XCSP 2.1 Benchmark Database

Instance: normalized-4-insertions-4-3-ext
Number of variables: 475
Number of constraints: 1795
Satisfiable: True
Timestamp: 2025-07-27 21:34:49
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 475
Number of constraints: 1795

General features

Coarse blocks: 10,770
Value tables: 475

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

Arity 2 2 2.00 2.00 3,590 MAX VALUE 1,244.20 0.00 0.00 0.00

Coarse blocks size 2 2 2.00 2.00 21,540 MAX VALUE 7,465.20 0.00 0.00 0.00

Relational linkage 0.67 0.67 0.67 0.67 950.00 0.00 -577.79 0.00 0.00 0.00

Tightness 0.33 0.33 0.33 0.33 598.33 0.00 -1,972.01 0.00 0.00 0.00

Tuples 6 6 6.00 6.00 10,770 MAX VALUE 3,216.21 0.00 0.00 0.00

Values 3 3 3.00 3.00 1,425 MAX VALUE 521.84 0.00 0.00 0.00

Value table constraints 4 79 7.56 8.00 3,590 MAX VALUE 938.22 4.02 0.53 0.98

Value table partitions 3 3 3.00 3.00 1,425 MAX VALUE 521.84 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	3,590	MAX VALUE	1,244.20	0.00	0.00	0.00
Coarse blocks size	2	2	2.00	2.00	21,540	MAX VALUE	7,465.20	0.00	0.00	0.00
Relational linkage	0.67	0.67	0.67	0.67	950.00	0.00	-577.79	0.00	0.00	0.00
Tightness	0.33	0.33	0.33	0.33	598.33	0.00	-1,972.01	0.00	0.00	0.00
Tuples	6	6	6.00	6.00	10,770	MAX VALUE	3,216.21	0.00	0.00	0.00
Values	3	3	3.00	3.00	1,425	MAX VALUE	521.84	0.00	0.00	0.00
Value table constraints	4	79	7.56	8.00	3,590	MAX VALUE	938.22	4.02	0.53	0.98
Value table partitions	3	3	3.00	3.00	1,425	MAX VALUE	521.84	0.00	0.00	0.00

Tree decomposition

Number of clusters: 322
Number of leaves: 234
Tree depth: 10
CIR: 0.66
Independent Cluster Pairs: 33,763
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/Tree1.json

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

Cluster constraints 0 55 8.45 6.00 2,721 0 None 8.19 0.97 2.10

Variables per cluster 5 95 13.31 9.00 4,285 MAX VALUE 750.84 13.06 0.98 2.36

Separator constraints 0 39 2.88 0.00 926 0 None 7.46 2.60 0.82

Separator variables 0 77 11.83 8.00 3,810 0 None 11.51 0.97 2.36

Clusters per var 1 139 9.02 3.00 4,285 MAX VALUE 640.09 11.43 1.27 2.31

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	55	8.45	6.00	2,721	0	None	8.19	0.97	2.10
Variables per cluster	5	95	13.31	9.00	4,285	MAX VALUE	750.84	13.06	0.98	2.36
Separator constraints	0	39	2.88	0.00	926	0	None	7.46	2.60	0.82
Separator variables	0	77	11.83	8.00	3,810	0	None	11.51	0.97	2.36
Clusters per var	1	139	9.02	3.00	4,285	MAX VALUE	640.09	11.43	1.27	2.31

Dual tree decomposition

Number of clusters: 473
Number of leaves: 206
Tree depth: 9
CIR: 0.87
Independent Cluster Pairs: 96,503
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/DualTree1.json

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

Cluster constraints 25 3,387 113.29 56.00 53,588 MAX VALUE 2,024.54 249.48 2.20 3.69

Variables per cluster 10 416 32.70 18.00 15,465 MAX VALUE 1,480.71 44.20 1.35 3.41

Separator constraints 0 2,645 80.31 42.00 37,988 0 None 164.95 2.05 3.59

Separator variables 0 300 28.90 17.00 13,670 0 None 35.39 1.22 3.29

Clusters per variable 1 18 8.62 9.00 15,465 MAX VALUE 3,360.15 5.13 0.59 2.79

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	3,387	113.29	56.00	53,588	MAX VALUE	2,024.54	249.48	2.20	3.69
Variables per cluster	10	416	32.70	18.00	15,465	MAX VALUE	1,480.71	44.20	1.35	3.41
Separator constraints	0	2,645	80.31	42.00	37,988	0	None	164.95	2.05	3.59
Separator variables	0	300	28.90	17.00	13,670	0	None	35.39	1.22	3.29
Clusters per variable	1	18	8.62	9.00	15,465	MAX VALUE	3,360.15	5.13	0.59	2.79

