XCSP 2.1 Benchmark Database

Instance: normalized-2-insertions-4-4-ext
Number of variables: 149
Number of constraints: 541
Satisfiable: True
Timestamp: 2025-07-27 21:34:49
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 149
Number of constraints: 541

General features

Coarse blocks: 4,328
Value tables: 149

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

Arity 2 2 2.00 2.00 1,082 MAX VALUE 374.99 0.00 0.00 0.00

Coarse blocks size 3 3 3.00 3.00 12,984 MAX VALUE 4,754.79 0.00 0.00 0.00

Relational linkage 0.75 0.75 0.75 0.75 447.00 0.00 -171.46 0.00 0.00 0.00

Tightness 0.25 0.25 0.25 0.25 135.25 0.00 -749.99 0.00 0.00 0.00

Tuples 12 12 12.00 12.00 6,492 MAX VALUE 1,344.33 0.00 0.00 0.00

Values 4 4 4.00 4.00 596 MAX VALUE 206.56 0.00 0.00 0.00

Value table constraints 4 37 7.26 8.00 1,082 MAX VALUE 287.33 3.23 0.45 1.27

Value table partitions 4 4 4.00 4.00 596 MAX VALUE 206.56 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	1,082	MAX VALUE	374.99	0.00	0.00	0.00
Coarse blocks size	3	3	3.00	3.00	12,984	MAX VALUE	4,754.79	0.00	0.00	0.00
Relational linkage	0.75	0.75	0.75	0.75	447.00	0.00	-171.46	0.00	0.00	0.00
Tightness	0.25	0.25	0.25	0.25	135.25	0.00	-749.99	0.00	0.00	0.00
Tuples	12	12	12.00	12.00	6,492	MAX VALUE	1,344.33	0.00	0.00	0.00
Values	4	4	4.00	4.00	596	MAX VALUE	206.56	0.00	0.00	0.00
Value table constraints	4	37	7.26	8.00	1,082	MAX VALUE	287.33	3.23	0.45	1.27
Value table partitions	4	4	4.00	4.00	596	MAX VALUE	206.56	0.00	0.00	0.00

Tree decomposition

Number of clusters: 106
Number of leaves: 72
Tree depth: 12
CIR: 0.34
Independent Cluster Pairs: 1,830
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Tree1.json

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

Cluster constraints 0 37 9.94 6.00 1,054 0 None 8.65 0.87 2.41

Variables per cluster 5 39 11.97 7.00 1,269 MAX VALUE 241.24 8.87 0.74 2.41

Separator constraints 0 32 4.84 0.00 513 0 None 9.01 1.86 1.25

Separator variables 0 34 10.57 6.00 1,120 0 None 8.41 0.80 2.40

Clusters per var 1 68 8.52 3.00 1,269 MAX VALUE 197.90 9.91 1.16 2.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	37	9.94	6.00	1,054	0	None	8.65	0.87	2.41
Variables per cluster	5	39	11.97	7.00	1,269	MAX VALUE	241.24	8.87	0.74	2.41
Separator constraints	0	32	4.84	0.00	513	0	None	9.01	1.86	1.25
Separator variables	0	34	10.57	6.00	1,120	0	None	8.41	0.80	2.40
Clusters per var	1	68	8.52	3.00	1,269	MAX VALUE	197.90	9.91	1.16	2.23

Dual tree decomposition

Number of clusters: 147
Number of leaves: 62
Tree depth: 8
CIR: 0.68
Independent Cluster Pairs: 7,153
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/DualTree1.json

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

Cluster constraints 25 738 91.13 56.00 13,396 MAX VALUE 613.76 115.01 1.26 3.56

Variables per cluster 10 174 27.73 17.00 4,077 MAX VALUE 448.43 27.64 1.00 3.26

Separator constraints 0 561 62.78 42.00 9,229 0 None 75.49 1.20 3.39

Separator variables 0 130 24.05 16.00 3,536 0 None 21.61 0.90 3.24

Clusters per variable 1 14 7.54 8.00 4,077 MAX VALUE 961.65 4.07 0.54 2.56

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	738	91.13	56.00	13,396	MAX VALUE	613.76	115.01	1.26	3.56
Variables per cluster	10	174	27.73	17.00	4,077	MAX VALUE	448.43	27.64	1.00	3.26
Separator constraints	0	561	62.78	42.00	9,229	0	None	75.49	1.20	3.39
Separator variables	0	130	24.05	16.00	3,536	0	None	21.61	0.90	3.24
Clusters per variable	1	14	7.54	8.00	4,077	MAX VALUE	961.65	4.07	0.54	2.56

Primal graph

Density: 4.91%
MCB compute time (ms): None
MCB cycles: None
Triangles: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-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 37 7.26 8.00 1,082 MAX VALUE 287.33 3.23 0.45 1.27

