XCSP 2.1 Benchmark Database

Instance: normalized-3-fullins-3-6-ext
Number of variables: 80
Number of constraints: 346
Satisfiable: True
Timestamp: 2025-07-20 22:08:24
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 80
Number of constraints: 346

General features

Coarse blocks: 4,152
Value tables: 80

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

Arity 2 2 2.00 2.00 692 MAX VALUE 239.83 0.00 0.00 0.00

Coarse blocks size 5 5 5.00 5.00 20,760 MAX VALUE 6,682.39 0.00 0.00 0.00

Relational linkage 0.83 0.83 0.83 0.83 400.00 0.00 -87.51 0.00 0.00 0.00

Tightness 0.17 0.17 0.17 0.17 57.67 0.00 -619.95 0.00 0.00 0.00

Tuples 30 30 30.00 30.00 10,380 MAX VALUE 1,176.81 0.00 0.00 0.00

Values 6 6 6.00 6.00 480 MAX VALUE 143.34 0.00 0.00 0.00

Value table constraints 4 19 8.65 7.00 692 MAX VALUE 165.13 3.99 0.46 1.88

Value table partitions 6 6 6.00 6.00 480 MAX VALUE 143.34 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	692	MAX VALUE	239.83	0.00	0.00	0.00
Coarse blocks size	5	5	5.00	5.00	20,760	MAX VALUE	6,682.39	0.00	0.00	0.00
Relational linkage	0.83	0.83	0.83	0.83	400.00	0.00	-87.51	0.00	0.00	0.00
Tightness	0.17	0.17	0.17	0.17	57.67	0.00	-619.95	0.00	0.00	0.00
Tuples	30	30	30.00	30.00	10,380	MAX VALUE	1,176.81	0.00	0.00	0.00
Values	6	6	6.00	6.00	480	MAX VALUE	143.34	0.00	0.00	0.00
Value table constraints	4	19	8.65	7.00	692	MAX VALUE	165.13	3.99	0.46	1.88
Value table partitions	6	6	6.00	6.00	480	MAX VALUE	143.34	0.00	0.00	0.00

Tree decomposition

Number of clusters: 50
Number of leaves: 29
Tree depth: 8
CIR: 0.40
Independent Cluster Pairs: 466
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/Tree1.json

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

Cluster constraints 4 50 16.06 9.00 803 MAX VALUE 122.83 13.55 0.84 2.60

Variables per cluster 5 26 11.36 8.50 568 MAX VALUE 114.84 6.20 0.55 2.48

Separator constraints 0 40 9.14 1.00 457 0 None 12.78 1.40 2.17

Separator variables 0 22 9.76 7.00 488 0 None 5.83 0.60 2.45

Clusters per var 1 23 7.10 6.50 568 MAX VALUE 109.30 6.32 0.89 2.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	50	16.06	9.00	803	MAX VALUE	122.83	13.55	0.84	2.60
Variables per cluster	5	26	11.36	8.50	568	MAX VALUE	114.84	6.20	0.55	2.48
Separator constraints	0	40	9.14	1.00	457	0	None	12.78	1.40	2.17
Separator variables	0	22	9.76	7.00	488	0	None	5.83	0.60	2.45
Clusters per var	1	23	7.10	6.50	568	MAX VALUE	109.30	6.32	0.89	2.26

Dual tree decomposition

Number of clusters: 78
Number of leaves: 29
Tree depth: 8
CIR: 0.50
Independent Cluster Pairs: 1,465
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/DualTree1.json

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

Cluster constraints 12 538 134.60 88.00 10,499 MAX VALUE 344.45 134.52 1.00 3.77

Variables per cluster 7 120 30.28 22.00 2,362 MAX VALUE 245.35 24.98 0.83 3.39

Separator constraints 0 335 92.51 56.50 7,216 0 None 86.84 0.94 3.77

Separator variables 0 87 25.85 20.50 2,016 0 None 19.13 0.74 3.33

Clusters per variable 1 15 6.83 7.00 2,362 MAX VALUE 602.22 3.27 0.48 2.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	12	538	134.60	88.00	10,499	MAX VALUE	344.45	134.52	1.00	3.77
Variables per cluster	7	120	30.28	22.00	2,362	MAX VALUE	245.35	24.98	0.83	3.39
Separator constraints	0	335	92.51	56.50	7,216	0	None	86.84	0.94	3.77
Separator variables	0	87	25.85	20.50	2,016	0	None	19.13	0.74	3.33
Clusters per variable	1	15	6.83	7.00	2,362	MAX VALUE	602.22	3.27	0.48	2.49

