XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-8-753-100-63-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 7.20 7.00 86,764 MAX VALUE 23,693.70 0.85 0.12 1.15

Relational linkage 0.38 0.88 0.63 0.62 202.00 0.00 -150.27 0.08 0.13 1.01

Tightness 0.00 0.22 0.10 0.09 75.16 0.00 None 0.04 0.38 2.29

Tuples 50 64 57.61 58.00 43,382 MAX VALUE 3,051.78 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 35 39 37.65 38.00 1,506 MAX VALUE 145.11 1.17 0.03 1.44

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	7.20	7.00	86,764	MAX VALUE	23,693.70	0.85	0.12	1.15
Relational linkage	0.38	0.88	0.63	0.62	202.00	0.00	-150.27	0.08	0.13	1.01
Tightness	0.00	0.22	0.10	0.09	75.16	0.00	None	0.04	0.38	2.29
Tuples	50	64	57.61	58.00	43,382	MAX VALUE	3,051.78	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	35	39	37.65	38.00	1,506	MAX VALUE	145.11	1.17	0.03	1.44
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-2-40-8-753-100-63-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/Tree1.json

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

Cluster constraints 575 680 644.67 679.00 1,934 265,489,000 19.40 49.26 0.08 1.10

Variables per cluster 35 38 37.00 38.00 111 50,540 10.83 1.41 0.04 0.64

Separator constraints 0 643 394.67 541.00 1,184 0 None 282.16 0.71 1.10

Separator variables 0 37 23.67 34.00 71 0 None 16.78 0.71 1.10

Clusters per var 1 3 2.77 3.00 111 1.78e+17 39.72 0.52 0.19 0.57

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	575	680	644.67	679.00	1,934	265,489,000	19.40	49.26	0.08	1.10
Variables per cluster	35	38	37.00	38.00	111	50,540	10.83	1.41	0.04	0.64
Separator constraints	0	643	394.67	541.00	1,184	0	None	282.16	0.71	1.10
Separator variables	0	37	23.67	34.00	71	0	None	16.78	0.71	1.10
Clusters per var	1	3	2.77	3.00	111	1.78e+17	39.72	0.52	0.19	0.57

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-2-40-8-753-100-63-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/DualTree1.json

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

Cluster constraints 1,185 11,467 3,018.47 1,520.00 114,702 MAX VALUE 295.01 2,570.55 0.85 3.00

Variables per cluster 68 485 145.95 77.00 5,546 MAX VALUE 181.74 108.25 0.74 2.75

Separator constraints 0 6,627 2,297.21 1,444.00 87,294 0 None 1,501.13 0.65 3.00

Separator variables 0 366 126.21 76.00 4,796 0 None 82.63 0.65 2.75

Clusters per variable 1 9 7.39 8.00 5,546 MAX VALUE 1,454.33 1.92 0.26 1.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,185	11,467	3,018.47	1,520.00	114,702	MAX VALUE	295.01	2,570.55	0.85	3.00
Variables per cluster	68	485	145.95	77.00	5,546	MAX VALUE	181.74	108.25	0.74	2.75
Separator constraints	0	6,627	2,297.21	1,444.00	87,294	0	None	1,501.13	0.65	3.00
Separator variables	0	366	126.21	76.00	4,796	0	None	82.63	0.65	2.75
Clusters per variable	1	9	7.39	8.00	5,546	MAX VALUE	1,454.33	1.92	0.26	1.52

Primal graph

Density: 96.54%
MCB compute time (ms): None
MCB cycles: None
Triangles: 8,890
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/Primal1.json

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

Clustering coefficient 0.96 0.97 0.97 0.97 38.62 0.25 -1.40 0.00 0.00 2.19

Degree 35 39 37.65 38.00 1,506 MAX VALUE 145.11 1.17 0.03 1.44

Eccentricity 1 2 1.68 2.00 67 134,218,000 18.71 0.47 0.28 0.63

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	0.97	38.62	0.25	-1.40	0.00	0.00	2.19
Degree	35	39	37.65	38.00	1,506	MAX VALUE	145.11	1.17	0.03	1.44
Eccentricity	1	2	1.68	2.00	67	134,218,000	18.71	0.47	0.28	0.63
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: 9,697

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 0.57

Degree 35 39 38.75 39.00 1,550 MAX VALUE 146.28 0.73 0.02 0.55

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	0.57
Degree	35	39	38.75	39.00	1,550	MAX VALUE	146.28	0.73	0.02	0.55
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: 9.76%
MCB compute time (ms): 27,049
MCB cycles: 26,873
Triangles: 337,846
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/Dual1.json

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

Clustering coefficient 0.51 0.51 0.51 0.51 381.54 0.00 -511.93 0.00 0.00 2.21

Degree 69 76 73.37 73.00 55,250 MAX VALUE 3,234.37 1.61 0.02 1.85

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 80,619 MAX VALUE 29,523.00 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	381.54	0.00	-511.93	0.00	0.00	2.21
Degree	69	76	73.37	73.00	55,250	MAX VALUE	3,234.37	1.61	0.02	1.85
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	80,619	MAX VALUE	29,523.00	0.00	0.00	0.00

Minimal dual graph

Density: 0.52%
MCB compute time (ms): 9,732
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 1,002.09 0.96 0.25 1.26

Eccentricity 8 14 11.70 12.00 8,813 MAX VALUE 1,848.20 1.21 0.10 1.60

MCB cycle size 3 15 6.09 6.00 4,354 MAX VALUE 1,275.32 1.29 0.21 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	1,002.09	0.96	0.25	1.26
Eccentricity	8	14	11.70	12.00	8,813	MAX VALUE	1,848.20	1.21	0.10	1.60
MCB cycle size	3	15	6.09	6.00	4,354	MAX VALUE	1,275.32	1.29	0.21	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: 6.80%

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

Clustering coefficient 0.52 1.00 0.82 0.77 614.57 0.00 -165.91 0.15 0.18 4.06

Degree 2 211 51.14 9.00 38,506 MAX VALUE 2,078.52 71.32 1.39 3.74

Eccentricity 3 5 3.96 4.00 2,983 MAX VALUE 1,027.92 0.59 0.15 0.89

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.52	1.00	0.82	0.77	614.57	0.00	-165.91	0.15	0.18	4.06
Degree	2	211	51.14	9.00	38,506	MAX VALUE	2,078.52	71.32	1.39	3.74
Eccentricity	3	5	3.96	4.00	2,983	MAX VALUE	1,027.92	0.59	0.15	0.89

Incidence graph

Density: 0.48%
MCB compute time (ms): 937
MCB cycles: 714
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-63-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 3,211 MAX VALUE 1,107.20 0.28 0.07 0.32

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