Eccentricity 4 4 4.00 4.00 596 MAX VALUE 206.56 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	37	7.26	8.00	1,082	MAX VALUE	287.33	3.23	0.45	1.27
Eccentricity	4	4	4.00	4.00	596	MAX VALUE	206.56	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 18.38%
MCB compute time (ms): None
MCB cycles: None
Triangles: 20,931

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

Clustering coefficient 0.27 1.00 0.83 0.85 124.08 0.00 -31.13 0.18 0.21 2.81

Degree 4 110 27.21 12.00 4,054 MAX VALUE 414.13 24.74 0.91 3.12

Eccentricity 2 3 2.66 3.00 396 MAX VALUE 143.01 0.47 0.18 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	0.27	1.00	0.83	0.85	124.08	0.00	-31.13	0.18	0.21	2.81
Degree	4	110	27.21	12.00	4,054	MAX VALUE	414.13	24.74	0.91	3.12
Eccentricity	2	3	2.66	3.00	396	MAX VALUE	143.01	0.47	0.18	0.64
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 2.85%
MCB compute time (ms): 8,664
MCB cycles: 5,052
Triangles: 15,720
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Dual1.json

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

Clustering coefficient 0.44 0.85 0.51 0.47 277.85 0.00 -368.85 0.10 0.20 1.76

Degree 9 45 15.40 14.00 8,334 MAX VALUE 1,440.43 7.31 0.47 1.69

Eccentricity 5 5 5.00 5.00 2,705 MAX VALUE 870.71 0.00 0.00 0.00

MCB cycle size 3 9 3.57 3.00 18,029 MAX VALUE 6,299.47 0.88 0.25 0.93

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.85	0.51	0.47	277.85	0.00	-368.85	0.10	0.20	1.76
Degree	9	45	15.40	14.00	8,334	MAX VALUE	1,440.43	7.31	0.47	1.69
Eccentricity	5	5	5.00	5.00	2,705	MAX VALUE	870.71	0.00	0.00	0.00
MCB cycle size	3	9	3.57	3.00	18,029	MAX VALUE	6,299.47	0.88	0.25	0.93

Minimal dual graph

Density: 0.64%
MCB compute time (ms): 3,073
MCB cycles: 393

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 3.45 3.00 1,866 MAX VALUE 660.09 0.67 0.19 0.97

Eccentricity 8 12 9.74 10.00 5,271 MAX VALUE 1,230.46 0.64 0.07 0.97

MCB cycle size 4 12 7.21 7.00 2,834 MAX VALUE 767.99 1.49 0.21 1.73

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	3.45	3.00	1,866	MAX VALUE	660.09	0.67	0.19	0.97
Eccentricity	8	12	9.74	10.00	5,271	MAX VALUE	1,230.46	0.64	0.07	0.97
MCB cycle size	4	12	7.21	7.00	2,834	MAX VALUE	767.99	1.49	0.21	1.73

Triangulated dual graph

Density: 24.36%
Triangles: 1,787,410

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

Clustering coefficient 0.65 1.00 0.82 0.79 441.44 0.00 -113.99 0.10 0.12 5.36

Degree 9 283 131.56 109.00 71,174 MAX VALUE 2,380.87 100.53 0.76 4.70

Eccentricity 2 3 2.70 3.00 1,460 MAX VALUE 528.26 0.46 0.17 0.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.65	1.00	0.82	0.79	441.44	0.00	-113.99	0.10	0.12	5.36
Degree	9	283	131.56	109.00	71,174	MAX VALUE	2,380.87	100.53	0.76	4.70
Eccentricity	2	3	2.70	3.00	1,460	MAX VALUE	528.26	0.46	0.17	0.61

Triangulated minimal dual graph

Density: 6.13%

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

Clustering coefficient 0.45 1.00 0.80 0.75 433.21 0.00 -130.41 0.16 0.19 3.63

Degree 2 141 33.08 7.00 17,898 MAX VALUE 1,330.05 46.20 1.40 3.40

Eccentricity 3 6 4.67 5.00 2,528 MAX VALUE 829.88 0.57 0.12 0.85

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	1.00	0.80	0.75	433.21	0.00	-130.41	0.16	0.19	3.63
Degree	2	141	33.08	7.00	17,898	MAX VALUE	1,330.05	46.20	1.40	3.40
Eccentricity	3	6	4.67	5.00	2,528	MAX VALUE	829.88	0.57	0.12	0.85

Incidence graph

Density: 0.46%
MCB compute time (ms): 2,807
MCB cycles: 393
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-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 37 3.14 2.00 2,164 MAX VALUE 662.32 2.64 0.84 0.80

Eccentricity 9 10 9.78 10.00 6,751 MAX VALUE 1,573.08 0.41 0.04 0.52

MCB cycle size 8 18 8.03 8.00 3,154 MAX VALUE 818.03 0.50 0.06 0.02

XCSP 2.1 Benchmarks