XCSP 2.1 Benchmark Database

Instance: normalized-ii-8b1-ext
Number of variables: 672
Number of constraints: 2398
Satisfiable: True
Timestamp: 2025-07-27 21:34:21
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 672
Number of constraints: 2398

General features

Coarse blocks: 29,832
Value tables: 876

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

Arity 2 8 2.20 2.00 5,280 MAX VALUE 1,780.97 1.02 0.46 0.19

Coarse blocks size 1 128 8.35 2.00 249,228 MAX VALUE 36,954.30 21.44 2.57 1.71

Relational linkage 0.50 1.00 0.95 1.00 10,424.20 0.00 -743.81 0.15 0.15 0.56

Tightness 0.00 0.25 0.24 0.25 576.84 0.00 -3,659.82 0.05 0.19 0.19

Tuples 3 255 9.68 3.00 23,202 MAX VALUE 2,996.16 38.02 3.93 0.19

Values 2 2 2.00 2.00 1,344 MAX VALUE 465.80 0.00 0.00 0.00

Value table constraints 2 34 6.51 2.00 5,700 MAX VALUE 1,284.72 6.47 0.99 1.54

Value table partitions 2 128 12.52 2.00 10,968 MAX VALUE 1,206.08 25.59 2.04 0.94

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	8	2.20	2.00	5,280	MAX VALUE	1,780.97	1.02	0.46	0.19
Coarse blocks size	1	128	8.35	2.00	249,228	MAX VALUE	36,954.30	21.44	2.57	1.71
Relational linkage	0.50	1.00	0.95	1.00	10,424.20	0.00	-743.81	0.15	0.15	0.56
Tightness	0.00	0.25	0.24	0.25	576.84	0.00	-3,659.82	0.05	0.19	0.19
Tuples	3	255	9.68	3.00	23,202	MAX VALUE	2,996.16	38.02	3.93	0.19
Values	2	2	2.00	2.00	1,344	MAX VALUE	465.80	0.00	0.00	0.00
Value table constraints	2	34	6.51	2.00	5,700	MAX VALUE	1,284.72	6.47	0.99	1.54
Value table partitions	2	128	12.52	2.00	10,968	MAX VALUE	1,206.08	25.59	2.04	0.94

Tree decomposition

Number of clusters: 544
Number of leaves: 64
Tree depth: 37
CIR: 0.78
Independent Cluster Pairs: 114,381
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Tree1.json

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

Cluster constraints 0 215 11.48 3.00 6,245 0 None 32.65 2.84 2.00

Variables per cluster 2 108 19.91 13.00 10,833 MAX VALUE 1,412.93 21.99 1.10 2.19

Separator constraints 0 199 7.07 0.00 3,847 0 None 28.17 3.98 1.15

Separator variables 0 100 18.68 12.00 10,161 0 None 21.61 1.16 2.19

Clusters per var 1 164 16.12 7.00 10,833 MAX VALUE 1,343.39 25.77 1.60 3.22

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	215	11.48	3.00	6,245	0	None	32.65	2.84	2.00
Variables per cluster	2	108	19.91	13.00	10,833	MAX VALUE	1,412.93	21.99	1.10	2.19
Separator constraints	0	199	7.07	0.00	3,847	0	None	28.17	3.98	1.15
Separator variables	0	100	18.68	12.00	10,161	0	None	21.61	1.16	2.19
Clusters per var	1	164	16.12	7.00	10,833	MAX VALUE	1,343.39	25.77	1.60	3.22

Dual tree decomposition

Number of clusters: 630
Number of leaves: 264
Tree depth: 13
CIR: 0.82
Independent Cluster Pairs: 161,432
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/DualTree1.json

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

Cluster constraints 36 1,558 236.36 174.00 148,907 MAX VALUE 3,052.23 278.70 1.18 3.29

Variables per cluster 10 213 35.47 27.00 22,349 MAX VALUE 2,004.65 37.90 1.07 2.79

Separator constraints 0 888 184.06 141.00 115,961 0 None 191.66 1.04 3.29

Separator variables 0 160 31.67 26.00 19,951 0 None 30.38 0.96 2.80

Clusters per variable 1 58 9.32 10.00 22,349 MAX VALUE 4,721.51 6.01 0.65 2.62

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	36	1,558	236.36	174.00	148,907	MAX VALUE	3,052.23	278.70	1.18	3.29
Variables per cluster	10	213	35.47	27.00	22,349	MAX VALUE	2,004.65	37.90	1.07	2.79
Separator constraints	0	888	184.06	141.00	115,961	0	None	191.66	1.04	3.29
Separator variables	0	160	31.67	26.00	19,951	0	None	30.38	0.96	2.80
Clusters per variable	1	58	9.32	10.00	22,349	MAX VALUE	4,721.51	6.01	0.65	2.62

Primal graph

Density: 1.50%
MCB compute time (ms): None
MCB cycles: None
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Primal1.json

