XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-8-753-100-19-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 7.19 7.00 86,674 MAX VALUE 23,680.00 0.85 0.12 1.16

Relational linkage 0.38 0.75 0.63 0.62 201.88 0.00 -150.10 0.08 0.13 0.97

Tightness 0.00 0.23 0.10 0.09 75.86 0.00 None 0.04 0.39 2.31

Tuples 49 64 57.55 58.00 43,337 MAX VALUE 3,050.97 2.49 0.04 2.31

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 145.12 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	7.19	7.00	86,674	MAX VALUE	23,680.00	0.85	0.12	1.16
Relational linkage	0.38	0.75	0.63	0.62	201.88	0.00	-150.10	0.08	0.13	0.97
Tightness	0.00	0.23	0.10	0.09	75.86	0.00	None	0.04	0.39	2.31
Tuples	49	64	57.55	58.00	43,337	MAX VALUE	3,050.97	2.49	0.04	2.31
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	145.12	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-2-40-8-753-100-19-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-ext/Tree1.json

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

Cluster constraints 610 683 657.67 680.00 1,973 283,308,000 19.46 33.73 0.05 1.10

Variables per cluster 36 38 37.33 38.00 112 51,984 10.86 0.94 0.03 0.64

Separator constraints 0 646 407.00 575.00 1,221 0 None 289.25 0.71 1.10

Separator variables 0 37 24.00 35.00 72 0 None 16.99 0.71 1.10

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	610	683	657.67	680.00	1,973	283,308,000	19.46	33.73	0.05	1.10
Variables per cluster	36	38	37.33	38.00	112	51,984	10.86	0.94	0.03	0.64
Separator constraints	0	646	407.00	575.00	1,221	0	None	289.25	0.71	1.10
Separator variables	0	37	24.00	35.00	72	0	None	16.99	0.71	1.10
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-2-40-8-753-100-19-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-ext/DualTree1.json

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

Cluster constraints 1,221 11,631 3,021.92 1,520.00 114,833 MAX VALUE 295.18 2,552.94 0.84 2.96

Variables per cluster 69 487 146.00 77.00 5,548 MAX VALUE 181.82 107.74 0.74 2.82

Separator constraints 0 6,525 2,297.00 1,444.00 87,286 0 None 1,479.25 0.64 2.96

Separator variables 0 363 126.21 76.00 4,796 0 None 82.03 0.65 2.82

Clusters per variable 1 9 7.38 8.00 5,548 MAX VALUE 1,456.54 1.92 0.26 1.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1,221	11,631	3,021.92	1,520.00	114,833	MAX VALUE	295.18	2,552.94	0.84	2.96
Variables per cluster	69	487	146.00	77.00	5,548	MAX VALUE	181.82	107.74	0.74	2.82
Separator constraints	0	6,525	2,297.00	1,444.00	87,286	0	None	1,479.25	0.64	2.96
Separator variables	0	363	126.21	76.00	4,796	0	None	82.03	0.65	2.82
Clusters per variable	1	9	7.38	8.00	5,548	MAX VALUE	1,456.54	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-2-40-8-753-100-19-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-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 2.12

Degree 35 39 37.65 38.00 1,506 MAX VALUE 145.12 1.13 0.03 1.41

Eccentricity 1 2 1.70 2.00 68 268,435,000 19.41 0.46 0.27 0.61

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	2.12
Degree	35	39	37.65	38.00	1,506	MAX VALUE	145.12	1.13	0.03	1.41
Eccentricity	1	2	1.70	2.00	68	268,435,000	19.41	0.46	0.27	0.61
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): 32,542
MCB cycles: 26,871
Triangles: 337,771
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-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 2.18

Degree 68 76 73.37 74.00 55,246 MAX VALUE 3,234.33 1.55 0.02 1.82

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	2.18
Degree	68	76	73.37	74.00	55,246	MAX VALUE	3,234.33	1.55	0.02	1.82
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): 10,422
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 1,002.21 0.96 0.25 1.26

Eccentricity 9 14 11.39 11.00 8,576 MAX VALUE 1,827.98 1.14 0.10 1.53

MCB cycle size 3 10 6.06 6.00 4,330 MAX VALUE 1,270.43 1.27 0.21 1.61

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	1,002.21	0.96	0.25	1.26
Eccentricity	9	14	11.39	11.00	8,576	MAX VALUE	1,827.98	1.14	0.10	1.53
MCB cycle size	3	10	6.06	6.00	4,330	MAX VALUE	1,270.43	1.27	0.21	1.61

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: 6.70%

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

Clustering coefficient 0.47 1.00 0.81 0.77 613.15 0.00 -167.80 0.15 0.19 4.07

Degree 2 207 50.40 9.00 37,950 MAX VALUE 2,076.95 70.05 1.39 3.74

Eccentricity 3 6 4.15 4.00 3,126 MAX VALUE 1,062.98 0.63 0.15 0.94

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.81	0.77	613.15	0.00	-167.80	0.15	0.19	4.07
Degree	2	207	50.40	9.00	37,950	MAX VALUE	2,076.95	70.05	1.39	3.74
Eccentricity	3	6	4.15	4.00	3,126	MAX VALUE	1,062.98	0.63	0.15	0.94

Incidence graph

Density: 0.48%
MCB compute time (ms): 969
MCB cycles: 714
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.1/normalized-rand-2-40-8-753-100-19-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 3,214 MAX VALUE 1,107.93 0.28 0.07 0.33

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