XCSP2 Benchmark Database

Instance: normalized-will199GPIA-7-ext
Number of variables: 701
Number of constraints: 6772
Satisfiable: True
Timestamp: 2025-07-27 21:35:01
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 701
Number of constraints: 6772

General features

Coarse blocks: 94,808
Value tables: 701

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

Arity 2 2 2.00 2.00 13,544 MAX VALUE 4,693.99 0.00 0.00 0.00

Coarse blocks size 6 6 6.00 6.00 568,848 MAX VALUE 169,873.00 0.00 0.00 0.00

Relational linkage 0.86 0.86 0.86 0.86 4,206.00 0.00 -756.42 0.00 0.00 0.00

Tightness 0.14 0.14 0.14 0.14 967.43 0.00 -13,177.70 0.00 0.00 0.00

Tuples 42 42 42.00 42.00 284,424 MAX VALUE 25,311.50 0.00 0.00 0.00

Values 7 7 7.00 7.00 4,907 MAX VALUE 1,364.08 0.00 0.00 0.00

Value table constraints 2 38 19.32 17.00 13,544 MAX VALUE 2,028.71 7.23 0.37 3.01

Value table partitions 7 7 7.00 7.00 4,907 MAX VALUE 1,364.08 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	13,544	MAX VALUE	4,693.99	0.00	0.00	0.00
Coarse blocks size	6	6	6.00	6.00	568,848	MAX VALUE	169,873.00	0.00	0.00	0.00
Relational linkage	0.86	0.86	0.86	0.86	4,206.00	0.00	-756.42	0.00	0.00	0.00
Tightness	0.14	0.14	0.14	0.14	967.43	0.00	-13,177.70	0.00	0.00	0.00
Tuples	42	42	42.00	42.00	284,424	MAX VALUE	25,311.50	0.00	0.00	0.00
Values	7	7	7.00	7.00	4,907	MAX VALUE	1,364.08	0.00	0.00	0.00
Value table constraints	2	38	19.32	17.00	13,544	MAX VALUE	2,028.71	7.23	0.37	3.01
Value table partitions	7	7	7.00	7.00	4,907	MAX VALUE	1,364.08	0.00	0.00	0.00

Tree decomposition

Number of clusters: 285
Number of leaves: 53
Tree depth: 20
CIR: 0.80
Independent Cluster Pairs: 32,205
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/Tree1.json

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

Cluster constraints 3 584 130.44 92.00 37,174 MAX VALUE 1,295.72 111.36 0.85 4.58

Variables per cluster 3 109 30.30 25.00 8,636 MAX VALUE 924.19 19.08 0.63 3.73

Separator constraints 0 485 106.67 77.00 30,402 0 None 91.70 0.86 4.50

Separator variables 0 83 27.84 24.00 7,935 0 None 16.41 0.59 3.72

Clusters per var 1 31 12.32 12.00 8,636 MAX VALUE 1,523.58 8.06 0.65 3.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	584	130.44	92.00	37,174	MAX VALUE	1,295.72	111.36	0.85	4.58
Variables per cluster	3	109	30.30	25.00	8,636	MAX VALUE	924.19	19.08	0.63	3.73
Separator constraints	0	485	106.67	77.00	30,402	0	None	91.70	0.86	4.50
Separator variables	0	83	27.84	24.00	7,935	0	None	16.41	0.59	3.72
Clusters per var	1	31	12.32	12.00	8,636	MAX VALUE	1,523.58	8.06	0.65	3.26

Dual tree decomposition

Number of clusters: 699
Number of leaves: 306
Tree depth: 19
CIR: 0.88
Independent Cluster Pairs: 213,637
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/DualTree1.json

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

Cluster constraints 65 9,023 908.41 500.00 634,980 MAX VALUE 4,397.82 1,171.94 1.29 5.67

Variables per cluster 13 760 88.23 53.00 61,676 MAX VALUE 2,870.32 103.02 1.17 4.69

Separator constraints 0 5,300 704.74 427.00 492,612 0 None 797.47 1.13 5.62

Separator variables 0 575 78.55 52.00 54,904 0 None 80.73 1.03 4.65

Clusters per variable 1 36 9.11 9.00 61,676 MAX VALUE 13,883.60 4.54 0.50 2.72

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	65	9,023	908.41	500.00	634,980	MAX VALUE	4,397.82	1,171.94	1.29	5.67
Variables per cluster	13	760	88.23	53.00	61,676	MAX VALUE	2,870.32	103.02	1.17	4.69
Separator constraints	0	5,300	704.74	427.00	492,612	0	None	797.47	1.13	5.62
Separator variables	0	575	78.55	52.00	54,904	0	None	80.73	1.03	4.65
Clusters per variable	1	36	9.11	9.00	61,676	MAX VALUE	13,883.60	4.54	0.50	2.72

