XCSP 2.1 Benchmark Database

Instance: normalized-queen5-5-4-ext
Number of variables: 25
Number of constraints: 160
Satisfiable: True
Timestamp: 2025-07-20 22:08:29
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 25
Number of constraints: 160

General features

Coarse blocks: 1,280
Value tables: 25

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

Arity 2 2 2.00 2.00 320 MAX VALUE 110.90 0.00 0.00 0.00

Coarse blocks size 3 3 3.00 3.00 3,840 MAX VALUE 1,406.22 0.00 0.00 0.00

Relational linkage 0.75 0.75 0.75 0.75 75.00 0.00 -28.77 0.00 0.00 0.00

Tightness 0.25 0.25 0.25 0.25 40.00 0.00 -221.81 0.00 0.00 0.00

Tuples 12 12 12.00 12.00 1,920 MAX VALUE 397.58 0.00 0.00 0.00

Values 4 4 4.00 4.00 100 1.13e+15 34.66 0.00 0.00 0.00

Value table constraints 12 16 12.80 12.00 320 4.37e+27 63.64 1.13 0.09 0.78

Value table partitions 4 4 4.00 4.00 100 1.13e+15 34.66 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	320	MAX VALUE	110.90	0.00	0.00	0.00
Coarse blocks size	3	3	3.00	3.00	3,840	MAX VALUE	1,406.22	0.00	0.00	0.00
Relational linkage	0.75	0.75	0.75	0.75	75.00	0.00	-28.77	0.00	0.00	0.00
Tightness	0.25	0.25	0.25	0.25	40.00	0.00	-221.81	0.00	0.00	0.00
Tuples	12	12	12.00	12.00	1,920	MAX VALUE	397.58	0.00	0.00	0.00
Values	4	4	4.00	4.00	100	1.13e+15	34.66	0.00	0.00	0.00
Value table constraints	12	16	12.80	12.00	320	4.37e+27	63.64	1.13	0.09	0.78
Value table partitions	4	4	4.00	4.00	100	1.13e+15	34.66	0.00	0.00	0.00

Tree decomposition

Number of clusters: 7
Number of leaves: 5
Tree depth: 2
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/Tree1.json

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

Cluster constraints 44 87 61.29 59.00 429 2.51e+12 28.55 17.09 0.28 1.75

Variables per cluster 13 19 15.29 15.00 107 178,451,000 19.00 2.49 0.16 1.08

Separator constraints 0 77 38.43 34.00 269 0 None 21.25 0.55 1.75

Separator variables 0 18 11.71 12.00 82 0 None 5.17 0.44 1.28

Clusters per var 1 6 4.28 5.00 107 1.09e+14 32.33 1.78 0.42 1.36

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	44	87	61.29	59.00	429	2.51e+12	28.55	17.09	0.28	1.75
Variables per cluster	13	19	15.29	15.00	107	178,451,000	19.00	2.49	0.16	1.08
Separator constraints	0	77	38.43	34.00	269	0	None	21.25	0.55	1.75
Separator variables	0	18	11.71	12.00	82	0	None	5.17	0.44	1.28
Clusters per var	1	6	4.28	5.00	107	1.09e+14	32.33	1.78	0.42	1.36

Dual tree decomposition

Number of clusters: 23
Number of leaves: 12
Tree depth: 4
CIR: 0.05
Independent Cluster Pairs: 12
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/DualTree1.json

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

Cluster constraints 138 575 253.61 191.00 5,833 MAX VALUE 124.66 132.14 0.52 2.42

Variables per cluster 23 87 39.30 27.00 904 4.00e+35 81.98 19.77 0.50 2.28

Separator constraints 0 307 170.83 164.00 3,929 0 None 71.20 0.42 2.42

Separator variables 0 66 32.35 26.00 744 0 None 15.01 0.46 2.22

Clusters per variable 1 8 5.65 6.00 904 MAX VALUE 258.90 2.06 0.36 1.86

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	138	575	253.61	191.00	5,833	MAX VALUE	124.66	132.14	0.52	2.42
Variables per cluster	23	87	39.30	27.00	904	4.00e+35	81.98	19.77	0.50	2.28
Separator constraints	0	307	170.83	164.00	3,929	0	None	71.20	0.42	2.42
Separator variables	0	66	32.35	26.00	744	0	None	15.01	0.46	2.22
Clusters per variable	1	8	5.65	6.00	904	MAX VALUE	258.90	2.06	0.36	1.86

