XCSP 2.1 Benchmark Database

Instance: normalized-bqwh-18-141-50-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: 7,329
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 3.33 3.00 24,416 MAX VALUE 8,426.25 1.00 0.30 1.41

Relational linkage 0.50 0.80 0.63 0.67 335.83 0.00 -247.63 0.09 0.14 1.04

Tightness 0.00 0.33 0.12 0.12 118.27 0.00 None 0.06 0.49 2.68

Tuples 2 27 12.64 13.00 12,208 MAX VALUE 2,369.28 4.86 0.38 2.86

Values 1 6 3.79 4.00 534 MAX VALUE 181.93 1.01 0.27 1.42

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 3.79 4.00 534 MAX VALUE 181.93 1.01 0.27 1.42

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	3.33	3.00	24,416	MAX VALUE	8,426.25	1.00	0.30	1.41
Relational linkage	0.50	0.80	0.63	0.67	335.83	0.00	-247.63	0.09	0.14	1.04
Tightness	0.00	0.33	0.12	0.12	118.27	0.00	None	0.06	0.49	2.68
Tuples	2	27	12.64	13.00	12,208	MAX VALUE	2,369.28	4.86	0.38	2.86
Values	1	6	3.79	4.00	534	MAX VALUE	181.93	1.01	0.27	1.42
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	3.79	4.00	534	MAX VALUE	181.93	1.01	0.27	1.42

Tree decomposition

Number of clusters: 56
Number of leaves: 25
Tree depth: 7
CIR: 0.20
Independent Cluster Pairs: 297
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-ext/Tree1.json

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

Cluster constraints 6 214 64.21 49.00 3,596 MAX VALUE 221.49 43.89 0.68 3.58

Variables per cluster 5 68 22.61 16.50 1,266 MAX VALUE 164.33 14.88 0.66 3.08

Separator constraints 0 146 48.38 36.00 2,709 0 None 34.78 0.72 3.54

Separator variables 0 55 20.09 14.00 1,125 0 None 13.05 0.65 3.08

Clusters per var 1 20 8.98 11.00 1,266 MAX VALUE 259.50 5.42 0.60 2.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	214	64.21	49.00	3,596	MAX VALUE	221.49	43.89	0.68	3.58
Variables per cluster	5	68	22.61	16.50	1,266	MAX VALUE	164.33	14.88	0.66	3.08
Separator constraints	0	146	48.38	36.00	2,709	0	None	34.78	0.72	3.54
Separator variables	0	55	20.09	14.00	1,125	0	None	13.05	0.65	3.08
Clusters per var	1	20	8.98	11.00	1,266	MAX VALUE	259.50	5.42	0.60	2.66

Dual tree decomposition

Number of clusters: 139
Number of leaves: 69
Tree depth: 7
CIR: 0.51
Independent Cluster Pairs: 4,861
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-ext/DualTree1.json

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

Cluster constraints 62 1,483 285.49 188.00 39,683 MAX VALUE 756.56 234.50 0.82 4.00

Variables per cluster 14 313 51.52 27.00 7,161 MAX VALUE 510.60 50.71 0.98 3.56

Separator constraints 0 832 210.12 162.00 29,206 0 None 150.59 0.72 4.00

Separator variables 0 217 45.14 26.00 6,274 0 None 39.60 0.88 3.55

Clusters per variable 1 15 8.07 9.00 7,161 MAX VALUE 1,674.36 3.99 0.49 2.42

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	62	1,483	285.49	188.00	39,683	MAX VALUE	756.56	234.50	0.82	4.00
Variables per cluster	14	313	51.52	27.00	7,161	MAX VALUE	510.60	50.71	0.98	3.56
Separator constraints	0	832	210.12	162.00	29,206	0	None	150.59	0.72	4.00
Separator variables	0	217	45.14	26.00	6,274	0	None	39.60	0.88	3.55
Clusters per variable	1	15	8.07	9.00	7,161	MAX VALUE	1,674.36	3.99	0.49	2.42

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-18-141-50-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-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: 45.26%
MCB compute time (ms): None
MCB cycles: None
Triangles: 85,994

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

Clustering coefficient 0.69 1.00 0.82 0.83 116.00 0.00 -28.55 0.10 0.12 3.56

Degree 12 98 63.36 63.00 8,934 MAX VALUE 560.35 30.21 0.48 2.90

Eccentricity 2 3 2.32 2.00 327 MAX VALUE 115.98 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	0.83	116.00	0.00	-28.55	0.10	0.12	3.56
Degree	12	98	63.36	63.00	8,934	MAX VALUE	560.35	30.21	0.48	2.90
Eccentricity	2	3	2.32	2.00	327	MAX VALUE	115.98	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): 108,131
MCB cycles: 14,152
Triangles: 49,998
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-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 0.99

Degree 22 26 25.45 26.00 24,580 MAX VALUE 3,125.87 0.89 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 3.22 3.00 45,510 MAX VALUE 16,418.30 0.43 0.13 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	-672.25	0.00	0.00	0.99
Degree	22	26	25.45	26.00	24,580	MAX VALUE	3,125.87	0.89	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	3.22	3.00	45,510	MAX VALUE	16,418.30	0.43	0.13	0.55

Minimal dual graph

Density: 0.38%
MCB compute time (ms): 20,010
MCB cycles: 831

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 7 3.71 4.00 3,582 MAX VALUE 1,244.34 0.81 0.22 1.14

Eccentricity 8 12 9.90 10.00 9,560 MAX VALUE 2,211.64 0.72 0.07 1.10

MCB cycle size 3 11 6.72 7.00 5,583 MAX VALUE 1,558.04 1.59 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	0.83	0.00	None	0.02	18.62	0.02
Degree	2	7	3.71	4.00	3,582	MAX VALUE	1,244.34	0.81	0.22	1.14
Eccentricity	8	12	9.90	10.00	9,560	MAX VALUE	2,211.64	0.72	0.07	1.10
MCB cycle size	3	11	6.72	7.00	5,583	MAX VALUE	1,558.04	1.59	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: 6.43%

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

Clustering coefficient 0.51 1.00 0.83 0.80 799.05 0.00 -198.61 0.14 0.17 4.12

Degree 2 257 62.01 8.00 59,898 MAX VALUE 2,655.17 92.76 1.50 3.66

Eccentricity 3 6 4.51 5.00 4,355 MAX VALUE 1,446.52 0.58 0.13 0.86

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.51	1.00	0.83	0.80	799.05	0.00	-198.61	0.14	0.17	4.12
Degree	2	257	62.01	8.00	59,898	MAX VALUE	2,655.17	92.76	1.50	3.66
Eccentricity	3	6	4.51	5.00	4,355	MAX VALUE	1,446.52	0.58	0.13	0.86

Incidence graph

Density: 0.32%
MCB compute time (ms): 10,356
MCB cycles: 826
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-50-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