XCSP 2.1 Benchmark Database

Instance: normalized-ash958GPIA-3-ext
Number of variables: 1916
Number of constraints: 12506
Satisfiable: True
Timestamp: 2025-07-27 21:35:01
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 1916
Number of constraints: 12506

General features

Coarse blocks: 75,033
Value tables: 1,915

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

Arity 2 2 2.00 2.00 25,012 MAX VALUE 8,668.50 0.00 0.00 0.00

Coarse blocks size 2 2 2.00 2.00 150,066 MAX VALUE 52,008.90 0.00 0.00 0.00

Relational linkage 0.67 0.67 0.67 0.67 3,830.00 0.00 -2,329.40 0.00 0.00 0.00

Tightness 0.33 0.33 0.33 0.33 4,168.67 0.00 -13,739.20 0.00 0.00 0.00

Tuples 6 6 6.00 6.00 75,036 MAX VALUE 22,407.70 0.00 0.00 0.00

Values 3 3 3.00 3.00 5,748 MAX VALUE 2,104.94 0.00 0.00 0.00

Value table constraints 6 24 13.06 13.00 25,011 MAX VALUE 4,875.29 2.80 0.21 2.42

Value table partitions 3 3 3.00 3.00 5,745 MAX VALUE 2,103.84 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	25,012	MAX VALUE	8,668.50	0.00	0.00	0.00
Coarse blocks size	2	2	2.00	2.00	150,066	MAX VALUE	52,008.90	0.00	0.00	0.00
Relational linkage	0.67	0.67	0.67	0.67	3,830.00	0.00	-2,329.40	0.00	0.00	0.00
Tightness	0.33	0.33	0.33	0.33	4,168.67	0.00	-13,739.20	0.00	0.00	0.00
Tuples	6	6	6.00	6.00	75,036	MAX VALUE	22,407.70	0.00	0.00	0.00
Values	3	3	3.00	3.00	5,748	MAX VALUE	2,104.94	0.00	0.00	0.00
Value table constraints	6	24	13.06	13.00	25,011	MAX VALUE	4,875.29	2.80	0.21	2.42
Value table partitions	3	3	3.00	3.00	5,745	MAX VALUE	2,103.84	0.00	0.00	0.00

Tree decomposition

Number of clusters: 913
Number of leaves: 487
Tree depth: 47
CIR: 0.92
Independent Cluster Pairs: 381,909
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Tree1.json

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

Cluster constraints 1 228 37.50 19.00 34,236 MAX VALUE 2,995.28 36.01 0.96 4.11

Variables per cluster 2 140 25.95 16.00 23,689 MAX VALUE 2,768.69 20.21 0.78 3.73

Separator constraints 0 162 23.80 4.00 21,730 0 None 31.79 1.34 3.45

Separator variables 0 103 23.85 15.00 21,773 0 None 17.73 0.74 3.69

Clusters per var 1 53 12.36 11.00 23,689 MAX VALUE 3,709.78 10.19 0.82 3.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	228	37.50	19.00	34,236	MAX VALUE	2,995.28	36.01	0.96	4.11
Variables per cluster	2	140	25.95	16.00	23,689	MAX VALUE	2,768.69	20.21	0.78	3.73
Separator constraints	0	162	23.80	4.00	21,730	0	None	31.79	1.34	3.45
Separator variables	0	103	23.85	15.00	21,773	0	None	17.73	0.74	3.69
Clusters per var	1	53	12.36	11.00	23,689	MAX VALUE	3,709.78	10.19	0.82	3.17

Dual tree decomposition

Number of clusters: 1,914
Number of leaves: 954
Tree depth: 36
CIR: 0.97
Independent Cluster Pairs: 1,770,340
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/DualTree1.json

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

Cluster constraints 15 3,030 335.01 211.00 641,203 MAX VALUE 10,508.90 330.63 0.99 4.95

Variables per cluster 6 484 57.41 34.00 109,879 MAX VALUE 7,138.69 62.69 1.09 4.13

