XCSP 2.1 Benchmark Database

Instance: normalized-4-insertions-3-3-ext
Number of variables: 79
Number of constraints: 156
Satisfiable: True
Timestamp: 2025-07-20 22:08:24
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 79
Number of constraints: 156

General features

Coarse blocks: 936
Value tables: 79

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

Arity 2 2 2.00 2.00 312 MAX VALUE 108.13 0.00 0.00 0.00

Coarse blocks size 2 2 2.00 2.00 1,872 MAX VALUE 648.79 0.00 0.00 0.00

Relational linkage 0.67 0.67 0.67 0.67 158.00 0.00 -96.10 0.00 0.00 0.00

Tightness 0.33 0.33 0.33 0.33 52.00 0.00 -171.38 0.00 0.00 0.00

Tuples 6 6 6.00 6.00 936 MAX VALUE 279.51 0.00 0.00 0.00

Values 3 3 3.00 3.00 237 4.93e+37 86.79 0.00 0.00 0.00

Value table constraints 3 13 3.95 4.00 312 MAX VALUE 106.96 1.09 0.28 0.51

Value table partitions 3 3 3.00 3.00 237 4.93e+37 86.79 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	312	MAX VALUE	108.13	0.00	0.00	0.00
Coarse blocks size	2	2	2.00	2.00	1,872	MAX VALUE	648.79	0.00	0.00	0.00
Relational linkage	0.67	0.67	0.67	0.67	158.00	0.00	-96.10	0.00	0.00	0.00
Tightness	0.33	0.33	0.33	0.33	52.00	0.00	-171.38	0.00	0.00	0.00
Tuples	6	6	6.00	6.00	936	MAX VALUE	279.51	0.00	0.00	0.00
Values	3	3	3.00	3.00	237	4.93e+37	86.79	0.00	0.00	0.00
Value table constraints	3	13	3.95	4.00	312	MAX VALUE	106.96	1.09	0.28	0.51
Value table partitions	3	3	3.00	3.00	237	4.93e+37	86.79	0.00	0.00	0.00

Tree decomposition

Number of clusters: 61
Number of leaves: 39
Tree depth: 6
CIR: 0.53
Independent Cluster Pairs: 937
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/Tree1.json

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

Cluster constraints 0 5 2.87 4.00 175 0 None 1.54 0.54 1.25

Variables per cluster 4 16 6.48 5.00 395 MAX VALUE 109.05 2.91 0.45 1.70

Separator constraints 0 3 0.31 0.00 19 0 None 0.76 2.43 0.47

Separator variables 0 13 5.18 4.00 316 0 None 2.60 0.50 1.70

Clusters per var 1 32 5.00 3.00 395 9.84e+35 82.88 5.26 1.05 1.90

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	5	2.87	4.00	175	0	None	1.54	0.54	1.25
Variables per cluster	4	16	6.48	5.00	395	MAX VALUE	109.05	2.91	0.45	1.70
Separator constraints	0	3	0.31	0.00	19	0	None	0.76	2.43	0.47
Separator variables	0	13	5.18	4.00	316	0	None	2.60	0.50	1.70
Clusters per var	1	32	5.00	3.00	395	9.84e+35	82.88	5.26	1.05	1.90

Dual tree decomposition

Number of clusters: 77
Number of leaves: 35
Tree depth: 6
CIR: 0.71
Independent Cluster Pairs: 2,037
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/DualTree1.json

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

Cluster constraints 8 85 12.62 12.00 972 MAX VALUE 187.71 9.68 0.77 1.62

Variables per cluster 6 31 10.30 8.00 793 MAX VALUE 171.54 5.65 0.55 2.19

Separator constraints 0 41 6.04 6.00 465 0 None 5.09 0.84 1.45

Separator variables 0 23 8.27 7.00 637 0 None 4.25 0.51 2.11

Clusters per variable 1 12 5.08 4.00 793 MAX VALUE 206.35 3.43 0.67 2.27

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	8	85	12.62	12.00	972	MAX VALUE	187.71	9.68	0.77	1.62
Variables per cluster	6	31	10.30	8.00	793	MAX VALUE	171.54	5.65	0.55	2.19
Separator constraints	0	41	6.04	6.00	465	0	None	5.09	0.84	1.45
Separator variables	0	23	8.27	7.00	637	0	None	4.25	0.51	2.11
Clusters per variable	1	12	5.08	4.00	793	MAX VALUE	206.35	3.43	0.67	2.27

