XCSP 2.1 Benchmark Database

Instance: normalized-bqwh-18-141-66-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: 7,330
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 24,402 MAX VALUE 8,360.18 1.10 0.33 1.50

Relational linkage 0.50 1.00 0.62 0.67 328.70 0.00 -264.02 0.09 0.15 1.00

Tightness 0.00 0.33 0.13 0.12 121.03 0.00 None 0.06 0.50 2.67

Tuples 3 32 12.63 12.00 12,201 MAX VALUE 2,354.14 5.56 0.44 2.95

Values 2 6 3.78 4.00 533 MAX VALUE 180.86 1.12 0.30 1.50

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 3.78 4.00 533 MAX VALUE 180.86 1.12 0.30 1.50

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	24,402	MAX VALUE	8,360.18	1.10	0.33	1.50
Relational linkage	0.50	1.00	0.62	0.67	328.70	0.00	-264.02	0.09	0.15	1.00
Tightness	0.00	0.33	0.13	0.12	121.03	0.00	None	0.06	0.50	2.67
Tuples	3	32	12.63	12.00	12,201	MAX VALUE	2,354.14	5.56	0.44	2.95
Values	2	6	3.78	4.00	533	MAX VALUE	180.86	1.12	0.30	1.50
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	3.78	4.00	533	MAX VALUE	180.86	1.12	0.30	1.50

Tree decomposition

Number of clusters: 56
Number of leaves: 22
Tree depth: 8
CIR: 0.20
Independent Cluster Pairs: 291
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-ext/Tree1.json

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

Cluster constraints 11 222 66.93 47.50 3,748 MAX VALUE 221.95 51.23 0.77 3.68

Variables per cluster 6 69 23.54 16.50 1,318 MAX VALUE 165.60 16.57 0.70 3.16

Separator constraints 0 168 51.11 36.00 2,862 0 None 42.37 0.83 3.55

Separator variables 0 60 21.02 15.00 1,177 0 None 14.92 0.71 3.16

Clusters per var 1 20 9.35 11.00 1,318 MAX VALUE 264.59 5.81 0.62 2.77

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	11	222	66.93	47.50	3,748	MAX VALUE	221.95	51.23	0.77	3.68
Variables per cluster	6	69	23.54	16.50	1,318	MAX VALUE	165.60	16.57	0.70	3.16
Separator constraints	0	168	51.11	36.00	2,862	0	None	42.37	0.83	3.55
Separator variables	0	60	21.02	15.00	1,177	0	None	14.92	0.71	3.16
Clusters per var	1	20	9.35	11.00	1,318	MAX VALUE	264.59	5.81	0.62	2.77

Dual tree decomposition

Number of clusters: 139
Number of leaves: 67
Tree depth: 7
CIR: 0.52
Independent Cluster Pairs: 4,915
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-ext/DualTree1.json

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

Cluster constraints 52 1,606 286.45 188.00 39,817 MAX VALUE 754.95 253.59 0.89 4.05

Variables per cluster 14 325 51.86 27.00 7,209 MAX VALUE 510.25 53.14 1.02 3.63

Separator constraints 0 954 211.25 162.00 29,364 0 None 164.72 0.78 4.07

Separator variables 0 249 45.49 26.00 6,323 0 None 41.73 0.92 3.57

Clusters per variable 1 14 8.14 9.00 7,209 MAX VALUE 1,675.50 4.05 0.50 2.41

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	52	1,606	286.45	188.00	39,817	MAX VALUE	754.95	253.59	0.89	4.05
Variables per cluster	14	325	51.86	27.00	7,209	MAX VALUE	510.25	53.14	1.02	3.63
Separator constraints	0	954	211.25	162.00	29,364	0	None	164.72	0.78	4.07
Separator variables	0	249	45.49	26.00	6,323	0	None	41.73	0.92	3.57
Clusters per variable	1	14	8.14	9.00	7,209	MAX VALUE	1,675.50	4.05	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-18-141-66-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-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: 47.93%
MCB compute time (ms): None
MCB cycles: None
Triangles: 99,506

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

Clustering coefficient 0.73 1.00 0.83 0.81 117.55 0.00 -26.39 0.09 0.10 3.27

Degree 12 100 67.11 79.00 9,462 MAX VALUE 567.16 32.00 0.48 2.80

Eccentricity 2 3 2.27 2.00 320 MAX VALUE 113.14 0.44 0.20 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	0.73	1.00	0.83	0.81	117.55	0.00	-26.39	0.09	0.10	3.27
Degree	12	100	67.11	79.00	9,462	MAX VALUE	567.16	32.00	0.48	2.80
Eccentricity	2	3	2.27	2.00	320	MAX VALUE	113.14	0.44	0.20	0.58
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 2.64%
MCB compute time (ms): 166,139
MCB cycles: 13,065
Triangles: 49,986
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-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 3.15 3.00 41,099 MAX VALUE 14,897.40 0.36 0.12 0.43

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	3.15	3.00	41,099	MAX VALUE	14,897.40	0.36	0.12	0.43

Minimal dual graph

Density: 0.38%
MCB compute time (ms): 18,528
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 1,243.19 0.83 0.22 1.15

Eccentricity 8 12 9.79 10.00 9,456 MAX VALUE 2,201.57 0.65 0.07 0.98

MCB cycle size 3 11 6.70 7.00 5,573 MAX VALUE 1,555.65 1.63 0.24 1.85

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	1,243.19	0.83	0.22	1.15
Eccentricity	8	12	9.79	10.00	9,456	MAX VALUE	2,201.57	0.65	0.07	0.98
MCB cycle size	3	11	6.70	7.00	5,573	MAX VALUE	1,555.65	1.63	0.24	1.85

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: 5.97%

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

Clustering coefficient 0.48 1.00 0.82 0.79 789.15 0.00 -211.25 0.15 0.18 4.14

Degree 2 257 57.60 8.00 55,638 MAX VALUE 2,628.08 86.76 1.51 3.68

Eccentricity 3 6 4.71 5.00 4,553 MAX VALUE 1,490.26 0.58 0.12 0.87

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	1.00	0.82	0.79	789.15	0.00	-211.25	0.15	0.18	4.14
Degree	2	257	57.60	8.00	55,638	MAX VALUE	2,628.08	86.76	1.51	3.68
Eccentricity	3	6	4.71	5.00	4,553	MAX VALUE	1,490.26	0.58	0.12	0.87

Incidence graph

Density: 0.32%
MCB compute time (ms): 10,118
MCB cycles: 826
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-66-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