Separator constraints 0 1,846 252.30 182.00 482,899 0 None 218.21 0.86 4.87

Separator variables 0 338 50.87 32.00 97,373 0 None 48.53 0.95 3.92

Clusters per variable 1 27 8.79 8.00 109,879 MAX VALUE 24,667.70 4.60 0.52 2.78

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	15	3,030	335.01	211.00	641,203	MAX VALUE	10,508.90	330.63	0.99	4.95
Variables per cluster	6	484	57.41	34.00	109,879	MAX VALUE	7,138.69	62.69	1.09	4.13
Separator constraints	0	1,846	252.30	182.00	482,899	0	None	218.21	0.86	4.87
Separator variables	0	338	50.87	32.00	97,373	0	None	48.53	0.95	3.92
Clusters per variable	1	27	8.79	8.00	109,879	MAX VALUE	24,667.70	4.60	0.52	2.78

Primal graph

Density: 0.68%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,728
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Primal1.json

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

Clustering coefficient None None None 0.03 None None None None None 3.50

Degree 1 24 13.05 13.00 25,012 MAX VALUE 4,875.29 2.81 0.22 2.43

Eccentricity 14 26 19.59 20.00 37,534 MAX VALUE 5,673.52 3.22 0.16 2.48

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	None	None	None	0.03	None	None	None	None	None	3.50
Degree	1	24	13.05	13.00	25,012	MAX VALUE	4,875.29	2.81	0.22	2.43
Eccentricity	14	26	19.59	20.00	37,534	MAX VALUE	5,673.52	3.22	0.16	2.48
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: None%
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 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

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

Dual graph

Density: 0.20%
MCB compute time (ms): None
MCB cycles: None
Triangles: 650,145
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Dual1.json

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

Clustering coefficient 0.44 1.00 0.48 0.48 6,054.32 0.00 -9,074.38 0.01 0.02 4.20

Degree 5 46 25.32 25.00 316,608 MAX VALUE 40,141.60 5.19 0.21 3.05

Eccentricity 14 27 20.10 20.00 251,366 MAX VALUE 37,356.80 3.27 0.16 2.47

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	0.44	1.00	0.48	0.48	6,054.32	0.00	-9,074.38	0.01	0.02	4.20
Degree	5	46	25.32	25.00	316,608	MAX VALUE	40,141.60	5.19	0.21	3.05
Eccentricity	14	27	20.10	20.00	251,366	MAX VALUE	37,356.80	3.27	0.16	2.47
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Minimal dual graph

Density: 0.03%
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 0.33 0.00 0.00 1.33 0.00 None 0.01 48.41 0.00

Degree 2 6 3.69 4.00 46,192 MAX VALUE 16,139.80 0.67 0.18 0.98

Eccentricity 25 50 37.67 38.00 471,145 MAX VALUE 45,231.60 5.80 0.15 3.06

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	0.33	0.00	0.00	1.33	0.00	None	0.01	48.41	0.00
Degree	2	6	3.69	4.00	46,192	MAX VALUE	16,139.80	0.67	0.18	0.98
Eccentricity	25	50	37.67	38.00	471,145	MAX VALUE	45,231.60	5.80	0.15	3.06
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: 0.89%

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

Clustering coefficient 0.34 1.00 0.81 0.80 10,148.50 0.00 -2,866.47 0.16 0.20 5.04

Degree 2 1,138 111.45 8.00 1,393,800 MAX VALUE 36,623.10 198.35 1.78 4.31

Eccentricity 6 12 8.56 9.00 107,063 MAX VALUE 26,786.30 0.89 0.10 1.29

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.34	1.00	0.81	0.80	10,148.50	0.00	-2,866.47	0.16	0.20	5.04
Degree	2	1,138	111.45	8.00	1,393,800	MAX VALUE	36,623.10	198.35	1.78	4.31
Eccentricity	6	12	8.56	9.00	107,063	MAX VALUE	26,786.30	0.89	0.10	1.29

Incidence graph

Density: 0.02%
MCB compute time (ms): None
MCB cycles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-hosExtConvert/normalized-ash958GPIA-3-ext/Incidence1.json

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

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

Degree 1 24 3.47 2.00 50,024 MAX VALUE 13,543.80 3.89 1.12 0.71

Eccentricity 28 54 40.23 40.00 580,208 MAX VALUE 53,091.10 6.50 0.16 2.91

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

XCSP 2.1 Benchmarks