XCSP 2.1 Benchmark Database

Instance: normalized-bqwh-18-141-42-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: 7,180
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 3.27 3.00 23,474 MAX VALUE 8,128.93 0.99 0.30 1.40

Relational linkage 0.50 0.80 0.62 0.67 325.55 0.00 -253.23 0.09 0.14 0.90

Tightness 0.00 0.50 0.12 0.12 117.36 0.00 None 0.06 0.50 2.66

Tuples 2 27 12.15 11.00 11,737 MAX VALUE 2,334.90 4.77 0.39 2.81

Values 2 6 3.71 4.00 523 MAX VALUE 179.44 0.99 0.27 1.37

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 3.71 4.00 523 MAX VALUE 179.44 0.99 0.27 1.37

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	3.27	3.00	23,474	MAX VALUE	8,128.93	0.99	0.30	1.40
Relational linkage	0.50	0.80	0.62	0.67	325.55	0.00	-253.23	0.09	0.14	0.90
Tightness	0.00	0.50	0.12	0.12	117.36	0.00	None	0.06	0.50	2.66
Tuples	2	27	12.15	11.00	11,737	MAX VALUE	2,334.90	4.77	0.39	2.81
Values	2	6	3.71	4.00	523	MAX VALUE	179.44	0.99	0.27	1.37
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	3.71	4.00	523	MAX VALUE	179.44	0.99	0.27	1.37

Tree decomposition

Number of clusters: 58
Number of leaves: 28
Tree depth: 7
CIR: 0.21
Independent Cluster Pairs: 329
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/Tree1.json

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

Cluster constraints 13 205 60.14 42.50 3,488 MAX VALUE 226.11 41.32 0.69 3.51

Variables per cluster 7 68 22.21 15.00 1,288 MAX VALUE 168.95 14.85 0.67 3.20

Separator constraints 0 130 45.07 30.00 2,614 0 None 33.02 0.73 3.58

Separator variables 0 53 19.78 13.50 1,147 0 None 13.13 0.66 3.15

Clusters per var 1 22 9.13 11.00 1,288 MAX VALUE 257.35 5.81 0.64 2.70

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	13	205	60.14	42.50	3,488	MAX VALUE	226.11	41.32	0.69	3.51
Variables per cluster	7	68	22.21	15.00	1,288	MAX VALUE	168.95	14.85	0.67	3.20
Separator constraints	0	130	45.07	30.00	2,614	0	None	33.02	0.73	3.58
Separator variables	0	53	19.78	13.50	1,147	0	None	13.13	0.66	3.15
Clusters per var	1	22	9.13	11.00	1,288	MAX VALUE	257.35	5.81	0.64	2.70

Dual tree decomposition

Number of clusters: 139
Number of leaves: 68
Tree depth: 7
CIR: 0.52
Independent Cluster Pairs: 4,942
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/DualTree1.json

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

Cluster constraints 63 1,581 280.44 188.00 38,981 MAX VALUE 752.56 246.47 0.88 4.09

Variables per cluster 15 333 51.42 29.00 7,147 MAX VALUE 509.00 52.79 1.03 3.67

Separator constraints 0 985 207.40 162.00 28,828 0 None 160.46 0.77 4.03

Separator variables 0 251 45.13 26.00 6,273 0 None 41.44 0.92 3.63

Clusters per variable 1 14 8.18 9.00 7,147 MAX VALUE 1,658.89 4.03 0.49 2.43

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	63	1,581	280.44	188.00	38,981	MAX VALUE	752.56	246.47	0.88	4.09
Variables per cluster	15	333	51.42	29.00	7,147	MAX VALUE	509.00	52.79	1.03	3.67
Separator constraints	0	985	207.40	162.00	28,828	0	None	160.46	0.77	4.03
Separator variables	0	251	45.13	26.00	6,273	0	None	41.44	0.92	3.63
Clusters per variable	1	14	8.18	9.00	7,147	MAX VALUE	1,658.89	4.03	0.49	2.43

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-18-141-42-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-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: 44.90%
MCB compute time (ms): None
MCB cycles: None
Triangles: 84,564

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

Clustering coefficient 0.68 1.00 0.82 0.81 115.80 0.00 -28.80 0.10 0.12 3.35

Degree 12 100 62.87 74.00 8,864 MAX VALUE 559.24 30.07 0.48 2.57

Eccentricity 2 3 2.41 2.00 340 MAX VALUE 121.25 0.49 0.20 0.68

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	0.81	115.80	0.00	-28.80	0.10	0.12	3.35
Degree	12	100	62.87	74.00	8,864	MAX VALUE	559.24	30.07	0.48	2.57
Eccentricity	2	3	2.41	2.00	340	MAX VALUE	121.25	0.49	0.20	0.68
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 2.64%
MCB compute time (ms): 177,970
MCB cycles: 13,426
Triangles: 49,986
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/Dual1.json

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

Clustering coefficient 0.50 0.50 0.50 0.50 481.68 0.00 -672.23 0.00 0.00 0.99

Degree 22 26 25.44 26.00 24,578 MAX VALUE 3,125.84 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 3.17 3.00 42,583 MAX VALUE 15,406.80 0.40 0.12 0.48

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	0.50	0.50	0.50	481.68	0.00	-672.23	0.00	0.00	0.99
Degree	22	26	25.44	26.00	24,578	MAX VALUE	3,125.84	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	3.17	3.00	42,583	MAX VALUE	15,406.80	0.40	0.12	0.48

Minimal dual graph

Density: 0.38%
MCB compute time (ms): 20,041
MCB cycles: 830

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

Clustering coefficient 0.00 0.33 0.00 0.00 1.20 0.00 None 0.02 14.10 0.04

Degree 2 6 3.71 4.00 3,582 MAX VALUE 1,244.03 0.82 0.22 1.12

Eccentricity 8 12 9.83 10.00 9,500 MAX VALUE 2,205.79 0.69 0.07 1.04

MCB cycle size 3 11 6.71 7.00 5,573 MAX VALUE 1,554.20 1.64 0.24 1.86

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	1.20	0.00	None	0.02	14.10	0.04
Degree	2	6	3.71	4.00	3,582	MAX VALUE	1,244.03	0.82	0.22	1.12
Eccentricity	8	12	9.83	10.00	9,500	MAX VALUE	2,205.79	0.69	0.07	1.04
MCB cycle size	3	11	6.71	7.00	5,573	MAX VALUE	1,554.20	1.64	0.24	1.86

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: 6.23%

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

Clustering coefficient 0.48 1.00 0.82 0.80 794.99 0.00 -203.78 0.15 0.18 4.12

Degree 2 255 60.10 8.00 58,058 MAX VALUE 2,649.56 90.08 1.50 3.58

Eccentricity 3 6 4.47 4.00 4,317 MAX VALUE 1,438.12 0.57 0.13 0.85

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	1.00	0.82	0.80	794.99	0.00	-203.78	0.15	0.18	4.12
Degree	2	255	60.10	8.00	58,058	MAX VALUE	2,649.56	90.08	1.50	3.58
Eccentricity	3	6	4.47	4.00	4,317	MAX VALUE	1,438.12	0.57	0.13	0.85

Incidence graph

Density: 0.32%
MCB compute time (ms): 9,961
MCB cycles: 826
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-42-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