Primal graph

Density: 10.95%
MCB compute time (ms): 12
MCB cycles: 349
Triangles: 73
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/Primal1.json

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

Clustering coefficient 0.00 0.36 0.05 0.00 4.14 0.00 None 0.08 1.63 1.64

Degree 4 19 8.65 7.00 692 MAX VALUE 165.13 3.99 0.46 1.88

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.85 4.00 1,343 MAX VALUE 468.57 0.36 0.09 0.43

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.36	0.05	0.00	4.14	0.00	None	0.08	1.63	1.64
Degree	4	19	8.65	7.00	692	MAX VALUE	165.13	3.99	0.46	1.88
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.85	4.00	1,343	MAX VALUE	468.57	0.36	0.09	0.43

Triangulated primal graph

Density: 28.99%
MCB compute time (ms): 62
MCB cycles: 847
Triangles: 6,605

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

Clustering coefficient 0.42 1.00 0.82 0.78 65.22 0.00 -18.17 0.17 0.21 2.75

Degree 4 46 22.90 24.50 1,832 MAX VALUE 224.35 15.68 0.68 3.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 2,541 MAX VALUE 930.52 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.42	1.00	0.82	0.78	65.22	0.00	-18.17	0.17	0.21	2.75
Degree	4	46	22.90	24.50	1,832	MAX VALUE	224.35	15.68	0.68	3.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	2,541	MAX VALUE	930.52	0.00	0.00	0.00

Dual graph

Density: 5.50%
MCB compute time (ms): 633
MCB cycles: 4,821
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/Dual1.json

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

Clustering coefficient 0.40 0.75 0.52 0.50 180.22 0.00 -228.51 0.07 0.13 3.02

Degree 6 36 18.98 19.00 6,566 MAX VALUE 996.18 6.43 0.34 2.66

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.69 3.00 17,790 MAX VALUE 6,174.34 0.85 0.23 0.98

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	0.75	0.52	0.50	180.22	0.00	-228.51	0.07	0.13	3.02
Degree	6	36	18.98	19.00	6,566	MAX VALUE	996.18	6.43	0.34	2.66
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.69	3.00	17,790	MAX VALUE	6,174.34	0.85	0.23	0.98

Minimal dual graph

Density: 1.03%
MCB compute time (ms): 479
MCB cycles: 267

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 6 3.54 3.00 1,224 MAX VALUE 431.70 0.65 0.18 0.93

Eccentricity None None None None None None None None None None

MCB cycle size 4 11 7.05 7.00 1,882 MAX VALUE 514.93 1.48 0.21 1.67

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	6	3.54	3.00	1,224	MAX VALUE	431.70	0.65	0.18	0.93
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	11	7.05	7.00	1,882	MAX VALUE	514.93	1.48	0.21	1.67

Triangulated dual graph

Density: 32.85%
Triangles: 718,723

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

Clustering coefficient 0.61 1.00 0.81 0.82 280.42 0.00 -75.79 0.11 0.13 5.15

Degree 6 220 113.34 114.00 39,216 MAX VALUE 1,532.63 67.28 0.59 4.52

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	0.61	1.00	0.81	0.82	280.42	0.00	-75.79	0.11	0.13	5.15
Degree	6	220	113.34	114.00	39,216	MAX VALUE	1,532.63	67.28	0.59	4.52
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 7.56%

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

Clustering coefficient 0.46 1.00 0.79 0.76 274.11 0.00 -87.80 0.16 0.20 3.56

Degree 2 108 26.08 7.00 9,022 MAX VALUE 844.99 31.77 1.22 3.37

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	0.46	1.00	0.79	0.76	274.11	0.00	-87.80	0.16	0.20	3.56
Degree	2	108	26.08	7.00	9,022	MAX VALUE	844.99	31.77	1.22	3.37
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 0.76%
MCB compute time (ms): 195
MCB cycles: 267
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-full-insertionExtConvert/normalized-3-fullins-3-6-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 19 3.25 2.00 1,384 MAX VALUE 404.96 3.12 0.96 0.84

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 7.63 8.00 2,036 MAX VALUE 540.83 0.78 0.10 0.48

XCSP 2.1 Benchmarks