XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-8-753-100-51-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 86,838 MAX VALUE 23,703.00 0.85 0.12 1.15

Relational linkage 0.38 0.88 0.63 0.62 200.12 0.00 -153.26 0.08 0.13 1.02

Tightness 0.00 0.22 0.10 0.09 74.58 0.00 None 0.04 0.38 2.28

Tuples 50 64 57.66 58.00 43,419 MAX VALUE 3,052.45 2.40 0.04 2.28

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 1.13 0.03 1.41

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	86,838	MAX VALUE	23,703.00	0.85	0.12	1.15
Relational linkage	0.38	0.88	0.63	0.62	200.12	0.00	-153.26	0.08	0.13	1.02
Tightness	0.00	0.22	0.10	0.09	74.58	0.00	None	0.04	0.38	2.28
Tuples	50	64	57.66	58.00	43,419	MAX VALUE	3,052.45	2.40	0.04	2.28
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	1.13	0.03	1.41
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-2-40-8-753-100-51-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-ext/Tree1.json

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

Cluster constraints 577 681 634.33 645.00 1,903 253,444,000 19.35 43.12 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 0 609 384.00 543.00 1,152 0 None 272.86 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	577	681	634.33	645.00	1,903	253,444,000	19.35	43.12	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	609	384.00	543.00	1,152	0	None	272.86	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-2-40-8-753-100-51-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-ext/DualTree1.json

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

Cluster constraints 1,221 11,670 3,008.97 1,520.00 114,341 MAX VALUE 295.06 2,535.10 0.84 2.95

Variables per cluster 69 487 145.68 77.00 5,536 MAX VALUE 181.75 107.30 0.74 2.75

Separator constraints 0 6,411 2,286.00 1,444.00 86,868 0 None 1,462.33 0.64 2.95

Separator variables 0 360 125.92 76.00 4,785 0 None 81.59 0.65 2.75

Clusters per variable 1 9 7.37 8.00 5,536 MAX VALUE 1,454.01 1.92 0.26 1.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,221	11,670	3,008.97	1,520.00	114,341	MAX VALUE	295.06	2,535.10	0.84	2.95
Variables per cluster	69	487	145.68	77.00	5,536	MAX VALUE	181.75	107.30	0.74	2.75
Separator constraints	0	6,411	2,286.00	1,444.00	86,868	0	None	1,462.33	0.64	2.95
Separator variables	0	360	125.92	76.00	4,785	0	None	81.59	0.65	2.75
Clusters per variable	1	9	7.37	8.00	5,536	MAX VALUE	1,454.01	1.92	0.26	1.52

Primal graph

Density: 96.54%
MCB compute time (ms): None
MCB cycles: None
Triangles: 8,889
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-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 38.62 0.25 -1.41 0.00 0.00 2.42

Degree 34 39 37.65 38.00 1,506 MAX VALUE 145.12 1.13 0.03 1.41

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	38.62	0.25	-1.41	0.00	0.00	2.42
Degree	34	39	37.65	38.00	1,506	MAX VALUE	145.12	1.13	0.03	1.41
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: 9,627

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): 46,017
MCB cycles: 26,871
Triangles: 337,767
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 381.53 0.00 -511.95 0.00 0.00 2.22

Degree 68 76 73.37 73.00 55,246 MAX VALUE 3,234.33 1.54 0.02 1.81

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 80,613 MAX VALUE 29,520.80 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	381.53	0.00	-511.95	0.00	0.00	2.22
Degree	68	76	73.37	73.00	55,246	MAX VALUE	3,234.33	1.54	0.02	1.81
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	80,613	MAX VALUE	29,520.80	0.00	0.00	0.00

Minimal dual graph

Density: 0.52%
MCB compute time (ms): 10,171
MCB cycles: 716

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 1,001.90 0.96 0.25 1.25

Eccentricity 9 14 11.74 12.00 8,841 MAX VALUE 1,851.30 1.11 0.09 1.51

MCB cycle size 3 13 6.03 6.00 4,316 MAX VALUE 1,268.75 1.31 0.22 1.62

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	1,001.90	0.96	0.25	1.25
Eccentricity	9	14	11.74	12.00	8,841	MAX VALUE	1,851.30	1.11	0.09	1.51
MCB cycle size	3	13	6.03	6.00	4,316	MAX VALUE	1,268.75	1.31	0.22	1.62

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: 6.43%

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

Clustering coefficient 0.48 1.00 0.81 0.77 609.98 0.00 -172.28 0.15 0.19 4.05

Degree 2 221 48.36 9.00 36,418 MAX VALUE 2,066.14 66.64 1.38 3.76

Eccentricity 3 6 4.43 4.00 3,336 MAX VALUE 1,113.37 0.61 0.14 0.93

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	1.00	0.81	0.77	609.98	0.00	-172.28	0.15	0.19	4.05
Degree	2	221	48.36	9.00	36,418	MAX VALUE	2,066.14	66.64	1.38	3.76
Eccentricity	3	6	4.43	4.00	3,336	MAX VALUE	1,113.37	0.61	0.14	0.93

Incidence graph

Density: 0.48%
MCB compute time (ms): 1,212
MCB cycles: 714
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-51-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 667.05 7.81 2.06 0.27

Eccentricity 3 5 4.05 4.00 3,213 MAX VALUE 1,107.83 0.27 0.07 0.31

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