Primal graph

Density: 5.06%
MCB compute time (ms): 6
MCB cycles: 78
Triangles: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-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 3 13 3.95 4.00 312 MAX VALUE 106.96 1.09 0.28 0.51

Eccentricity None None None None None None None None None None

MCB cycle size 4 13 4.12 4.00 321 MAX VALUE 109.31 1.01 0.25 0.07

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	3	13	3.95	4.00	312	MAX VALUE	106.96	1.09	0.28	0.51
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	13	4.12	4.00	321	MAX VALUE	109.31	1.01	0.25	0.07

Triangulated primal graph

Density: 15.38%
MCB compute time (ms): 9
MCB cycles: 414
Triangles: 1,649

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

Clustering coefficient 0.26 1.00 0.78 0.75 61.77 0.00 -23.10 0.22 0.29 2.28

Degree 3 49 12.00 9.00 948 MAX VALUE 166.71 10.23 0.85 2.43

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,242 MAX VALUE 454.82 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.26	1.00	0.78	0.75	61.77	0.00	-23.10	0.22	0.29	2.28
Degree	3	49	12.00	9.00	948	MAX VALUE	166.71	10.23	0.85	2.43
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,242	MAX VALUE	454.82	0.00	0.00	0.00

Dual graph

Density: 4.19%
MCB compute time (ms): 44
MCB cycles: 403
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/Dual1.json

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

Clustering coefficient 0.40 0.74 0.43 0.40 66.77 0.00 -135.01 0.09 0.22 0.29

Degree 5 14 6.50 6.00 1,014 MAX VALUE 285.79 2.29 0.35 0.72

Eccentricity None None None None None None None None None None

MCB cycle size 3 13 3.47 3.00 1,397 MAX VALUE 492.19 0.85 0.24 0.85

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	0.74	0.43	0.40	66.77	0.00	-135.01	0.09	0.22	0.29
Degree	5	14	6.50	6.00	1,014	MAX VALUE	285.79	2.29	0.35	0.72
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	13	3.47	3.00	1,397	MAX VALUE	492.19	0.85	0.24	0.85

Minimal dual graph

Density: 1.93%
MCB compute time (ms): 26
MCB cycles: 78

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 4 2.99 3.00 466 MAX VALUE 169.28 0.39 0.13 0.54

Eccentricity None None None None None None None None None None

MCB cycle size 4 13 6.24 6.00 487 MAX VALUE 141.54 1.25 0.20 1.40

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	4	2.99	3.00	466	MAX VALUE	169.28	0.39	0.13	0.54
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	13	6.24	6.00	487	MAX VALUE	141.54	1.25	0.20	1.40

Triangulated dual graph

Density: 15.74%
Triangles: 14,863

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

Clustering coefficient 0.53 1.00 0.77 0.76 119.65 0.00 -44.70 0.16 0.21 3.51

Degree 5 62 24.40 15.00 3,806 MAX VALUE 444.56 19.17 0.79 3.22

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	0.53	1.00	0.77	0.76	119.65	0.00	-44.70	0.16	0.21	3.51
Degree	5	62	24.40	15.00	3,806	MAX VALUE	444.56	19.17	0.79	3.22
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 7.34%

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

Clustering coefficient 0.37 1.00 0.75 0.67 116.86 0.00 -51.81 0.22 0.29 2.82

Degree 2 41 11.38 5.00 1,776 MAX VALUE 302.69 11.72 1.03 2.76

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	0.37	1.00	0.75	0.67	116.86	0.00	-51.81	0.22	0.29	2.82
Degree	2	41	11.38	5.00	1,776	MAX VALUE	302.69	11.72	1.03	2.76
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.13%
MCB compute time (ms): 38
MCB cycles: 78
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-4-insertions-3-3-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 13 2.66 2.00 624 MAX VALUE 215.09 1.12 0.42 0.81

Eccentricity None None None None None None None None None None

MCB cycle size 8 26 8.23 8.00 642 MAX VALUE 163.38 2.02 0.25 0.07

XCSP 2.1 Benchmarks