XCSP 2.1 Benchmark Database

Instance: normalized-3-insertions-4-4-ext
Number of variables: 281
Number of constraints: 1046
Satisfiable: True
Timestamp: 2025-07-27 21:34:49
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 281
Number of constraints: 1046

General features

Coarse blocks: 8,368
Value tables: 281

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

Arity 2 2 2.00 2.00 2,092 MAX VALUE 725.03 0.00 0.00 0.00

Coarse blocks size 3 3 3.00 3.00 25,104 MAX VALUE 9,193.19 0.00 0.00 0.00

Relational linkage 0.75 0.75 0.75 0.75 843.00 0.00 -323.36 0.00 0.00 0.00

Tightness 0.25 0.25 0.25 0.25 261.50 0.00 -1,450.06 0.00 0.00 0.00

Tuples 12 12 12.00 12.00 12,552 MAX VALUE 2,599.21 0.00 0.00 0.00

Values 4 4 4.00 4.00 1,124 MAX VALUE 389.55 0.00 0.00 0.00

Value table constraints 4 56 7.44 8.00 2,092 MAX VALUE 549.76 3.66 0.49 1.10

Value table partitions 4 4 4.00 4.00 1,124 MAX VALUE 389.55 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	2,092	MAX VALUE	725.03	0.00	0.00	0.00
Coarse blocks size	3	3	3.00	3.00	25,104	MAX VALUE	9,193.19	0.00	0.00	0.00
Relational linkage	0.75	0.75	0.75	0.75	843.00	0.00	-323.36	0.00	0.00	0.00
Tightness	0.25	0.25	0.25	0.25	261.50	0.00	-1,450.06	0.00	0.00	0.00
Tuples	12	12	12.00	12.00	12,552	MAX VALUE	2,599.21	0.00	0.00	0.00
Values	4	4	4.00	4.00	1,124	MAX VALUE	389.55	0.00	0.00	0.00
Value table constraints	4	56	7.44	8.00	2,092	MAX VALUE	549.76	3.66	0.49	1.10
Value table partitions	4	4	4.00	4.00	1,124	MAX VALUE	389.55	0.00	0.00	0.00

Tree decomposition

Number of clusters: 193
Number of leaves: 137
Tree depth: 12
CIR: 0.52
Independent Cluster Pairs: 9,478
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/Tree1.json

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

Cluster constraints 0 47 8.79 6.00 1,696 0 None 7.99 0.91 2.20

Variables per cluster 5 64 12.55 9.00 2,422 MAX VALUE 444.21 10.70 0.85 2.38

Separator constraints 0 32 3.37 0.00 650 0 None 7.57 2.25 0.97

Separator variables 0 55 11.09 8.00 2,141 0 None 9.59 0.86 2.38

Clusters per var 1 104 8.62 3.00 2,422 MAX VALUE 371.81 10.64 1.23 2.29

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	47	8.79	6.00	1,696	0	None	7.99	0.91	2.20
Variables per cluster	5	64	12.55	9.00	2,422	MAX VALUE	444.21	10.70	0.85	2.38
Separator constraints	0	32	3.37	0.00	650	0	None	7.57	2.25	0.97
Separator variables	0	55	11.09	8.00	2,141	0	None	9.59	0.86	2.38
Clusters per var	1	104	8.62	3.00	2,422	MAX VALUE	371.81	10.64	1.23	2.29

Dual tree decomposition

Number of clusters: 279
Number of leaves: 123
Tree depth: 9
CIR: 0.80
Independent Cluster Pairs: 30,702
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/DualTree1.json

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

Cluster constraints 25 1,687 107.60 56.00 30,020 MAX VALUE 1,185.40 187.30 1.74 3.62

Variables per cluster 10 294 31.13 18.00 8,685 MAX VALUE 865.62 38.32 1.23 3.34

Separator constraints 0 1,216 76.69 42.00 21,396 0 None 126.55 1.65 3.63

Separator variables 0 228 27.38 16.00 7,639 0 None 30.51 1.11 3.29

Clusters per variable 1 17 8.30 8.00 8,685 MAX VALUE 1,935.00 4.70 0.57 2.68

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	1,687	107.60	56.00	30,020	MAX VALUE	1,185.40	187.30	1.74	3.62
Variables per cluster	10	294	31.13	18.00	8,685	MAX VALUE	865.62	38.32	1.23	3.34
Separator constraints	0	1,216	76.69	42.00	21,396	0	None	126.55	1.65	3.63
Separator variables	0	228	27.38	16.00	7,639	0	None	30.51	1.11	3.29
Clusters per variable	1	17	8.30	8.00	8,685	MAX VALUE	1,935.00	4.70	0.57	2.68