Primal graph

Density: 53.33%
MCB compute time (ms): 1
MCB cycles: 137
Triangles: 320
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/Primal1.json

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

Clustering coefficient 0.48 0.53 0.50 0.52 12.58 0.00 -17.19 0.02 0.03 1.44

Degree 12 16 12.80 12.00 320 4.37e+27 63.64 1.13 0.09 0.78

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 411 MAX VALUE 150.51 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.53	0.50	0.52	12.58	0.00	-17.19	0.02	0.03	1.44
Degree	12	16	12.80	12.00	320	4.37e+27	63.64	1.13	0.09	0.78
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	411	MAX VALUE	150.51	0.00	0.00	0.00

Triangulated primal graph

Density: 84.33%
MCB compute time (ms): 3
MCB cycles: 238
Triangles: 1,502

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

Clustering coefficient 0.85 1.00 0.91 0.89 22.70 0.09 -2.45 0.05 0.05 1.92

Degree 12 23 20.24 22.00 506 2.58e+32 74.63 3.81 0.19 1.49

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 714 MAX VALUE 261.47 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.85	1.00	0.91	0.89	22.70	0.09	-2.45	0.05	0.05	1.92
Degree	12	23	20.24	22.00	506	2.58e+32	74.63	3.81	0.19	1.49
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	714	MAX VALUE	261.47	0.00	0.00	0.00

Dual graph

Density: 14.97%
MCB compute time (ms): 135
MCB cycles: 1,814
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/Dual1.json

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

Clustering coefficient 0.49 0.52 0.50 0.50 80.34 0.00 -110.23 0.01 0.01 2.34

Degree 22 28 23.80 24.00 3,808 MAX VALUE 506.74 1.72 0.07 1.19

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 5,442 MAX VALUE 1,992.88 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.52	0.50	0.50	80.34	0.00	-110.23	0.01	0.01	2.34
Degree	22	28	23.80	24.00	3,808	MAX VALUE	506.74	1.72	0.07	1.19
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	5,442	MAX VALUE	1,992.88	0.00	0.00	0.00

Minimal dual graph

Density: 2.32%
MCB compute time (ms): 52
MCB cycles: 136

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

Clustering coefficient 0.00 0.33 0.01 0.00 0.83 0.00 None 0.04 7.52 0.11

Degree 2 6 3.69 4.00 590 MAX VALUE 205.06 0.82 0.22 1.16

Eccentricity None None None None None None None None None None

MCB cycle size 3 8 6.24 6.00 848 MAX VALUE 246.53 1.11 0.18 1.48

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	0.83	0.00	None	0.04	7.52	0.11
Degree	2	6	3.69	4.00	590	MAX VALUE	205.06	0.82	0.22	1.16
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	8	6.24	6.00	848	MAX VALUE	246.53	1.11	0.18	1.48

Triangulated dual graph

Density: 59.41%
Triangles: 216,597

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

Clustering coefficient 0.75 1.00 0.85 0.85 136.19 0.00 -26.42 0.08 0.09 3.81

Degree 22 131 94.46 105.00 15,114 MAX VALUE 710.96 34.90 0.37 3.15

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	0.75	1.00	0.85	0.85	136.19	0.00	-26.42	0.08	0.09	3.81
Degree	22	131	94.46	105.00	15,114	MAX VALUE	710.96	34.90	0.37	3.15
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.55%

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

Clustering coefficient 0.45 1.00 0.79 0.74 126.75 0.00 -40.51 0.16 0.20 3.30

Degree 2 61 19.96 7.00 3,194 MAX VALUE 378.42 20.77 1.04 3.18

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	0.45	1.00	0.79	0.74	126.75	0.00	-40.51	0.16	0.20	3.30
Degree	2	61	19.96	7.00	3,194	MAX VALUE	378.42	20.77	1.04	3.18
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.88%
MCB compute time (ms): 20
MCB cycles: 136
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen5-5-4-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 16 3.46 2.00 640 MAX VALUE 174.55 3.72 1.07 0.50

Eccentricity None None None None None None None None None None

MCB cycle size 6 6 6.00 6.00 816 MAX VALUE 243.68 0.00 0.00 0.00

XCSP 2.1 Benchmarks