XCSP 2.1 Benchmark Database

Instance: normalized-3-fullins-4-6-ext
Number of variables: 405
Number of constraints: 3524
Satisfiable: True
Timestamp: 2025-07-27 21:34:20
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 405
Number of constraints: 3524

General features

Coarse blocks: 42,288
Value tables: 405

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

Arity 2 2 2.00 2.00 7,048 MAX VALUE 2,442.65 0.00 0.00 0.00

Coarse blocks size 5 5 5.00 5.00 211,440 MAX VALUE 68,059.90 0.00 0.00 0.00

Relational linkage 0.83 0.83 0.83 0.83 2,025.00 0.00 -443.04 0.00 0.00 0.00

Tightness 0.17 0.17 0.17 0.17 587.33 0.00 -6,314.16 0.00 0.00 0.00

Tuples 30 30 30.00 30.00 105,720 MAX VALUE 11,985.80 0.00 0.00 0.00

Values 6 6 6.00 6.00 2,430 MAX VALUE 725.66 0.00 0.00 0.00

Value table constraints 6 84 17.40 15.00 7,048 MAX VALUE 1,104.73 10.85 0.62 2.63

Value table partitions 6 6 6.00 6.00 2,430 MAX VALUE 725.66 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	7,048	MAX VALUE	2,442.65	0.00	0.00	0.00
Coarse blocks size	5	5	5.00	5.00	211,440	MAX VALUE	68,059.90	0.00	0.00	0.00
Relational linkage	0.83	0.83	0.83	0.83	2,025.00	0.00	-443.04	0.00	0.00	0.00
Tightness	0.17	0.17	0.17	0.17	587.33	0.00	-6,314.16	0.00	0.00	0.00
Tuples	30	30	30.00	30.00	105,720	MAX VALUE	11,985.80	0.00	0.00	0.00
Values	6	6	6.00	6.00	2,430	MAX VALUE	725.66	0.00	0.00	0.00
Value table constraints	6	84	17.40	15.00	7,048	MAX VALUE	1,104.73	10.85	0.62	2.63
Value table partitions	6	6	6.00	6.00	2,430	MAX VALUE	725.66	0.00	0.00	0.00

Tree decomposition

Number of clusters: 240
Number of leaves: 174
Tree depth: 12
CIR: 0.47
Independent Cluster Pairs: 13,301
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/Tree1.json

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

Cluster constraints 7 330 33.50 15.00 8,041 MAX VALUE 719.79 46.06 1.37 3.39

Variables per cluster 7 119 22.78 15.50 5,468 MAX VALUE 688.51 20.35 0.89 3.18

Separator constraints 0 229 18.82 1.00 4,517 0 None 39.41 2.09 2.06

Separator variables 0 91 21.10 14.00 5,063 0 None 18.88 0.89 3.19

Clusters per var 1 113 13.50 5.00 5,468 MAX VALUE 648.49 15.89 1.18 2.65

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	330	33.50	15.00	8,041	MAX VALUE	719.79	46.06	1.37	3.39
Variables per cluster	7	119	22.78	15.50	5,468	MAX VALUE	688.51	20.35	0.89	3.18
Separator constraints	0	229	18.82	1.00	4,517	0	None	39.41	2.09	2.06
Separator variables	0	91	21.10	14.00	5,063	0	None	18.88	0.89	3.19
Clusters per var	1	113	13.50	5.00	5,468	MAX VALUE	648.49	15.89	1.18	2.65

Dual tree decomposition

Number of clusters: 403
Number of leaves: 162
Tree depth: 9
CIR: 0.71
Independent Cluster Pairs: 57,022
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/DualTree1.json

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

Cluster constraints 51 19,029 1,039.62 291.00 418,967 MAX VALUE 2,430.53 2,151.14 2.07 4.95

Variables per cluster 14 1,363 95.47 48.00 38,473 MAX VALUE 1,610.79 158.87 1.66 4.38

Separator constraints 0 11,634 837.08 259.00 337,342 0 None 1,522.47 1.82 5.01

Separator variables 0 1,026 86.72 46.00 34,949 0 None 128.53 1.48 4.40

Clusters per variable 1 19 10.92 12.00 38,473 MAX VALUE 7,895.77 4.32 0.40 2.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	51	19,029	1,039.62	291.00	418,967	MAX VALUE	2,430.53	2,151.14	2.07	4.95
Variables per cluster	14	1,363	95.47	48.00	38,473	MAX VALUE	1,610.79	158.87	1.66	4.38
Separator constraints	0	11,634	837.08	259.00	337,342	0	None	1,522.47	1.82	5.01
Separator variables	0	1,026	86.72	46.00	34,949	0	None	128.53	1.48	4.40
Clusters per variable	1	19	10.92	12.00	38,473	MAX VALUE	7,895.77	4.32	0.40	2.67

