XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-8-753-100-76-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 2 8 7.19 7.00 86,646 MAX VALUE 23,674.90 0.86 0.12 1.16

Relational linkage 0.25 0.75 0.62 0.62 198.12 0.00 -156.66 0.08 0.14 1.01

Tightness 0.02 0.23 0.10 0.09 76.08 0.00 -1,787.49 0.04 0.37 2.28

Tuples 49 63 57.53 58.00 43,323 MAX VALUE 3,050.76 2.42 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 36 39 37.65 38.00 1,506 MAX VALUE 145.12 0.85 0.02 1.24

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	7.19	7.00	86,646	MAX VALUE	23,674.90	0.86	0.12	1.16
Relational linkage	0.25	0.75	0.62	0.62	198.12	0.00	-156.66	0.08	0.14	1.01
Tightness	0.02	0.23	0.10	0.09	76.08	0.00	-1,787.49	0.04	0.37	2.28
Tuples	49	63	57.53	58.00	43,323	MAX VALUE	3,050.76	2.42	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	36	39	37.65	38.00	1,506	MAX VALUE	145.12	0.85	0.02	1.24
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-2-40-8-753-100-76-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/Tree1.json

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

Cluster constraints 645 681 657.33 646.00 1,972 283,752,000 19.46 16.74 0.03 1.10

Variables per cluster 37 38 37.33 37.00 112 52,022 10.86 0.47 0.01 0.64

Separator constraints 0 610 406.33 609.00 1,219 0 None 287.32 0.71 1.10

Separator variables 0 36 24.00 36.00 72 0 None 16.97 0.71 0.64

Clusters per var 1 3 2.80 3.00 112 2.67e+17 40.13 0.51 0.18 0.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	645	681	657.33	646.00	1,972	283,752,000	19.46	16.74	0.03	1.10
Variables per cluster	37	38	37.33	37.00	112	52,022	10.86	0.47	0.01	0.64
Separator constraints	0	610	406.33	609.00	1,219	0	None	287.32	0.71	1.10
Separator variables	0	36	24.00	36.00	72	0	None	16.97	0.71	0.64
Clusters per var	1	3	2.80	3.00	112	2.67e+17	40.13	0.51	0.18	0.52

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-2-40-8-753-100-76-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/DualTree1.json

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

Cluster constraints 1,292 11,876 3,035.68 1,520.00 115,356 MAX VALUE 295.32 2,578.03 0.85 2.82

Variables per cluster 71 492 146.40 77.00 5,563 MAX VALUE 181.89 108.38 0.74 2.49

Separator constraints 0 6,622 2,309.05 1,444.00 87,744 0 None 1,495.06 0.65 2.82

Separator variables 0 366 126.58 76.00 4,810 0 None 82.57 0.65 2.49

Clusters per variable 1 9 7.39 8.00 5,563 MAX VALUE 1,459.61 1.92 0.26 1.51

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,292	11,876	3,035.68	1,520.00	115,356	MAX VALUE	295.32	2,578.03	0.85	2.82
Variables per cluster	71	492	146.40	77.00	5,563	MAX VALUE	181.89	108.38	0.74	2.49
Separator constraints	0	6,622	2,309.05	1,444.00	87,744	0	None	1,495.06	0.65	2.82
Separator variables	0	366	126.58	76.00	4,810	0	None	82.57	0.65	2.49
Clusters per variable	1	9	7.39	8.00	5,563	MAX VALUE	1,459.61	1.92	0.26	1.51

Primal graph

Density: 96.54%
MCB compute time (ms): None
MCB cycles: None
Triangles: 8,877
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/Primal1.json

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

Clustering coefficient 0.96 0.97 0.96 0.96 38.58 0.24 -1.45 0.00 0.00 2.14

Degree 36 39 37.65 38.00 1,506 MAX VALUE 145.12 0.85 0.02 1.24

Eccentricity 1 2 1.85 2.00 74 1.72e+10 23.57 0.36 0.19 0.42

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	0.96	0.96	38.58	0.24	-1.45	0.00	0.00	2.14
Degree	36	39	37.65	38.00	1,506	MAX VALUE	145.12	0.85	0.02	1.24
Eccentricity	1	2	1.85	2.00	74	1.72e+10	23.57	0.36	0.19	0.42
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 99.36%
MCB compute time (ms): None
MCB cycles: None
Triangles: 9,696

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

Clustering coefficient 0.99 1.00 0.99 0.99 39.76 0.79 -0.24 0.00 0.00 0.52

Degree 36 39 38.75 39.00 1,550 MAX VALUE 146.28 0.70 0.02 0.52

Eccentricity 1 2 1.15 1.00 46 64 4.16 0.36 0.31 0.42

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	39.76	0.79	-0.24	0.00	0.00	0.52
Degree	36	39	38.75	39.00	1,550	MAX VALUE	146.28	0.70	0.02	0.52
Eccentricity	1	2	1.15	1.00	46	64	4.16	0.36	0.31	0.42
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 9.75%
MCB compute time (ms): 24,119
MCB cycles: 26,860
Triangles: 337,359
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 381.44 0.00 -512.13 0.00 0.00 1.96

Degree 70 76 73.34 73.00 55,224 MAX VALUE 3,234.10 1.17 0.02 1.57

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 80,580 MAX VALUE 29,508.70 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	381.44	0.00	-512.13	0.00	0.00	1.96
Degree	70	76	73.34	73.00	55,224	MAX VALUE	3,234.10	1.17	0.02	1.57
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	80,580	MAX VALUE	29,508.70	0.00	0.00	0.00

Minimal dual graph

Density: 0.52%
MCB compute time (ms): 10,441
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 1,002.43 0.95 0.24 1.25

Eccentricity 9 15 11.84 12.00 8,917 MAX VALUE 1,857.21 1.20 0.10 1.58

MCB cycle size 3 13 6.13 6.00 4,384 MAX VALUE 1,280.36 1.27 0.21 1.59

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	1,002.43	0.95	0.24	1.25
Eccentricity	9	15	11.84	12.00	8,917	MAX VALUE	1,857.21	1.20	0.10	1.58
MCB cycle size	3	13	6.13	6.00	4,384	MAX VALUE	1,280.36	1.27	0.21	1.59

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: 6.60%

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

Clustering coefficient 0.48 1.00 0.82 0.77 614.73 0.00 -166.03 0.15 0.19 4.03

Degree 2 214 49.64 9.00 37,378 MAX VALUE 2,066.25 69.11 1.39 3.71

Eccentricity 3 6 4.56 5.00 3,436 MAX VALUE 1,137.11 0.56 0.12 0.84

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	1.00	0.82	0.77	614.73	0.00	-166.03	0.15	0.19	4.03
Degree	2	214	49.64	9.00	37,378	MAX VALUE	2,066.25	69.11	1.39	3.71
Eccentricity	3	6	4.56	5.00	3,436	MAX VALUE	1,137.11	0.56	0.12	0.84

Incidence graph

Density: 0.48%
MCB compute time (ms): 876
MCB cycles: 714
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-76-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 7.80 2.05 0.26

Eccentricity 3 5 4.04 4.00 3,202 MAX VALUE 1,105.64 0.23 0.06 0.23

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