XCSP 2.1 Benchmark Database

Instance: normalized-queen8-8-9-ext
Number of variables: 64
Number of constraints: 728
Satisfiable: True
Timestamp: 2025-07-27 21:29:54
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 64
Number of constraints: 728

General features

Coarse blocks: 13,104
Value tables: 64

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

Arity 2 2 2.00 2.00 1,456 MAX VALUE 504.61 0.00 0.00 0.00

Coarse blocks size 8 8 8.00 8.00 104,832 MAX VALUE 27,249.00 0.00 0.00 0.00

Relational linkage 0.89 0.89 0.89 0.89 512.00 0.00 -67.84 0.00 0.00 0.00

Tightness 0.11 0.11 0.11 0.11 80.89 0.00 -1,599.58 0.00 0.00 0.00

Tuples 72 72 72.00 72.00 52,416 MAX VALUE 3,113.41 0.00 0.00 0.00

Values 9 9 9.00 9.00 576 MAX VALUE 140.62 0.00 0.00 0.00

Value table constraints 21 27 22.75 23.00 1,456 MAX VALUE 199.77 1.85 0.08 1.21

Value table partitions 9 9 9.00 9.00 576 MAX VALUE 140.62 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	1,456	MAX VALUE	504.61	0.00	0.00	0.00
Coarse blocks size	8	8	8.00	8.00	104,832	MAX VALUE	27,249.00	0.00	0.00	0.00
Relational linkage	0.89	0.89	0.89	0.89	512.00	0.00	-67.84	0.00	0.00	0.00
Tightness	0.11	0.11	0.11	0.11	80.89	0.00	-1,599.58	0.00	0.00	0.00
Tuples	72	72	72.00	72.00	52,416	MAX VALUE	3,113.41	0.00	0.00	0.00
Values	9	9	9.00	9.00	576	MAX VALUE	140.62	0.00	0.00	0.00
Value table constraints	21	27	22.75	23.00	1,456	MAX VALUE	199.77	1.85	0.08	1.21
Value table partitions	9	9	9.00	9.00	576	MAX VALUE	140.62	0.00	0.00	0.00

Tree decomposition

Number of clusters: 15
Number of leaves: 6
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/Tree1.json

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

Cluster constraints 107 414 242.07 194.00 3,631 8.83e+34 80.47 115.75 0.48 2.52

Variables per cluster 22 49 34.73 32.00 521 6.46e+22 52.52 10.32 0.30 2.12

Separator constraints 0 381 193.53 173.00 2,903 0 None 117.32 0.61 2.52

Separator variables 0 47 30.47 31.00 457 0 None 12.51 0.41 2.12

Clusters per var 1 13 8.14 9.00 521 MAX VALUE 122.71 3.41 0.42 2.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	107	414	242.07	194.00	3,631	8.83e+34	80.47	115.75	0.48	2.52
Variables per cluster	22	49	34.73	32.00	521	6.46e+22	52.52	10.32	0.30	2.12
Separator constraints	0	381	193.53	173.00	2,903	0	None	117.32	0.61	2.52
Separator variables	0	47	30.47	31.00	457	0	None	12.51	0.41	2.12
Clusters per var	1	13	8.14	9.00	521	MAX VALUE	122.71	3.41	0.42	2.28

Dual tree decomposition

Number of clusters: 62
Number of leaves: 32
Tree depth: 5
CIR: 0.10
Independent Cluster Pairs: 192
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/DualTree1.json

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

Cluster constraints 426 4,326 1,039.89 714.00 64,473 MAX VALUE 416.12 870.12 0.84 3.01

Variables per cluster 41 369 92.06 53.00 5,708 MAX VALUE 266.04 76.49 0.83 2.76

Separator constraints 0 2,464 782.73 607.50 48,529 0 None 511.18 0.65 3.03

Separator variables 0 284 80.32 50.00 4,980 0 None 58.73 0.73 2.74

Clusters per variable 1 11 7.84 9.00 5,708 MAX VALUE 1,421.28 2.73 0.35 1.93

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	426	4,326	1,039.89	714.00	64,473	MAX VALUE	416.12	870.12	0.84	3.01
Variables per cluster	41	369	92.06	53.00	5,708	MAX VALUE	266.04	76.49	0.83	2.76
Separator constraints	0	2,464	782.73	607.50	48,529	0	None	511.18	0.65	3.03
Separator variables	0	284	80.32	50.00	4,980	0	None	58.73	0.73	2.74
Clusters per variable	1	11	7.84	9.00	5,708	MAX VALUE	1,421.28	2.73	0.35	1.93

