XCSP 2.1 Benchmark Database

Instance: normalized-1-fullins-4-4-ext
Number of variables: 93
Number of constraints: 593
Satisfiable: True
Timestamp: 2025-07-27 21:34:20
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 93
Number of constraints: 593

General features

Coarse blocks: 4,744
Value tables: 93

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

Arity 2 2 2.00 2.00 1,186 MAX VALUE 411.04 0.00 0.00 0.00

Coarse blocks size 3 3 3.00 3.00 14,232 MAX VALUE 5,211.82 0.00 0.00 0.00

Relational linkage 0.75 0.75 0.75 0.75 279.00 0.00 -107.02 0.00 0.00 0.00

Tightness 0.25 0.25 0.25 0.25 148.25 0.00 -822.07 0.00 0.00 0.00

Tuples 12 12 12.00 12.00 7,116 MAX VALUE 1,473.55 0.00 0.00 0.00

Values 4 4 4.00 4.00 372 MAX VALUE 128.93 0.00 0.00 0.00

Value table constraints 6 32 12.75 11.00 1,186 MAX VALUE 229.43 5.52 0.43 2.71

Value table partitions 4 4 4.00 4.00 372 MAX VALUE 128.93 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	1,186	MAX VALUE	411.04	0.00	0.00	0.00
Coarse blocks size	3	3	3.00	3.00	14,232	MAX VALUE	5,211.82	0.00	0.00	0.00
Relational linkage	0.75	0.75	0.75	0.75	279.00	0.00	-107.02	0.00	0.00	0.00
Tightness	0.25	0.25	0.25	0.25	148.25	0.00	-822.07	0.00	0.00	0.00
Tuples	12	12	12.00	12.00	7,116	MAX VALUE	1,473.55	0.00	0.00	0.00
Values	4	4	4.00	4.00	372	MAX VALUE	128.93	0.00	0.00	0.00
Value table constraints	6	32	12.75	11.00	1,186	MAX VALUE	229.43	5.52	0.43	2.71
Value table partitions	4	4	4.00	4.00	372	MAX VALUE	128.93	0.00	0.00	0.00

Tree decomposition

Number of clusters: 54
Number of leaves: 37
Tree depth: 6
CIR: 0.14
Independent Cluster Pairs: 195
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/Tree1.json

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

Cluster constraints 7 77 20.39 11.50 1,101 MAX VALUE 145.41 20.22 0.99 2.77

Variables per cluster 7 34 13.57 11.00 733 MAX VALUE 135.04 7.10 0.52 2.52

Separator constraints 0 70 9.41 1.00 508 0 None 18.34 1.95 1.59

Separator variables 0 28 11.85 10.00 640 0 None 6.49 0.55 2.56

Clusters per var 1 37 7.88 4.00 733 MAX VALUE 122.63 8.39 1.07 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	77	20.39	11.50	1,101	MAX VALUE	145.41	20.22	0.99	2.77
Variables per cluster	7	34	13.57	11.00	733	MAX VALUE	135.04	7.10	0.52	2.52
Separator constraints	0	70	9.41	1.00	508	0	None	18.34	1.95	1.59
Separator variables	0	28	11.85	10.00	640	0	None	6.49	0.55	2.56
Clusters per var	1	37	7.88	4.00	733	MAX VALUE	122.63	8.39	1.07	2.21

Dual tree decomposition

Number of clusters: 91
Number of leaves: 41
Tree depth: 6
CIR: 0.37
Independent Cluster Pairs: 1,476
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/DualTree1.json

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

Cluster constraints 51 1,802 353.62 201.00 32,179 MAX VALUE 494.12 370.26 1.05 4.02

Variables per cluster 14 257 52.04 32.00 4,736 MAX VALUE 332.23 49.29 0.95 3.68

Separator constraints 0 947 261.44 174.00 23,791 0 None 233.84 0.89 4.06

Separator variables 0 187 45.53 30.00 4,143 0 None 38.13 0.84 3.69

Clusters per variable 1 13 7.99 9.00 4,736 MAX VALUE 1,142.59 3.26 0.41 2.38

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	51	1,802	353.62	201.00	32,179	MAX VALUE	494.12	370.26	1.05	4.02
Variables per cluster	14	257	52.04	32.00	4,736	MAX VALUE	332.23	49.29	0.95	3.68
Separator constraints	0	947	261.44	174.00	23,791	0	None	233.84	0.89	4.06
Separator variables	0	187	45.53	30.00	4,143	0	None	38.13	0.84	3.69
Clusters per variable	1	13	7.99	9.00	4,736	MAX VALUE	1,142.59	3.26	0.41	2.38

