XCSP 2.1 Benchmark Database

Instance: normalized-bqwh-18-141-69-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: 6,899
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 3.13 3.00 21,612 MAX VALUE 7,496.47 0.97 0.31 1.39

Relational linkage 0.50 0.80 0.62 0.67 309.60 0.00 -244.99 0.09 0.14 0.93

Tightness 0.00 0.33 0.12 0.12 114.63 0.00 None 0.07 0.55 2.54

Tuples 2 27 11.19 11.00 10,806 MAX VALUE 2,256.94 4.30 0.38 2.76

Values 1 6 3.57 4.00 503 MAX VALUE 173.55 0.98 0.27 1.39

Value table constraints 12 14 13.70 14.00 1,932 MAX VALUE 368.98 0.50 0.04 0.66

Value table partitions 1 6 3.57 4.00 503 MAX VALUE 173.55 0.98 0.27 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	3.13	3.00	21,612	MAX VALUE	7,496.47	0.97	0.31	1.39
Relational linkage	0.50	0.80	0.62	0.67	309.60	0.00	-244.99	0.09	0.14	0.93
Tightness	0.00	0.33	0.12	0.12	114.63	0.00	None	0.07	0.55	2.54
Tuples	2	27	11.19	11.00	10,806	MAX VALUE	2,256.94	4.30	0.38	2.76
Values	1	6	3.57	4.00	503	MAX VALUE	173.55	0.98	0.27	1.39
Value table constraints	12	14	13.70	14.00	1,932	MAX VALUE	368.98	0.50	0.04	0.66
Value table partitions	1	6	3.57	4.00	503	MAX VALUE	173.55	0.98	0.27	1.39

Tree decomposition

Number of clusters: 56
Number of leaves: 26
Tree depth: 6
CIR: 0.24
Independent Cluster Pairs: 359
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-ext/Tree1.json

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

Cluster constraints 4 232 56.62 41.50 3,171 MAX VALUE 212.56 44.72 0.79 3.72

Variables per cluster 4 72 21.11 15.50 1,182 MAX VALUE 159.84 14.82 0.70 3.13

Separator constraints 0 149 41.48 29.50 2,323 0 None 33.57 0.81 3.74

Separator variables 0 57 18.59 14.00 1,041 0 None 12.67 0.68 3.13

Clusters per var 1 18 8.38 10.00 1,182 MAX VALUE 250.63 5.07 0.60 2.59

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	232	56.62	41.50	3,171	MAX VALUE	212.56	44.72	0.79	3.72
Variables per cluster	4	72	21.11	15.50	1,182	MAX VALUE	159.84	14.82	0.70	3.13
Separator constraints	0	149	41.48	29.50	2,323	0	None	33.57	0.81	3.74
Separator variables	0	57	18.59	14.00	1,041	0	None	12.67	0.68	3.13
Clusters per var	1	18	8.38	10.00	1,182	MAX VALUE	250.63	5.07	0.60	2.59

Dual tree decomposition

Number of clusters: 139
Number of leaves: 67
Tree depth: 7
CIR: 0.52
Independent Cluster Pairs: 4,953
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-ext/DualTree1.json

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

Cluster constraints 68 1,400 256.71 188.00 35,683 MAX VALUE 742.65 210.54 0.82 4.17

Variables per cluster 14 307 48.88 29.00 6,795 MAX VALUE 503.52 48.62 0.99 3.67

Separator constraints 0 804 187.86 144.00 26,113 0 None 135.93 0.72 4.23

Separator variables 0 227 42.78 26.00 5,947 0 None 38.05 0.89 3.69

Clusters per variable 1 14 8.01 9.00 6,795 MAX VALUE 1,589.13 4.03 0.50 2.44

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	68	1,400	256.71	188.00	35,683	MAX VALUE	742.65	210.54	0.82	4.17
Variables per cluster	14	307	48.88	29.00	6,795	MAX VALUE	503.52	48.62	0.99	3.67
Separator constraints	0	804	187.86	144.00	26,113	0	None	135.93	0.72	4.23
Separator variables	0	227	42.78	26.00	5,947	0	None	38.05	0.89	3.69
Clusters per variable	1	14	8.01	9.00	6,795	MAX VALUE	1,589.13	4.03	0.50	2.44

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-18-141-69-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-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 65.06 0.00 -109.07 0.00 0.00 0.10

Degree 12 14 13.70 14.00 1,932 MAX VALUE 368.98 0.50 0.04 0.66

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	65.06	0.00	-109.07	0.00	0.00	0.10
Degree	12	14	13.70	14.00	1,932	MAX VALUE	368.98	0.50	0.04	0.66
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: 45.74%
MCB compute time (ms): None
MCB cycles: None
Triangles: 88,242

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

Clustering coefficient 0.68 1.00 0.82 0.80 116.21 0.00 -28.24 0.10 0.12 3.56

Degree 12 102 64.04 75.00 9,030 MAX VALUE 561.75 30.47 0.48 3.17

Eccentricity 2 3 2.28 2.00 321 MAX VALUE 113.55 0.45 0.20 0.59

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	0.80	116.21	0.00	-28.24	0.10	0.12	3.56
Degree	12	102	64.04	75.00	9,030	MAX VALUE	561.75	30.47	0.48	3.17
Eccentricity	2	3	2.28	2.00	321	MAX VALUE	113.55	0.45	0.20	0.59
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 2.64%
MCB compute time (ms): 206,111
MCB cycles: 12,911
Triangles: 49,974
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-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 24,576 MAX VALUE 3,125.80 0.83 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 6 3.14 3.00 40,490 MAX VALUE 14,685.50 0.36 0.11 0.41

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	24,576	MAX VALUE	3,125.80	0.83	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	6	3.14	3.00	40,490	MAX VALUE	14,685.50	0.36	0.11	0.41

Minimal dual graph

Density: 0.38%
MCB compute time (ms): 20,015
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 0.83 0.00 None 0.02 18.62 0.02

Degree 2 6 3.71 4.00 3,582 MAX VALUE 1,243.25 0.83 0.22 1.15

Eccentricity 8 12 9.88 10.00 9,543 MAX VALUE 2,210.43 0.65 0.07 0.98

MCB cycle size 3 11 6.68 7.00 5,542 MAX VALUE 1,548.18 1.67 0.25 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	0.83	0.00	None	0.02	18.62	0.02
Degree	2	6	3.71	4.00	3,582	MAX VALUE	1,243.25	0.83	0.22	1.15
Eccentricity	8	12	9.88	10.00	9,543	MAX VALUE	2,210.43	0.65	0.07	0.98
MCB cycle size	3	11	6.68	7.00	5,542	MAX VALUE	1,548.18	1.67	0.25	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: 6.00%

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

Clustering coefficient 0.49 1.00 0.82 0.79 790.42 0.00 -209.85 0.15 0.18 4.08

Degree 2 250 57.89 8.00 55,926 MAX VALUE 2,631.62 86.92 1.50 3.70

Eccentricity 3 6 4.10 4.00 3,963 MAX VALUE 1,352.98 0.60 0.15 0.91

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	1.00	0.82	0.79	790.42	0.00	-209.85	0.15	0.18	4.08
Degree	2	250	57.89	8.00	55,926	MAX VALUE	2,631.62	86.92	1.50	3.70
Eccentricity	3	6	4.10	4.00	3,963	MAX VALUE	1,352.98	0.60	0.15	0.91

Incidence graph

Density: 0.32%
MCB compute time (ms): 8,384
MCB cycles: 826
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/bqwh-18-141/normalized-bqwh-18-141-69-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 1,038.56 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