XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-8-753-100-39-ext
Number of variables: 40
Number of constraints: 753
Satisfiable: True
Timestamp: 2025-07-27 21:31:24
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 40
Number of constraints: 753

General features

Coarse blocks: 12,048
Value tables: 40

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

Arity 2 2 2.00 2.00 1,506 MAX VALUE 521.94 0.00 0.00 0.00

Coarse blocks size 3 8 7.21 7.00 86,836 MAX VALUE 23,706.60 0.84 0.12 1.14

Relational linkage 0.38 0.75 0.63 0.62 202.38 0.00 -149.75 0.09 0.14 1.02

Tightness 0.02 0.22 0.10 0.09 74.59 0.00 -1,803.15 0.04 0.38 2.27

Tuples 50 63 57.66 58.00 43,418 MAX VALUE 3,052.44 2.38 0.04 2.27

Values 8 8 8.00 8.00 320 1.33e+36 83.18 0.00 0.00 0.00

Value table constraints 35 39 37.65 38.00 1,506 MAX VALUE 145.12 1.06 0.03 1.37

Value table partitions 8 8 8.00 8.00 320 1.33e+36 83.18 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	1,506	MAX VALUE	521.94	0.00	0.00	0.00
Coarse blocks size	3	8	7.21	7.00	86,836	MAX VALUE	23,706.60	0.84	0.12	1.14
Relational linkage	0.38	0.75	0.63	0.62	202.38	0.00	-149.75	0.09	0.14	1.02
Tightness	0.02	0.22	0.10	0.09	74.59	0.00	-1,803.15	0.04	0.38	2.27
Tuples	50	63	57.66	58.00	43,418	MAX VALUE	3,052.44	2.38	0.04	2.27
Values	8	8	8.00	8.00	320	1.33e+36	83.18	0.00	0.00	0.00
Value table constraints	35	39	37.65	38.00	1,506	MAX VALUE	145.12	1.06	0.03	1.37
Value table partitions	8	8	8.00	8.00	320	1.33e+36	83.18	0.00	0.00	0.00

Tree decomposition

Number of clusters: 3
Number of leaves: 2
Tree depth: 1
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/Tree1.json

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

Cluster constraints 612 683 636.33 614.00 1,909 256,650,000 19.36 33.01 0.05 1.10

Variables per cluster 36 38 36.67 36.00 110 49,248 10.80 0.94 0.03 0.64

Separator constraints 0 579 385.33 577.00 1,156 0 None 272.47 0.71 1.10

Separator variables 0 35 23.33 35.00 70 0 None 16.50 0.71 0.64

Clusters per var 1 3 2.75 3.00 110 1.19e+17 39.31 0.54 0.19 0.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	612	683	636.33	614.00	1,909	256,650,000	19.36	33.01	0.05	1.10
Variables per cluster	36	38	36.67	36.00	110	49,248	10.80	0.94	0.03	0.64
Separator constraints	0	579	385.33	577.00	1,156	0	None	272.47	0.71	1.10
Separator variables	0	35	23.33	35.00	70	0	None	16.50	0.71	0.64
Clusters per var	1	3	2.75	3.00	110	1.19e+17	39.31	0.54	0.19	0.61

Dual tree decomposition

Number of clusters: 38
Number of leaves: 20
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/DualTree1.json

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

Cluster constraints 1,257 11,642 3,037.42 1,520.00 115,422 MAX VALUE 295.32 2,576.95 0.85 2.87

Variables per cluster 70 488 146.40 77.00 5,563 MAX VALUE 181.89 108.34 0.74 2.60

Separator constraints 0 6,597 2,310.58 1,444.00 87,802 0 None 1,499.36 0.65 2.87

Separator variables 0 365 126.58 76.00 4,810 0 None 82.60 0.65 2.57

Clusters per variable 1 9 7.39 8.00 5,563 MAX VALUE 1,459.55 1.92 0.26 1.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,257	11,642	3,037.42	1,520.00	115,422	MAX VALUE	295.32	2,576.95	0.85	2.87
Variables per cluster	70	488	146.40	77.00	5,563	MAX VALUE	181.89	108.34	0.74	2.60
Separator constraints	0	6,597	2,310.58	1,444.00	87,802	0	None	1,499.36	0.65	2.87
Separator variables	0	365	126.58	76.00	4,810	0	None	82.60	0.65	2.57
Clusters per variable	1	9	7.39	8.00	5,563	MAX VALUE	1,459.55	1.92	0.26	1.52

Primal graph

Density: 96.54%
MCB compute time (ms): None
MCB cycles: None
Triangles: 8,886
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/Primal1.json

