XCSP 2.1 Benchmark Database

Instance: normalized-queen6-6-7-ext
Number of variables: 36
Number of constraints: 290
Satisfiable: True
Timestamp: 2025-07-27 21:29:55
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0

Component #1

Number of variables: 36
Number of constraints: 290

General features

Coarse blocks: 4,060
Value tables: 36

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

Arity 2 2 2.00 2.00 580 MAX VALUE 201.01 0.00 0.00 0.00

Coarse blocks size 6 6 6.00 6.00 24,360 MAX VALUE 7,274.54 0.00 0.00 0.00

Relational linkage 0.86 0.86 0.86 0.86 216.00 0.00 -38.85 0.00 0.00 0.00

Tightness 0.14 0.14 0.14 0.14 41.43 0.00 -564.31 0.00 0.00 0.00

Tuples 42 42 42.00 42.00 12,180 MAX VALUE 1,083.92 0.00 0.00 0.00

Values 7 7 7.00 7.00 252 2.65e+30 70.05 0.00 0.00 0.00

Value table constraints 15 19 16.11 15.00 580 MAX VALUE 99.94 1.37 0.09 0.94

Value table partitions 7 7 7.00 7.00 252 2.65e+30 70.05 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	580	MAX VALUE	201.01	0.00	0.00	0.00
Coarse blocks size	6	6	6.00	6.00	24,360	MAX VALUE	7,274.54	0.00	0.00	0.00
Relational linkage	0.86	0.86	0.86	0.86	216.00	0.00	-38.85	0.00	0.00	0.00
Tightness	0.14	0.14	0.14	0.14	41.43	0.00	-564.31	0.00	0.00	0.00
Tuples	42	42	42.00	42.00	12,180	MAX VALUE	1,083.92	0.00	0.00	0.00
Values	7	7	7.00	7.00	252	2.65e+30	70.05	0.00	0.00	0.00
Value table constraints	15	19	16.11	15.00	580	MAX VALUE	99.94	1.37	0.09	0.94
Value table partitions	7	7	7.00	7.00	252	2.65e+30	70.05	0.00	0.00	0.00

Tree decomposition

Number of clusters: 10
Number of leaves: 4
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/Tree1.json

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

Cluster constraints 62 156 106.20 112.00 1,062 1.00e+20 46.05 34.99 0.33 2.16

Variables per cluster 16 27 21.40 22.50 214 1.64e+13 30.43 4.25 0.20 1.83

Separator constraints 0 133 77.20 77.00 772 0 None 40.52 0.52 2.03

Separator variables 0 25 17.80 19.00 178 0 None 7.05 0.40 1.83

Clusters per var 1 9 5.94 6.50 214 1.94e+25 58.23 2.54 0.43 2.03

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	62	156	106.20	112.00	1,062	1.00e+20	46.05	34.99	0.33	2.16
Variables per cluster	16	27	21.40	22.50	214	1.64e+13	30.43	4.25	0.20	1.83
Separator constraints	0	133	77.20	77.00	772	0	None	40.52	0.52	2.03
Separator variables	0	25	17.80	19.00	178	0	None	7.05	0.40	1.83
Clusters per var	1	9	5.94	6.50	214	1.94e+25	58.23	2.54	0.43	2.03

Dual tree decomposition

Number of clusters: 34
Number of leaves: 18
Tree depth: 4
CIR: 0.05
Independent Cluster Pairs: 28
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/DualTree1.json

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

Cluster constraints 216 1,303 447.12 352.00 15,202 MAX VALUE 202.01 287.34 0.64 2.44

Variables per cluster 29 156 55.18 37.00 1,876 MAX VALUE 131.20 34.50 0.63 2.21

Separator constraints 0 734 317.24 269.00 10,786 0 None 161.89 0.51 2.44

Separator variables 0 118 46.65 34.00 1,586 0 None 25.96 0.56 2.21

Clusters per variable 1 9 6.47 7.00 1,876 MAX VALUE 508.43 2.33 0.36 1.78

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	216	1,303	447.12	352.00	15,202	MAX VALUE	202.01	287.34	0.64	2.44
Variables per cluster	29	156	55.18	37.00	1,876	MAX VALUE	131.20	34.50	0.63	2.21
Separator constraints	0	734	317.24	269.00	10,786	0	None	161.89	0.51	2.44
Separator variables	0	118	46.65	34.00	1,586	0	None	25.96	0.56	2.21
Clusters per variable	1	9	6.47	7.00	1,876	MAX VALUE	508.43	2.33	0.36	1.78

Primal graph

Density: 46.03%
MCB compute time (ms): None
MCB cycles: None
Triangles: 672
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/Primal1.json

