XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-8-753-100-99-ext
Number of variables: 40
Number of constraints: 753
Satisfiable: True
Timestamp: 2025-07-27 21:31:25
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 2 8 7.20 7.00 86,732 MAX VALUE 23,688.90 0.85 0.12 1.16

Relational linkage 0.25 0.75 0.63 0.62 201.50 0.00 -151.30 0.09 0.14 1.00

Tightness 0.00 0.22 0.10 0.09 75.41 0.00 None 0.04 0.38 2.30

Tuples 50 64 57.59 58.00 43,366 MAX VALUE 3,051.50 2.45 0.04 2.30

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 1.11 0.03 1.40

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	2	8	7.20	7.00	86,732	MAX VALUE	23,688.90	0.85	0.12	1.16
Relational linkage	0.25	0.75	0.63	0.62	201.50	0.00	-151.30	0.09	0.14	1.00
Tightness	0.00	0.22	0.10	0.09	75.41	0.00	None	0.04	0.38	2.30
Tuples	50	64	57.59	58.00	43,366	MAX VALUE	3,051.50	2.45	0.04	2.30
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	1.11	0.03	1.40
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: 4
Number of leaves: 2
Tree depth: 2
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/Tree1.json

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

Cluster constraints 578 647 629.25 646.00 2,517 1.56e+11 25.77 29.59 0.05 1.04

Variables per cluster 35 37 36.50 37.00 146 1,772,860 14.39 0.87 0.02 0.56

Separator constraints 0 611 441.25 577.00 1,765 0 None 256.20 0.58 1.39

Separator variables 0 36 26.50 35.00 106 0 None 15.32 0.58 1.04

Clusters per var 1 4 3.65 4.00 146 5.98e+21 50.14 0.79 0.22 0.71

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	578	647	629.25	646.00	2,517	1.56e+11	25.77	29.59	0.05	1.04
Variables per cluster	35	37	36.50	37.00	146	1,772,860	14.39	0.87	0.02	0.56
Separator constraints	0	611	441.25	577.00	1,765	0	None	256.20	0.58	1.39
Separator variables	0	36	26.50	35.00	106	0	None	15.32	0.58	1.04
Clusters per var	1	4	3.65	4.00	146	5.98e+21	50.14	0.79	0.22	0.71

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-2-40-8-753-100-99-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/DualTree1.json

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

Cluster constraints 1,222 11,757 3,032.34 1,520.00 115,229 MAX VALUE 295.23 2,581.70 0.85 3.03

Variables per cluster 69 490 146.29 77.00 5,559 MAX VALUE 181.84 108.45 0.74 2.85

Separator constraints 0 6,635 2,307.42 1,444.00 87,682 0 None 1,502.85 0.65 3.03

Separator variables 0 366 126.50 76.00 4,807 0 None 82.70 0.65 2.85

Clusters per variable 1 9 7.39 8.00 5,559 MAX VALUE 1,458.09 1.92 0.26 1.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,222	11,757	3,032.34	1,520.00	115,229	MAX VALUE	295.23	2,581.70	0.85	3.03
Variables per cluster	69	490	146.29	77.00	5,559	MAX VALUE	181.84	108.45	0.74	2.85
Separator constraints	0	6,635	2,307.42	1,444.00	87,682	0	None	1,502.85	0.65	3.03
Separator variables	0	366	126.50	76.00	4,807	0	None	82.70	0.65	2.85
Clusters per variable	1	9	7.39	8.00	5,559	MAX VALUE	1,458.09	1.92	0.26	1.52

Primal graph

Density: 96.54%
MCB compute time (ms): None
MCB cycles: None
Triangles: 8,888
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-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 0.24 -1.41 0.00 0.00 2.37

Degree 34 39 37.65 38.00 1,506 MAX VALUE 145.12 1.11 0.03 1.40

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	0.24	-1.41	0.00	0.00	2.37
Degree	34	39	37.65	38.00	1,506	MAX VALUE	145.12	1.11	0.03	1.40
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: 98.97%
MCB compute time (ms): None
MCB cycles: None
Triangles: 9,591

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

Clustering coefficient 0.99 1.00 0.99 0.99 39.63 0.69 -0.37 0.00 0.00 0.80

Degree 34 39 38.60 39.00 1,544 MAX VALUE 146.12 0.99 0.03 0.74

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	39.63	0.69	-0.37	0.00	0.00	0.80
Degree	34	39	38.60	39.00	1,544	MAX VALUE	146.12	0.99	0.03	0.74
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): 24,195
MCB cycles: 26,870
Triangles: 337,730
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 381.52 0.00 -511.97 0.00 0.00 2.18

Degree 68 76 73.37 73.00 55,244 MAX VALUE 3,234.31 1.51 0.02 1.80

Eccentricity 2 3 2.00 2.00 1,508 MAX VALUE 522.75 0.05 0.03 0.02

MCB cycle size 3 3 3.00 3.00 80,610 MAX VALUE 29,519.70 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	381.52	0.00	-511.97	0.00	0.00	2.18
Degree	68	76	73.37	73.00	55,244	MAX VALUE	3,234.31	1.51	0.02	1.80
Eccentricity	2	3	2.00	2.00	1,508	MAX VALUE	522.75	0.05	0.03	0.02
MCB cycle size	3	3	3.00	3.00	80,610	MAX VALUE	29,519.70	0.00	0.00	0.00

Minimal dual graph

Density: 0.52%
MCB compute time (ms): 9,880
MCB cycles: 715

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 1,002.10 0.96 0.25 1.26

Eccentricity 9 15 11.89 12.00 8,955 MAX VALUE 1,860.53 1.20 0.10 1.59

MCB cycle size 3 15 6.08 6.00 4,349 MAX VALUE 1,275.25 1.25 0.21 1.55

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	1,002.10	0.96	0.25	1.26
Eccentricity	9	15	11.89	12.00	8,955	MAX VALUE	1,860.53	1.20	0.10	1.59
MCB cycle size	3	15	6.08	6.00	4,349	MAX VALUE	1,275.25	1.25	0.21	1.55

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: 7.16%

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

Clustering coefficient 0.47 1.00 0.82 0.78 617.77 0.00 -161.13 0.15 0.18 4.07

Degree 2 215 53.87 9.00 40,562 MAX VALUE 2,097.36 74.80 1.39 3.70

Eccentricity 3 5 4.15 4.00 3,123 MAX VALUE 1,063.23 0.59 0.14 0.89

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.82	0.78	617.77	0.00	-161.13	0.15	0.18	4.07
Degree	2	215	53.87	9.00	40,562	MAX VALUE	2,097.36	74.80	1.39	3.70
Eccentricity	3	5	4.15	4.00	3,123	MAX VALUE	1,063.23	0.59	0.14	0.89

Incidence graph

Density: 0.48%
MCB compute time (ms): 912
MCB cycles: 714
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-99-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 6 4.05 4.00 3,213 MAX VALUE 1,107.75 0.28 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