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

Clustering coefficient 0.00 0.77 None 0.33 None None None None None 1.38

Degree 1 34 10.09 9.00 6,780 MAX VALUE 1,463.51 5.72 0.57 1.77

Eccentricity 5 8 6.12 6.00 4,116 MAX VALUE 1,209.28 1.00 0.16 1.28

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	0.00	0.77	None	0.33	None	None	None	None	None	1.38
Degree	1	34	10.09	9.00	6,780	MAX VALUE	1,463.51	5.72	0.57	1.77
Eccentricity	5	8	6.12	6.00	4,116	MAX VALUE	1,209.28	1.00	0.16	1.28
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 7.59%
MCB compute time (ms): None
MCB cycles: None
Triangles: None

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

Clustering coefficient 0.32 1.00 None 0.78 None None None None None 4.21

Degree 1 277 50.94 21.00 34,230 MAX VALUE 2,155.56 63.32 1.24 3.91

Eccentricity 3 5 3.65 4.00 2,454 MAX VALUE 861.04 0.61 0.17 0.90

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	0.32	1.00	None	0.78	None	None	None	None	None	4.21
Degree	1	277	50.94	21.00	34,230	MAX VALUE	2,155.56	63.32	1.24	3.91
Eccentricity	3	5	3.65	4.00	2,454	MAX VALUE	861.04	0.61	0.17	0.90
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 1.15%
MCB compute time (ms): 2,990,460
MCB cycles: 38,691
Triangles: 195,666
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Dual1.json

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

Clustering coefficient 0.00 1.00 0.61 0.60 1,453.30 0.00 None 0.11 0.18 2.41

Degree 6 42 27.48 28.00 65,892 MAX VALUE 7,761.30 8.69 0.32 2.28

Eccentricity 5 8 6.01 6.00 14,402 MAX VALUE 4,290.98 0.50 0.08 0.65

MCB cycle size 3 10 3.30 3.00 127,854 MAX VALUE 45,701.70 0.67 0.20 0.65

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	0.61	0.60	1,453.30	0.00	None	0.11	0.18	2.41
Degree	6	42	27.48	28.00	65,892	MAX VALUE	7,761.30	8.69	0.32	2.28
Eccentricity	5	8	6.01	6.00	14,402	MAX VALUE	4,290.98	0.50	0.08	0.65
MCB cycle size	3	10	3.30	3.00	127,854	MAX VALUE	45,701.70	0.67	0.20	0.65

Minimal dual graph

Density: 0.15%
MCB compute time (ms): 217,338
MCB cycles: 1,953

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

Clustering coefficient 0.00 0.33 0.00 0.00 5.20 0.00 None 0.02 11.31 0.06

Degree 2 6 3.63 4.00 8,700 MAX VALUE 3,052.39 0.65 0.18 0.89

Eccentricity 10 16 13.54 14.00 32,465 MAX VALUE 6,238.52 1.20 0.09 1.59

MCB cycle size 3 10 6.89 7.00 13,452 MAX VALUE 3,692.65 1.87 0.27 1.95

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	5.20	0.00	None	0.02	11.31	0.06
Degree	2	6	3.63	4.00	8,700	MAX VALUE	3,052.39	0.65	0.18	0.89
Eccentricity	10	16	13.54	14.00	32,465	MAX VALUE	6,238.52	1.20	0.09	1.59
MCB cycle size	3	10	6.89	7.00	13,452	MAX VALUE	3,692.65	1.87	0.27	1.95

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: 1.62%

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

Clustering coefficient 0.22 1.00 0.79 0.73 1,896.37 0.00 -631.42 0.18 0.23 4.20

Degree 2 502 38.88 7.00 93,224 MAX VALUE 6,165.10 64.56 1.66 3.76

Eccentricity 4 6 4.96 5.00 11,896 MAX VALUE 3,823.27 0.59 0.12 0.89

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.22	1.00	0.79	0.73	1,896.37	0.00	-631.42	0.18	0.23	4.20
Degree	2	502	38.88	7.00	93,224	MAX VALUE	6,165.10	64.56	1.66	3.76
Eccentricity	4	6	4.96	5.00	11,896	MAX VALUE	3,823.27	0.59	0.12	0.89

Incidence graph

Density: 0.11%
MCB compute time (ms): 116,404
MCB cycles: 2,211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/pseudo-iiExtConvert/normalized-ii-8b1-ext/Incidence1.json

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

Clustering coefficient 0.00 0.00 None 0.00 None None None None None 0.40

Degree 1 34 3.44 2.00 10,560 MAX VALUE 2,915.98 4.06 1.18 0.80

Eccentricity 10 16 12.79 13.00 39,256 MAX VALUE 7,807.97 1.28 0.10 1.31

MCB cycle size 4 20 8.63 8.00 19,080 MAX VALUE 4,596.49 3.83 0.44 0.89

XCSP 2.1 Benchmarks