Primal graph

Density: 1.59%
MCB compute time (ms): None
MCB cycles: None
Triangles: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/Primal1.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 4 79 7.56 8.00 3,590 MAX VALUE 938.22 4.02 0.53 0.98

Eccentricity 6 6 6.00 6.00 2,850 MAX VALUE 851.09 0.00 0.00 0.00

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	4	79	7.56	8.00	3,590	MAX VALUE	938.22	4.02	0.53	0.98
Eccentricity	6	6	6.00	6.00	2,850	MAX VALUE	851.09	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 10.55%
MCB compute time (ms): None
MCB cycles: None
Triangles: 295,532

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

Clustering coefficient 0.23 1.00 0.84 0.88 399.82 0.00 -92.06 0.17 0.20 3.29

Degree 4 287 50.00 12.00 23,752 MAX VALUE 1,465.44 57.31 1.15 3.57

Eccentricity 2 4 3.23 3.00 1,536 MAX VALUE 552.83 0.46 0.14 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	0.23	1.00	0.84	0.88	399.82	0.00	-92.06	0.17	0.20	3.29
Degree	4	287	50.00	12.00	23,752	MAX VALUE	1,465.44	57.31	1.15	3.57
Eccentricity	2	4	3.23	3.00	1,536	MAX VALUE	552.83	0.46	0.14	0.64
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 0.97%
MCB compute time (ms): 195,897
MCB cycles: 20,306
Triangles: 112,645
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/Dual1.json

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

Clustering coefficient 0.44 0.93 0.51 0.46 909.19 0.00 -1,252.29 0.11 0.22 1.38

Degree 9 91 17.38 14.00 31,200 MAX VALUE 4,865.41 14.57 0.84 1.38

Eccentricity 7 7 7.00 7.00 12,565 MAX VALUE 3,492.91 0.00 0.00 0.00

MCB cycle size 3 13 3.64 3.00 73,891 MAX VALUE 25,673.20 0.94 0.26 0.93

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.93	0.51	0.46	909.19	0.00	-1,252.29	0.11	0.22	1.38
Degree	9	91	17.38	14.00	31,200	MAX VALUE	4,865.41	14.57	0.84	1.38
Eccentricity	7	7	7.00	7.00	12,565	MAX VALUE	3,492.91	0.00	0.00	0.00
MCB cycle size	3	13	3.64	3.00	73,891	MAX VALUE	25,673.20	0.94	0.26	0.93

Minimal dual graph

Density: 0.19%
MCB compute time (ms): 137,079
MCB cycles: 1,321

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 5 3.47 3.00 6,230 MAX VALUE 2,205.73 0.63 0.18 0.91

Eccentricity 11 15 12.92 13.00 23,193 MAX VALUE 4,591.36 0.57 0.04 0.86

MCB cycle size 4 16 7.40 8.00 9,775 MAX VALUE 2,616.78 1.51 0.20 1.70

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	5	3.47	3.00	6,230	MAX VALUE	2,205.73	0.63	0.18	0.91
Eccentricity	11	15	12.92	13.00	23,193	MAX VALUE	4,591.36	0.57	0.04	0.86
MCB cycle size	4	16	7.40	8.00	9,775	MAX VALUE	2,616.78	1.51	0.20	1.70

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: 4.21%

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

Clustering coefficient 0.47 1.00 0.82 0.80 1,465.36 0.00 -393.65 0.15 0.18 4.16

Degree 2 414 75.59 7.00 135,690 MAX VALUE 4,893.65 124.93 1.65 3.78

Eccentricity 3 6 4.58 5.00 8,227 MAX VALUE 2,717.70 0.58 0.13 0.87

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.82	0.80	1,465.36	0.00	-393.65	0.15	0.18	4.16
Degree	2	414	75.59	7.00	135,690	MAX VALUE	4,893.65	124.93	1.65	3.78
Eccentricity	3	6	4.58	5.00	8,227	MAX VALUE	2,717.70	0.58	0.13	0.87

Incidence graph

Density: 0.14%
MCB compute time (ms): 116,615
MCB cycles: 1,321
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-4-3-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 79 3.16 2.00 7,180 MAX VALUE 2,182.42 2.91 0.92 0.72

Eccentricity 13 14 13.79 14.00 31,305 MAX VALUE 5,955.46 0.41 0.03 0.51

MCB cycle size 8 26 8.01 8.00 10,586 MAX VALUE 2,748.12 0.50 0.06 0.01

XCSP 2.1 Benchmarks