XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-8-753-100-57-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 7.18 7.00 86,496 MAX VALUE 23,653.60 0.86 0.12 1.17

Relational linkage 0.38 0.75 0.62 0.62 199.88 0.00 -153.54 0.08 0.13 0.99

Tightness 0.02 0.22 0.10 0.09 77.25 0.00 -1,774.38 0.04 0.37 2.29

Tuples 50 63 57.43 58.00 43,248 MAX VALUE 3,049.44 2.44 0.04 2.29

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

Value table constraints 34 39 37.65 38.00 1,506 MAX VALUE 145.12 1.09 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	7.18	7.00	86,496	MAX VALUE	23,653.60	0.86	0.12	1.17
Relational linkage	0.38	0.75	0.62	0.62	199.88	0.00	-153.54	0.08	0.13	0.99
Tightness	0.02	0.22	0.10	0.09	77.25	0.00	-1,774.38	0.04	0.37	2.29
Tuples	50	63	57.43	58.00	43,248	MAX VALUE	3,049.44	2.44	0.04	2.29
Values	8	8	8.00	8.00	320	1.33e+36	83.18	0.00	0.00	0.00
Value table constraints	34	39	37.65	38.00	1,506	MAX VALUE	145.12	1.09	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-2-40-8-753-100-57-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-ext/Tree1.json

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

Cluster constraints 576 683 635.33 647.00 1,906 254,535,000 19.35 44.45 0.07 1.10

Variables per cluster 35 38 36.67 37.00 110 49,210 10.80 1.25 0.03 1.10

Separator constraints 0 611 384.33 542.00 1,153 0 None 273.22 0.71 1.10

Separator variables 0 36 23.33 34.00 70 0 None 16.52 0.71 1.10

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	576	683	635.33	647.00	1,906	254,535,000	19.35	44.45	0.07	1.10
Variables per cluster	35	38	36.67	37.00	110	49,210	10.80	1.25	0.03	1.10
Separator constraints	0	611	384.33	542.00	1,153	0	None	273.22	0.71	1.10
Separator variables	0	36	23.33	34.00	70	0	None	16.52	0.71	1.10
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-2-40-8-753-100-57-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-ext/DualTree1.json

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

Cluster constraints 1,185 11,854 3,036.97 1,520.00 115,405 MAX VALUE 295.31 2,579.28 0.85 2.89

Variables per cluster 68 491 146.40 77.00 5,563 MAX VALUE 181.89 108.31 0.74 2.62

Separator constraints 0 6,518 2,310.11 1,444.00 87,784 0 None 1,492.62 0.65 2.85

Separator variables 0 363 126.58 76.00 4,810 0 None 82.44 0.65 2.59

Clusters per variable 1 9 7.39 8.00 5,563 MAX VALUE 1,459.79 1.91 0.26 1.51

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,185	11,854	3,036.97	1,520.00	115,405	MAX VALUE	295.31	2,579.28	0.85	2.89
Variables per cluster	68	491	146.40	77.00	5,563	MAX VALUE	181.89	108.31	0.74	2.62
Separator constraints	0	6,518	2,310.11	1,444.00	87,784	0	None	1,492.62	0.65	2.85
Separator variables	0	363	126.58	76.00	4,810	0	None	82.44	0.65	2.59
Clusters per variable	1	9	7.39	8.00	5,563	MAX VALUE	1,459.79	1.91	0.26	1.51

Primal graph

Density: 96.54%
MCB compute time (ms): None
MCB cycles: None
Triangles: 8,887
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-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 2.45

Degree 34 39 37.65 38.00 1,506 MAX VALUE 145.12 1.09 0.03 1.37

Eccentricity 1 2 1.80 2.00 72 4.29e+09 22.18 0.40 0.22 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	0.96	0.97	0.97	0.96	38.61	0.24	-1.41	0.00	0.00	2.45
Degree	34	39	37.65	38.00	1,506	MAX VALUE	145.12	1.09	0.03	1.37
Eccentricity	1	2	1.80	2.00	72	4.29e+09	22.18	0.40	0.22	0.50
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: 9,627

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 0.71

Degree 34 39 38.65 39.00 1,546 MAX VALUE 146.17 0.94 0.02 0.65

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	0.71
Degree	34	39	38.65	39.00	1,546	MAX VALUE	146.17	0.94	0.02	0.65
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): 42,050
MCB cycles: 26,869
Triangles: 337,690
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 381.51 0.00 -511.99 0.00 0.00 2.17

Degree 67 76 73.36 74.00 55,242 MAX VALUE 3,234.29 1.48 0.02 1.75

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 80,607 MAX VALUE 29,518.60 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	381.51	0.00	-511.99	0.00	0.00	2.17
Degree	67	76	73.36	74.00	55,242	MAX VALUE	3,234.29	1.48	0.02	1.75
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	80,607	MAX VALUE	29,518.60	0.00	0.00	0.00

Minimal dual graph

Density: 0.52%
MCB compute time (ms): 10,747
MCB cycles: 714

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 16.43 0.03

Degree 2 7 3.89 4.00 2,932 MAX VALUE 1,002.17 0.96 0.25 1.26

Eccentricity 9 14 11.66 12.00 8,779 MAX VALUE 1,845.84 1.13 0.10 1.53

MCB cycle size 3 12 6.01 6.00 4,290 MAX VALUE 1,263.12 1.29 0.22 1.60

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	16.43	0.03
Degree	2	7	3.89	4.00	2,932	MAX VALUE	1,002.17	0.96	0.25	1.26
Eccentricity	9	14	11.66	12.00	8,779	MAX VALUE	1,845.84	1.13	0.10	1.53
MCB cycle size	3	12	6.01	6.00	4,290	MAX VALUE	1,263.12	1.29	0.22	1.60

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: 6.67%

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

Clustering coefficient 0.52 1.00 0.81 0.77 610.93 0.00 -170.05 0.15 0.18 4.11

Degree 2 209 50.17 9.00 37,776 MAX VALUE 2,079.84 69.62 1.39 3.77

Eccentricity 3 6 4.52 5.00 3,402 MAX VALUE 1,128.90 0.59 0.13 0.89

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.52	1.00	0.81	0.77	610.93	0.00	-170.05	0.15	0.18	4.11
Degree	2	209	50.17	9.00	37,776	MAX VALUE	2,079.84	69.62	1.39	3.77
Eccentricity	3	6	4.52	5.00	3,402	MAX VALUE	1,128.90	0.59	0.13	0.89

Incidence graph

Density: 0.48%
MCB compute time (ms): 1,109
MCB cycles: 714
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-57-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 1,107.74 0.26 0.06 0.28

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