9.00	7,058	MAX VALUE	1,655.08	4.02	0.50	2.38

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-18-141-34-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-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 65.07 0.00 -109.03 0.00 0.00 0.04

Degree 12 14 13.70 14.00 1,932 MAX VALUE 368.99 0.47 0.03 0.64

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	65.07	0.00	-109.03	0.00	0.00	0.04
Degree	12	14	13.70	14.00	1,932	MAX VALUE	368.99	0.47	0.03	0.64
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: 45.38%
MCB compute time (ms): None
MCB cycles: None
Triangles: 85,162

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

Clustering coefficient 0.68 1.00 0.82 0.83 115.77 0.00 -28.91 0.10 0.13 3.76

Degree 12 98 63.53 64.00 8,958 MAX VALUE 562.18 29.44 0.46 3.16

Eccentricity 2 3 2.26 2.00 319 MAX VALUE 112.74 0.44 0.19 0.58

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	0.68	1.00	0.82	0.83	115.77	0.00	-28.91	0.10	0.13	3.76
Degree	12	98	63.53	64.00	8,958	MAX VALUE	562.18	29.44	0.46	3.16
Eccentricity	2	3	2.26	2.00	319	MAX VALUE	112.74	0.44	0.19	0.58
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 2.64%
MCB compute time (ms): 27,466
MCB cycles: 19,158
Triangles: 49,950
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-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 0.97

Degree 23 26 25.44 26.00 24,572 MAX VALUE 3,125.71 0.77 0.03 0.98

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

MCB cycle size 3 6 3.48 3.00 66,749 MAX VALUE 23,629.10 0.62 0.18 0.87

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	0.97
Degree	23	26	25.44	26.00	24,572	MAX VALUE	3,125.71	0.77	0.03	0.98
Eccentricity	4	4	4.00	4.00	3,864	MAX VALUE	1,339.16	0.00	0.00	0.00
MCB cycle size	3	6	3.48	3.00	66,749	MAX VALUE	23,629.10	0.62	0.18	0.87

Minimal dual graph

Density: 0.38%
MCB compute time (ms): 20,322
MCB cycles: 832

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 7 3.71 4.00 3,582 MAX VALUE 1,244.34 0.81 0.22 1.13

Eccentricity 8 12 9.91 10.00 9,574 MAX VALUE 2,213.16 0.71 0.07 1.08

MCB cycle size 3 12 6.72 7.00 5,589 MAX VALUE 1,557.55 1.66 0.25 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	7	3.71	4.00	3,582	MAX VALUE	1,244.34	0.81	0.22	1.13
Eccentricity	8	12	9.91	10.00	9,574	MAX VALUE	2,213.16	0.71	0.07	1.08
MCB cycle size	3	12	6.72	7.00	5,589	MAX VALUE	1,557.55	1.66	0.25	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: 6.51%

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

Clustering coefficient 0.45 1.00 0.83 0.80 797.19 0.00 -200.59 0.14 0.17 4.10

Degree 2 270 62.82 8.00 60,686 MAX VALUE 2,670.16 93.16 1.48 3.73

Eccentricity 3 6 4.24 4.00 4,097 MAX VALUE 1,385.81 0.60 0.14 0.91

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	1.00	0.83	0.80	797.19	0.00	-200.59	0.14	0.17	4.10
Degree	2	270	62.82	8.00	60,686	MAX VALUE	2,670.16	93.16	1.48	3.73
Eccentricity	3	6	4.24	4.00	4,097	MAX VALUE	1,385.81	0.60	0.14	0.91

Incidence graph

Density: 0.32%
MCB compute time (ms): 8,947
MCB cycles: 826
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-34-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 1,038.57 3.90 1.12 0.46

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