Primal graph

Density: 13.86%
MCB compute time (ms): None
MCB cycles: None
Triangles: 119
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/Primal1.json

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

Clustering coefficient 0.00 0.23 0.04 0.03 3.63 0.00 None 0.04 1.08 2.99

Degree 6 32 12.75 11.00 1,186 MAX VALUE 229.43 5.52 0.43 2.71

Eccentricity 2 3 2.99 3.00 278 MAX VALUE 101.77 0.10 0.03 0.06

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	0.23	0.04	0.03	3.63	0.00	None	0.04	1.08	2.99
Degree	6	32	12.75	11.00	1,186	MAX VALUE	229.43	5.52	0.43	2.71
Eccentricity	2	3	2.99	3.00	278	MAX VALUE	101.77	0.10	0.03	0.06
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 31.81%
MCB compute time (ms): None
MCB cycles: None
Triangles: 12,653

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

Clustering coefficient 0.38 1.00 0.84 0.89 77.99 0.00 -18.77 0.18 0.21 2.61

Degree 6 73 29.27 27.00 2,722 MAX VALUE 284.57 20.51 0.70 3.37

Eccentricity 2 3 2.49 2.00 232 1.25e+36 83.11 0.50 0.20 0.69

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	0.38	1.00	0.84	0.89	77.99	0.00	-18.77	0.18	0.21	2.61
Degree	6	73	29.27	27.00	2,722	MAX VALUE	284.57	20.51	0.70	3.37
Eccentricity	2	3	2.49	2.00	232	1.25e+36	83.11	0.50	0.20	0.69
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 4.78%
MCB compute time (ms): 9,907
MCB cycles: 13,846
Triangles: 45,826
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/Dual1.json

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

Clustering coefficient 0.46 0.76 0.54 0.51 318.97 0.00 -371.96 0.07 0.13 4.54

Degree 13 62 28.29 27.00 16,776 MAX VALUE 1,959.04 8.00 0.28 3.33

Eccentricity 3 4 3.49 3.00 2,072 MAX VALUE 735.77 0.50 0.14 0.69

MCB cycle size 3 5 3.69 3.00 51,083 MAX VALUE 17,756.70 0.81 0.22 1.01

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.76	0.54	0.51	318.97	0.00	-371.96	0.07	0.13	4.54
Degree	13	62	28.29	27.00	16,776	MAX VALUE	1,959.04	8.00	0.28	3.33
Eccentricity	3	4	3.49	3.00	2,072	MAX VALUE	735.77	0.50	0.14	0.69
MCB cycle size	3	5	3.69	3.00	51,083	MAX VALUE	17,756.70	0.81	0.22	1.01

Minimal dual graph

Density: 0.62%
MCB compute time (ms): 4,992
MCB cycles: 501

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 7 3.69 3.00 2,186 MAX VALUE 759.29 0.85 0.23 1.12

Eccentricity 7 11 9.21 9.00 5,459 MAX VALUE 1,314.37 0.75 0.08 1.13

MCB cycle size 4 12 6.83 7.00 3,423 MAX VALUE 949.83 1.51 0.22 1.76

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	7	3.69	3.00	2,186	MAX VALUE	759.29	0.85	0.23	1.12
Eccentricity	7	11	9.21	9.00	5,459	MAX VALUE	1,314.37	0.75	0.08	1.13
MCB cycle size	4	12	6.83	7.00	3,423	MAX VALUE	949.83	1.51	0.22	1.76

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: 7.64%

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

Clustering coefficient 0.51 1.00 0.82 0.79 486.20 0.00 -127.09 0.14 0.18 3.81

Degree 2 180 45.25 9.00 26,832 MAX VALUE 1,577.23 62.05 1.37 3.50

Eccentricity 3 6 4.36 4.00 2,586 MAX VALUE 867.45 0.60 0.14 0.91

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.51	1.00	0.82	0.79	486.20	0.00	-127.09	0.14	0.18	3.81
Degree	2	180	45.25	9.00	26,832	MAX VALUE	1,577.23	62.05	1.37	3.50
Eccentricity	3	6	4.36	4.00	2,586	MAX VALUE	867.45	0.60	0.14	0.91

Incidence graph

Density: 0.50%
MCB compute time (ms): 2,186
MCB cycles: 501
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-1-fullins-4-4-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 32 3.46 2.00 2,372 MAX VALUE 640.47 4.21 1.22 0.76

Eccentricity 5 8 7.30 7.00 5,011 MAX VALUE 1,361.04 0.68 0.09 0.99

MCB cycle size 6 8 7.54 8.00 3,778 MAX VALUE 1,008.72 0.84 0.11 0.54

XCSP 2.1 Benchmarks