Primal graph

Density: 2.66%
MCB compute time (ms): None
MCB cycles: None
Triangles: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-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 56 7.44 8.00 2,092 MAX VALUE 549.76 3.66 0.49 1.10

Eccentricity 5 5 5.00 5.00 1,405 MAX VALUE 452.25 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	56	7.44	8.00	2,092	MAX VALUE	549.76	3.66	0.49	1.10
Eccentricity	5	5	5.00	5.00	1,405	MAX VALUE	452.25	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 13.65%
MCB compute time (ms): None
MCB cycles: None
Triangles: 90,687

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

Clustering coefficient 0.25 1.00 0.84 0.88 236.01 0.00 -55.50 0.17 0.20 3.07

Degree 4 191 38.21 12.00 10,736 MAX VALUE 830.99 39.65 1.04 3.34

Eccentricity 2 4 3.11 3.00 873 MAX VALUE 315.46 0.46 0.15 0.65

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	0.25	1.00	0.84	0.88	236.01	0.00	-55.50	0.17	0.20	3.07
Degree	4	191	38.21	12.00	10,736	MAX VALUE	830.99	39.65	1.04	3.34
Eccentricity	2	4	3.11	3.00	873	MAX VALUE	315.46	0.46	0.15	0.65
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 1.58%
MCB compute time (ms): 41,295
MCB cycles: 10,857
Triangles: 45,320
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/Dual1.json

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

Clustering coefficient 0.44 0.90 0.51 0.46 533.75 0.00 -721.55 0.11 0.21 1.54

Degree 9 66 16.49 14.00 17,248 MAX VALUE 2,818.00 10.79 0.65 1.54

Eccentricity 6 6 6.00 6.00 6,276 MAX VALUE 1,874.18 0.00 0.00 0.00

MCB cycle size 3 11 3.61 3.00 39,158 MAX VALUE 13,638.70 0.92 0.26 0.93

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.90	0.51	0.46	533.75	0.00	-721.55	0.11	0.21	1.54
Degree	9	66	16.49	14.00	17,248	MAX VALUE	2,818.00	10.79	0.65	1.54
Eccentricity	6	6	6.00	6.00	6,276	MAX VALUE	1,874.18	0.00	0.00	0.00
MCB cycle size	3	11	3.61	3.00	39,158	MAX VALUE	13,638.70	0.92	0.26	0.93

Minimal dual graph

Density: 0.33%
MCB compute time (ms): 25,895
MCB cycles: 766

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 3.46 3.00 3,622 MAX VALUE 1,281.88 0.64 0.19 0.94

Eccentricity 10 13 11.34 11.00 11,859 MAX VALUE 2,538.47 0.57 0.05 0.86

MCB cycle size 4 15 7.35 7.00 5,632 MAX VALUE 1,511.70 1.53 0.21 1.74

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	3.46	3.00	3,622	MAX VALUE	1,281.88	0.64	0.19	0.94
Eccentricity	10	13	11.34	11.00	11,859	MAX VALUE	2,538.47	0.57	0.05	0.86
MCB cycle size	4	15	7.35	7.00	5,632	MAX VALUE	1,511.70	1.53	0.21	1.74

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: 5.05%

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

Clustering coefficient 0.47 1.00 0.81 0.79 850.88 0.00 -234.32 0.15 0.19 3.93

Degree 2 265 52.77 7.00 55,196 MAX VALUE 2,730.02 81.93 1.55 3.62

Eccentricity 3 6 4.76 5.00 4,982 MAX VALUE 1,624.82 0.57 0.12 0.86

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.81	0.79	850.88	0.00	-234.32	0.15	0.19	3.93
Degree	2	265	52.77	7.00	55,196	MAX VALUE	2,730.02	81.93	1.55	3.62
Eccentricity	3	6	4.76	5.00	4,982	MAX VALUE	1,624.82	0.57	0.12	0.86

Incidence graph

Density: 0.24%
MCB compute time (ms): 21,921
MCB cycles: 766
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-insertions-4-4-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-3-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 56 3.15 2.00 4,184 MAX VALUE 1,274.79 2.79 0.88 0.75

Eccentricity 11 12 11.79 12.00 15,643 MAX VALUE 3,273.02 0.41 0.03 0.52

MCB cycle size 8 22 8.02 8.00 6,142 MAX VALUE 1,593.86 0.51 0.06 0.01

XCSP 2.1 Benchmarks