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

Clustering coefficient 0.45 0.47 0.46 0.46 16.41 0.00 -28.30 0.01 0.02 1.43

Degree 15 19 16.11 15.00 580 MAX VALUE 99.94 1.37 0.09 0.94

Eccentricity 2 2 2.00 2.00 72 6.87e+10 24.95 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	0.45	0.47	0.46	0.46	16.41	0.00	-28.30	0.01	0.02	1.43
Degree	15	19	16.11	15.00	580	MAX VALUE	99.94	1.37	0.09	0.94
Eccentricity	2	2	2.00	2.00	72	6.87e+10	24.95	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 83.97%
MCB compute time (ms): None
MCB cycles: None
Triangles: 4,669

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

Clustering coefficient 0.85 1.00 0.91 0.90 32.82 0.03 -3.37 0.04 0.05 2.91

Degree 15 34 29.39 31.50 1,058 MAX VALUE 120.81 5.64 0.19 2.21

Eccentricity 2 2 2.00 2.00 72 6.87e+10 24.95 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	0.85	1.00	0.91	0.90	32.82	0.03	-3.37	0.04	0.05	2.91
Degree	15	34	29.39	31.50	1,058	MAX VALUE	120.81	5.64	0.19	2.21
Eccentricity	2	2	2.00	2.00	72	6.87e+10	24.95	0.00	0.00	0.00
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 10.54%
MCB compute time (ms): 2,079
MCB cycles: 4,332
Triangles: 21,808
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/Dual1.json

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

Clustering coefficient 0.49 0.51 0.50 0.50 145.06 0.00 -200.90 0.00 0.01 2.62

Degree 28 36 30.46 30.00 8,832 MAX VALUE 990.03 2.11 0.07 1.39

Eccentricity 3 3 3.00 3.00 870 MAX VALUE 318.60 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 12,996 MAX VALUE 4,759.19 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	145.06	0.00	-200.90	0.00	0.01	2.62
Degree	28	36	30.46	30.00	8,832	MAX VALUE	990.03	2.11	0.07	1.39
Eccentricity	3	3	3.00	3.00	870	MAX VALUE	318.60	0.00	0.00	0.00
MCB cycle size	3	3	3.00	3.00	12,996	MAX VALUE	4,759.19	0.00	0.00	0.00

Minimal dual graph

Density: 1.30%
MCB compute time (ms): 559
MCB cycles: 255

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 0.03 10.17 0.06

Degree 2 7 3.75 4.00 1,088 MAX VALUE 376.38 0.86 0.23 1.18

Eccentricity 6 9 7.20 7.00 2,088 MAX VALUE 571.51 0.59 0.08 0.89

MCB cycle size 3 9 6.70 7.00 1,709 MAX VALUE 480.55 1.19 0.18 1.52

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	0.03	10.17	0.06
Degree	2	7	3.75	4.00	1,088	MAX VALUE	376.38	0.86	0.23	1.18
Eccentricity	6	9	7.20	7.00	2,088	MAX VALUE	571.51	0.59	0.08	0.89
MCB cycle size	3	9	6.70	7.00	1,709	MAX VALUE	480.55	1.19	0.18	1.52

Triangulated dual graph

Density: 55.83%
Triangles: 1,179,120

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

Clustering coefficient 0.76 1.00 0.85 0.84 246.64 0.00 -48.05 0.07 0.09 4.01

Degree 28 228 161.35 191.00 46,792 MAX VALUE 1,434.35 66.18 0.41 2.85

Eccentricity 2 3 2.08 2.00 604 MAX VALUE 210.74 0.28 0.13 0.29

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.76	1.00	0.85	0.84	246.64	0.00	-48.05	0.07	0.09	4.01
Degree	28	228	161.35	191.00	46,792	MAX VALUE	1,434.35	66.18	0.41	2.85
Eccentricity	2	3	2.08	2.00	604	MAX VALUE	210.74	0.28	0.13	0.29

Triangulated minimal dual graph

Density: 10.69%

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

Clustering coefficient 0.54 1.00 0.82 0.77 237.02 0.00 -62.93 0.14 0.17 3.64

Degree 2 98 30.89 8.00 8,958 MAX VALUE 741.84 36.67 1.19 3.23

Eccentricity 3 5 3.76 4.00 1,090 MAX VALUE 380.92 0.54 0.14 0.79

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.54	1.00	0.82	0.77	237.02	0.00	-62.93	0.14	0.17	3.64
Degree	2	98	30.89	8.00	8,958	MAX VALUE	741.84	36.67	1.19	3.23
Eccentricity	3	5	3.76	4.00	1,090	MAX VALUE	380.92	0.54	0.14	0.79

Incidence graph

Density: 1.09%
MCB compute time (ms): 287
MCB cycles: 255
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-sgb-queenExtConvert/normalized-queen6-6-7-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 19 3.56 2.00 1,160 MAX VALUE 300.95 4.45 1.25 0.45

Eccentricity 5 6 5.89 6.00 1,920 MAX VALUE 577.55 0.31 0.05 0.35

MCB cycle size 6 6 6.00 6.00 1,530 MAX VALUE 456.90 0.00 0.00 0.00

XCSP 2.1 Benchmarks