Primal graph

Density: 4.31%
MCB compute time (ms): None
MCB cycles: None
Triangles: 382
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/Primal1.json

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

Clustering coefficient 0.00 0.26 0.01 0.00 6.01 0.00 None 0.03 2.17 1.79

Degree 6 84 17.40 15.00 7,048 MAX VALUE 1,104.73 10.85 0.62 2.63

Eccentricity 2 4 3.68 4.00 1,490 MAX VALUE 523.93 0.47 0.13 0.64

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	0.26	0.01	0.00	6.01	0.00	None	0.03	2.17	1.79
Degree	6	84	17.40	15.00	7,048	MAX VALUE	1,104.73	10.85	0.62	2.63
Eccentricity	2	4	3.68	4.00	1,490	MAX VALUE	523.93	0.47	0.13	0.64
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 19.09%
MCB compute time (ms): None
MCB cycles: None
Triangles: 506,505

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

Clustering coefficient 0.34 1.00 0.86 0.89 346.42 0.00 -70.71 0.16 0.18 3.39

Degree 6 265 77.12 41.00 31,232 MAX VALUE 1,505.65 70.95 0.92 4.18

Eccentricity 2 3 2.70 3.00 1,093 MAX VALUE 395.47 0.46 0.17 0.61

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	0.34	1.00	0.86	0.89	346.42	0.00	-70.71	0.16	0.18	3.39
Degree	6	265	77.12	41.00	31,232	MAX VALUE	1,505.65	70.95	0.92	4.18
Eccentricity	2	3	2.70	3.00	1,093	MAX VALUE	395.47	0.46	0.17	0.61
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 1.31%
MCB compute time (ms): None
MCB cycles: None
Triangles: 963,203
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/Dual1.json

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

Clustering coefficient 0.46 0.89 0.56 0.52 1,971.22 0.00 -2,092.87 0.10 0.17 4.33

Degree 13 166 46.33 40.00 163,250 MAX VALUE 13,141.90 23.03 0.50 3.73

Eccentricity 3 5 4.06 4.00 14,292 MAX VALUE 4,923.55 0.32 0.08 0.39

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	0.46	0.89	0.56	0.52	1,971.22	0.00	-2,092.87	0.10	0.17	4.33
Degree	13	166	46.33	40.00	163,250	MAX VALUE	13,141.90	23.03	0.50	3.73
Eccentricity	3	5	4.06	4.00	14,292	MAX VALUE	4,923.55	0.32	0.08	0.39
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Minimal dual graph

Density: 0.11%
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 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 7 3.77 4.00 13,286 MAX VALUE 4,603.44 0.80 0.21 1.11

Eccentricity 10 14 12.24 12.00 43,140 MAX VALUE 8,820.06 0.77 0.06 1.16

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	0.00	0.00	0.00	0.00	0.00	None	0.00	None	0.00
Degree	2	7	3.77	4.00	13,286	MAX VALUE	4,603.44	0.80	0.21	1.11
Eccentricity	10	14	12.24	12.00	43,140	MAX VALUE	8,820.06	0.77	0.06	1.16
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: 5.60%

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

Clustering coefficient 0.50 1.00 0.85 0.82 2,978.23 0.00 -635.41 0.13 0.15 4.69

Degree 2 929 197.18 9.00 694,876 MAX VALUE 11,141.00 321.75 1.63 4.14

Eccentricity 3 6 4.18 4.00 14,722 MAX VALUE 4,998.93 0.61 0.15 0.92

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	1.00	0.85	0.82	2,978.23	0.00	-635.41	0.13	0.15	4.69
Degree	2	929	197.18	9.00	694,876	MAX VALUE	11,141.00	321.75	1.63	4.14
Eccentricity	3	6	4.18	4.00	14,722	MAX VALUE	4,998.93	0.61	0.15	0.92

Incidence graph

Density: 0.09%
MCB compute time (ms): None
MCB cycles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-4-6-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 84 3.59 2.00 14,096 MAX VALUE 3,547.38 5.84 1.63 0.60

Eccentricity 5 10 8.31 8.00 32,633 MAX VALUE 8,301.57 0.74 0.09 1.02

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

XCSP 2.1 Benchmarks