XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-78-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:31
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 180

General features

Coarse blocks: 9,000
Value tables: 40

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

Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Coarse blocks size 2 22 12.49 12.00 112,402 MAX VALUE 22,533.30 2.49 0.20 2.33

Relational linkage 0.08 0.64 0.36 0.36 356.44 0.00 -1,049.64 0.06 0.18 1.88

Tightness 0.46 0.56 0.50 0.50 90.08 0.00 -124.75 0.02 0.04 3.73

Tuples 276 339 312.23 311.00 56,201 MAX VALUE 1,033.73 12.25 0.04 3.73

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 2 16 9.00 9.00 360 1.54e+37 85.63 2.71 0.30 2.26

Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 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	360	MAX VALUE	124.77	0.00	0.00	0.00
Coarse blocks size	2	22	12.49	12.00	112,402	MAX VALUE	22,533.30	2.49	0.20	2.33
Relational linkage	0.08	0.64	0.36	0.36	356.44	0.00	-1,049.64	0.06	0.18	1.88
Tightness	0.46	0.56	0.50	0.50	90.08	0.00	-124.75	0.02	0.04	3.73
Tuples	276	339	312.23	311.00	56,201	MAX VALUE	1,033.73	12.25	0.04	3.73
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	2	16	9.00	9.00	360	1.54e+37	85.63	2.71	0.30	2.26
Value table partitions	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 20
Number of leaves: 11
Tree depth: 3
CIR: 0.11
Independent Cluster Pairs: 19
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/Tree1.json

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

Cluster constraints 3 60 22.15 18.50 443 3.54e+24 56.53 15.54 0.70 2.86

Variables per cluster 3 21 10.90 9.50 218 6.45e+19 45.61 4.89 0.45 2.28

Separator constraints 0 55 13.15 10.00 263 0 None 13.31 1.01 2.62

Separator variables 0 20 8.90 8.00 178 0 None 4.76 0.54 2.35

Clusters per var 1 13 5.45 6.50 218 1.59e+23 53.42 3.77 0.69 2.14

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	60	22.15	18.50	443	3.54e+24	56.53	15.54	0.70	2.86
Variables per cluster	3	21	10.90	9.50	218	6.45e+19	45.61	4.89	0.45	2.28
Separator constraints	0	55	13.15	10.00	263	0	None	13.31	1.01	2.62
Separator variables	0	20	8.90	8.00	178	0	None	4.76	0.54	2.35
Clusters per var	1	13	5.45	6.50	218	1.59e+23	53.42	3.77	0.69	2.14

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/DualTree1.json

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

Cluster constraints 27 371 128.55 97.00 4,885 MAX VALUE 175.56 89.86 0.70 3.46

Variables per cluster 9 83 29.24 21.50 1,111 MAX VALUE 121.47 19.12 0.65 3.32

Separator constraints 0 197 86.79 73.50 3,298 0 None 53.19 0.61 3.49

Separator variables 0 60 24.50 20.00 931 0 None 14.47 0.59 3.19

Clusters per variable 1 10 6.17 7.00 1,111 MAX VALUE 299.44 2.62 0.42 2.11

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	27	371	128.55	97.00	4,885	MAX VALUE	175.56	89.86	0.70	3.46
Variables per cluster	9	83	29.24	21.50	1,111	MAX VALUE	121.47	19.12	0.65	3.32
Separator constraints	0	197	86.79	73.50	3,298	0	None	53.19	0.61	3.49
Separator variables	0	60	24.50	20.00	931	0	None	14.47	0.59	3.19
Clusters per variable	1	10	6.17	7.00	1,111	MAX VALUE	299.44	2.62	0.42	2.11

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 173
Triangles: 125
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/Primal1.json

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

Clustering coefficient 0.10 1.00 0.26 0.24 10.27 0.00 -57.62 0.14 0.53 3.08

Degree 2 16 9.00 9.00 360 1.54e+37 85.63 2.71 0.30 2.26

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.36 3.00 582 MAX VALUE 208.18 0.48 0.14 0.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.10	1.00	0.26	0.24	10.27	0.00	-57.62	0.14	0.53	3.08
Degree	2	16	9.00	9.00	360	1.54e+37	85.63	2.71	0.30	2.26
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.36	3.00	582	MAX VALUE	208.18	0.48	0.14	0.66

Triangulated primal graph

Density: 49.74%
MCB compute time (ms): 9
MCB cycles: 362
Triangles: 2,260

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

Clustering coefficient 0.61 1.00 0.84 0.81 33.51 0.00 -7.50 0.12 0.14 2.96

Degree 2 32 19.40 25.50 776 MAX VALUE 110.88 9.61 0.50 2.72

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,086 MAX VALUE 397.70 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.61	1.00	0.84	0.81	33.51	0.00	-7.50	0.12	0.14	2.96
Degree	2	32	19.40	25.50	776	MAX VALUE	110.88	9.61	0.50	2.72
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,086	MAX VALUE	397.70	0.00	0.00	0.00

Dual graph

Density: 9.85%
MCB compute time (ms): 198
MCB cycles: 2,269
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/Dual1.json

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

Clustering coefficient 0.45 0.87 0.51 0.50 91.68 0.00 -122.02 0.05 0.09 4.17

Degree 8 28 17.63 17.00 3,174 MAX VALUE 512.77 3.53 0.20 2.62

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.41 3.00 7,744 MAX VALUE 2,755.47 0.58 0.17 0.80

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.87	0.51	0.50	91.68	0.00	-122.02	0.05	0.09	4.17
Degree	8	28	17.63	17.00	3,174	MAX VALUE	512.77	3.53	0.20	2.62
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.41	3.00	7,744	MAX VALUE	2,755.47	0.58	0.17	0.80

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 78
MCB cycles: 141

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 0.04 7.99 0.10

Degree 2 6 3.56 3.00 640 MAX VALUE 223.93 0.78 0.22 1.15

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.68 7.00 942 MAX VALUE 265.54 1.13 0.17 1.50

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	0.04	7.99	0.10
Degree	2	6	3.56	3.00	640	MAX VALUE	223.93	0.78	0.22	1.15
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.68	7.00	942	MAX VALUE	265.54	1.13	0.17	1.50

Triangulated dual graph

Density: 47.89%
Triangles: 207,604

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

Clustering coefficient 0.71 1.00 0.84 0.82 150.42 0.00 -33.29 0.09 0.10 4.69

Degree 8 133 85.72 102.00 15,430 MAX VALUE 766.66 40.50 0.47 3.91

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	0.71	1.00	0.84	0.82	150.42	0.00	-33.29	0.09	0.10	4.69
Degree	8	133	85.72	102.00	15,430	MAX VALUE	766.66	40.50	0.47	3.91
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.12%

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

Clustering coefficient 0.52 1.00 0.79 0.72 142.09 0.00 -46.13 0.16 0.20 3.30

Degree 2 64 19.90 7.00 3,582 MAX VALUE 415.60 21.84 1.10 3.08

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	0.52	1.00	0.79	0.72	142.09	0.00	-46.13	0.16	0.20	3.30
Degree	2	64	19.90	7.00	3,582	MAX VALUE	415.60	21.84	1.10	3.08
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 43
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-78-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 16 3.27 2.00 720 MAX VALUE 210.40 2.94 0.90 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.44 6.00 908 MAX VALUE 261.56 0.83 0.13 0.53

XCSP 2.1 Benchmarks