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

Clustering coefficient 0.96 0.97 0.97 0.96 38.61 0.24 -1.41 0.00 0.00 2.18

Degree 35 39 37.65 38.00 1,506 MAX VALUE 145.12 1.06 0.03 1.37

Eccentricity 1 2 1.75 2.00 70 1.07e+09 20.79 0.43 0.25 0.56

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	0.96	0.97	0.97	0.96	38.61	0.24	-1.41	0.00	0.00	2.18
Degree	35	39	37.65	38.00	1,506	MAX VALUE	145.12	1.06	0.03	1.37
Eccentricity	1	2	1.75	2.00	70	1.07e+09	20.79	0.43	0.25	0.56
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 99.10%
MCB compute time (ms): None
MCB cycles: None
Triangles: 9,626

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

Clustering coefficient 0.99 1.00 0.99 0.99 39.67 0.72 -0.33 0.00 0.00 0.61

Degree 35 39 38.65 39.00 1,546 MAX VALUE 146.17 0.91 0.02 0.61

Eccentricity 1 2 1.20 1.00 48 256 5.55 0.40 0.33 0.50

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	0.99	1.00	0.99	0.99	39.67	0.72	-0.33	0.00	0.00	0.61
Degree	35	39	38.65	39.00	1,546	MAX VALUE	146.17	0.91	0.02	0.61
Eccentricity	1	2	1.20	1.00	48	256	5.55	0.40	0.33	0.50
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 9.76%
MCB compute time (ms): 32,636
MCB cycles: 26,868
Triangles: 337,658
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 381.50 0.00 -512.00 0.00 0.00 2.14

Degree 69 76 73.36 73.00 55,240 MAX VALUE 3,234.27 1.45 0.02 1.76

Eccentricity 2 2 2.00 2.00 1,506 MAX VALUE 521.94 0.00 0.00 0.00

MCB cycle size 3 3 3.00 3.00 80,604 MAX VALUE 29,517.50 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.51	0.51	0.51	0.51	381.50	0.00	-512.00	0.00	0.00	2.14
Degree	69	76	73.36	73.00	55,240	MAX VALUE	3,234.27	1.45	0.02	1.76
Eccentricity	2	2	2.00	2.00	1,506	MAX VALUE	521.94	0.00	0.00	0.00
MCB cycle size	3	3	3.00	3.00	80,604	MAX VALUE	29,517.50	0.00	0.00	0.00

Minimal dual graph

Density: 0.52%
MCB compute time (ms): 9,214
MCB cycles: 717

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

Clustering coefficient 0.00 0.33 0.00 0.00 1.05 0.00 None 0.02 13.49 0.06

Degree 2 7 3.89 4.00 2,932 MAX VALUE 1,001.87 0.96 0.25 1.25

Eccentricity 9 14 11.63 12.00 8,760 MAX VALUE 1,844.36 1.11 0.10 1.50

MCB cycle size 3 14 6.04 6.00 4,331 MAX VALUE 1,272.61 1.29 0.21 1.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	1.05	0.00	None	0.02	13.49	0.06
Degree	2	7	3.89	4.00	2,932	MAX VALUE	1,001.87	0.96	0.25	1.25
Eccentricity	9	14	11.63	12.00	8,760	MAX VALUE	1,844.36	1.11	0.10	1.50
MCB cycle size	3	14	6.04	6.00	4,331	MAX VALUE	1,272.61	1.29	0.21	1.61

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: 6.63%

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

Clustering coefficient 0.47 1.00 0.81 0.77 611.25 0.00 -170.06 0.15 0.19 4.05

Degree 2 217 49.83 9.00 37,520 MAX VALUE 2,074.26 68.95 1.38 3.76

Eccentricity 3 5 4.04 4.00 3,041 MAX VALUE 1,042.54 0.60 0.15 0.90

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.81	0.77	611.25	0.00	-170.06	0.15	0.19	4.05
Degree	2	217	49.83	9.00	37,520	MAX VALUE	2,074.26	68.95	1.38	3.76
Eccentricity	3	5	4.04	4.00	3,041	MAX VALUE	1,042.54	0.60	0.15	0.90

Incidence graph

Density: 0.48%
MCB compute time (ms): 926
MCB cycles: 714
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-39-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 39 3.80 2.00 3,012 MAX VALUE 667.06 7.81 2.06 0.27

Eccentricity 3 5 4.05 4.00 3,212 MAX VALUE 1,107.61 0.27 0.07 0.30

MCB cycle size 6 6 6.00 6.00 4,284 MAX VALUE 1,279.32 0.00 0.00 0.00

XCSP 2.1 Benchmarks