Primal graph

Density: 36.11%
MCB compute time (ms): None
MCB cycles: None
Triangles: 2,152
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/Primal1.json

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

Clustering coefficient 0.40 0.43 0.41 0.40 25.93 0.00 -57.83 0.01 0.02 1.91

Degree 21 27 22.75 23.00 1,456 MAX VALUE 199.77 1.85 0.08 1.21

Eccentricity 2 2 2.00 2.00 128 1.84e+19 44.36 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	0.40	0.43	0.41	0.40	25.93	0.00	-57.83	0.01	0.02	1.91
Degree	21	27	22.75	23.00	1,456	MAX VALUE	199.77	1.85	0.08	1.21
Eccentricity	2	2	2.00	2.00	128	1.84e+19	44.36	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 83.33%
MCB compute time (ms): None
MCB cycles: None
Triangles: 27,412

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

Clustering coefficient 0.86 1.00 0.92 0.91 58.85 0.00 -5.42 0.04 0.04 3.55

Degree 21 61 52.50 57.00 3,360 MAX VALUE 251.32 11.18 0.21 2.46

Eccentricity 2 2 2.00 2.00 128 1.84e+19 44.36 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	0.86	1.00	0.92	0.91	58.85	0.00	-5.42	0.04	0.04	3.55
Degree	21	61	52.50	57.00	3,360	MAX VALUE	251.32	11.18	0.21	2.46
Eccentricity	2	2	2.00	2.00	128	1.84e+19	44.36	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 6.03%
MCB compute time (ms): 19,790
MCB cycles: 16,126
Triangles: 114,112
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/Dual1.json

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

Clustering coefficient 0.49 0.51 0.50 0.50 363.44 0.00 -505.74 0.00 0.01 3.38

Degree 40 52 43.80 44.00 31,888 MAX VALUE 2,750.02 2.91 0.07 1.71

Eccentricity 3 3 3.00 3.00 2,184 MAX VALUE 799.79 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 48,378 MAX VALUE 17,716.20 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.51	0.50	0.50	363.44	0.00	-505.74	0.00	0.01	3.38
Degree	40	52	43.80	44.00	31,888	MAX VALUE	2,750.02	2.91	0.07	1.71
Eccentricity	3	3	3.00	3.00	2,184	MAX VALUE	799.79	0.00	0.00	0.00
MCB cycle size	3	3	3.00	3.00	48,378	MAX VALUE	17,716.20	0.00	0.00	0.00

Minimal dual graph

Density: 0.53%
MCB compute time (ms): 12,599
MCB cycles: 665

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.02 16.16 0.03

Degree 2 7 3.82 4.00 2,784 MAX VALUE 958.42 0.89 0.23 1.20

Eccentricity 7 10 8.38 8.00 6,101 MAX VALUE 1,545.50 0.64 0.08 0.96

MCB cycle size 3 10 7.18 7.00 4,772 MAX VALUE 1,299.61 1.21 0.17 1.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.02	16.16	0.03
Degree	2	7	3.82	4.00	2,784	MAX VALUE	958.42	0.89	0.23	1.20
Eccentricity	7	10	8.38	8.00	6,101	MAX VALUE	1,545.50	0.64	0.08	0.96
MCB cycle size	3	10	7.18	7.00	4,772	MAX VALUE	1,299.61	1.21	0.17	1.55

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: 8.75%

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

Clustering coefficient 0.47 1.00 0.84 0.82 614.81 0.00 -132.47 0.13 0.16 4.04

Degree 2 230 63.58 9.00 46,284 MAX VALUE 2,065.84 87.15 1.37 3.56

Eccentricity 3 5 3.83 4.00 2,789 MAX VALUE 969.77 0.56 0.15 0.84

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.84	0.82	614.81	0.00	-132.47	0.13	0.16	4.04
Degree	2	230	63.58	9.00	46,284	MAX VALUE	2,065.84	87.15	1.37	3.56
Eccentricity	3	5	3.83	4.00	2,789	MAX VALUE	969.77	0.56	0.15	0.84

Incidence graph

Density: 0.46%
MCB compute time (ms): 4,192
MCB cycles: 665
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen8-8-9-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 27 3.68 2.00 2,912 MAX VALUE 704.38 5.68 1.54 0.38

Eccentricity 5 6 5.92 6.00 4,688 MAX VALUE 1,407.40 0.27 0.05 0.28

MCB cycle size 6 6 6.00 6.00 3,990 MAX VALUE 1,191.52 0.00 0.00 0.00

XCSP 2.1 Benchmarks