Primal graph

Density: 2.76%
MCB compute time (ms): None
MCB cycles: None
Triangles: 10,539
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/Primal1.json

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

Clustering coefficient 0.11 1.00 0.26 0.25 180.91 0.00 -984.75 0.09 0.33 4.55

Degree 2 38 19.32 17.00 13,544 MAX VALUE 2,028.71 7.23 0.37 3.01

Eccentricity 6 9 7.16 7.00 5,020 MAX VALUE 1,377.12 0.65 0.09 0.99

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	0.11	1.00	0.26	0.25	180.91	0.00	-984.75	0.09	0.33	4.55
Degree	2	38	19.32	17.00	13,544	MAX VALUE	2,028.71	7.23	0.37	3.01
Eccentricity	6	9	7.16	7.00	5,020	MAX VALUE	1,377.12	0.65	0.09	0.99
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 13.66%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,042,310

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

Clustering coefficient 0.41 1.00 0.78 0.78 548.12 0.00 -185.69 0.14 0.18 5.81

Degree 2 284 95.62 81.00 67,032 MAX VALUE 2,939.41 71.97 0.75 5.01

Eccentricity 3 5 3.94 4.00 2,761 MAX VALUE 952.71 0.60 0.15 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	0.41	1.00	0.78	0.78	548.12	0.00	-185.69	0.14	0.18	5.81
Degree	2	284	95.62	81.00	67,032	MAX VALUE	2,939.41	71.97	0.75	5.01
Eccentricity	3	5	3.94	4.00	2,761	MAX VALUE	952.71	0.60	0.15	0.90
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 0.62%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,095,640
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/Dual1.json

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

Clustering coefficient 0.48 0.87 0.51 0.50 3,469.50 0.00 -4,536.71 0.03 0.05 6.24

Degree 12 74 42.05 41.00 284,736 MAX VALUE 24,972.60 13.09 0.31 3.85

Eccentricity 6 9 7.69 8.00 52,093 MAX VALUE 13,792.50 0.65 0.08 0.98

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	0.48	0.87	0.51	0.50	3,469.50	0.00	-4,536.71	0.03	0.05	6.24
Degree	12	74	42.05	41.00	284,736	MAX VALUE	24,972.60	13.09	0.31	3.85
Eccentricity	6	9	7.69	8.00	52,093	MAX VALUE	13,792.50	0.65	0.08	0.98
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Minimal dual graph

Density: 0.06%
MCB compute time (ms): None
MCB cycles: None

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

Clustering coefficient 0.00 1.00 0.01 0.00 63.50 0.00 None 0.07 7.81 0.14

Degree 2 7 3.79 4.00 25,686 MAX VALUE 8,866.90 0.85 0.22 1.20

Eccentricity 14 22 17.59 18.00 119,116 MAX VALUE 19,397.90 1.33 0.08 1.70

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	1.00	0.01	0.00	63.50	0.00	None	0.07	7.81	0.14
Degree	2	7	3.79	4.00	25,686	MAX VALUE	8,866.90	0.85	0.22	1.20
Eccentricity	14	22	17.59	18.00	119,116	MAX VALUE	19,397.90	1.33	0.08	1.70
MCB cycle size	None	None	None	None	None	None	None	None	None	None

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: 2.40%

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

Clustering coefficient 0.39 1.00 0.82 0.80 5,542.32 0.00 -1,482.55 0.15 0.19 4.95

Degree 2 1,471 162.76 8.00 1,102,230 MAX VALUE 20,656.40 291.37 1.79 4.35

Eccentricity 5 9 6.16 6.00 41,746 MAX VALUE 12,273.40 0.70 0.11 1.05

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.39	1.00	0.82	0.80	5,542.32	0.00	-1,482.55	0.15	0.19	4.95
Degree	2	1,471	162.76	8.00	1,102,230	MAX VALUE	20,656.40	291.37	1.79	4.35
Eccentricity	5	9	6.16	6.00	41,746	MAX VALUE	12,273.40	0.70	0.11	1.05

Incidence graph

Density: 0.05%
MCB compute time (ms): None
MCB cycles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-will199GPIA-7-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 38 3.62 2.00 27,088 MAX VALUE 6,722.70 5.51 1.52 0.59

Eccentricity 12 19 15.47 16.00 115,616 MAX VALUE 20,444.40 1.24 0.08 1.41

MCB cycle size None None None None None None None None None None

XCSP2 Benchmarks