XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-11-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:23
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 4 22 12.42 12.00 111,788 MAX VALUE 22,479.80 2.50 0.20 2.33

Relational linkage 0.16 0.52 0.35 0.36 352.88 0.00 -1,058.20 0.06 0.17 1.84

Tightness 0.45 0.55 0.50 0.50 90.57 0.00 -123.77 0.02 0.04 3.76

Tuples 281 341 310.52 311.00 55,894 MAX VALUE 1,032.74 12.52 0.04 3.76

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

Value table constraints 4 13 9.00 9.00 360 3.65e+37 86.49 2.25 0.25 2.02

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	4	22	12.42	12.00	111,788	MAX VALUE	22,479.80	2.50	0.20	2.33
Relational linkage	0.16	0.52	0.35	0.36	352.88	0.00	-1,058.20	0.06	0.17	1.84
Tightness	0.45	0.55	0.50	0.50	90.57	0.00	-123.77	0.02	0.04	3.76
Tuples	281	341	310.52	311.00	55,894	MAX VALUE	1,032.74	12.52	0.04	3.76
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	13	9.00	9.00	360	3.65e+37	86.49	2.25	0.25	2.02
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: 19
Number of leaves: 9
Tree depth: 4
CIR: 0.06
Independent Cluster Pairs: 9
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/Tree1.json

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

Cluster constraints 5 61 24.26 17.00 461 1.59e+24 55.73 16.42 0.68 2.73

Variables per cluster 5 22 12.00 11.00 228 5.63e+19 45.48 5.07 0.42 2.16

Separator constraints 0 45 14.79 9.00 281 0 None 14.47 0.98 2.55

Separator variables 0 19 9.89 8.00 188 0 None 5.06 0.51 2.16

Clusters per var 1 12 5.70 7.00 228 3.42e+24 56.49 3.65 0.64 2.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	61	24.26	17.00	461	1.59e+24	55.73	16.42	0.68	2.73
Variables per cluster	5	22	12.00	11.00	228	5.63e+19	45.48	5.07	0.42	2.16
Separator constraints	0	45	14.79	9.00	281	0	None	14.47	0.98	2.55
Separator variables	0	19	9.89	8.00	188	0	None	5.06	0.51	2.16
Clusters per var	1	12	5.70	7.00	228	3.42e+24	56.49	3.65	0.64	2.23

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 130
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/DualTree1.json

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

Cluster constraints 21 369 125.03 102.50 4,751 MAX VALUE 175.26 83.57 0.67 3.53

Variables per cluster 9 87 29.32 23.00 1,114 MAX VALUE 121.95 18.75 0.64 3.24

Separator constraints 0 204 84.47 72.00 3,210 0 None 49.45 0.59 3.60

Separator variables 0 61 24.58 21.00 934 0 None 14.18 0.58 3.16

Clusters per variable 1 11 6.19 7.00 1,114 MAX VALUE 299.92 2.62 0.42 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	21	369	125.03	102.50	4,751	MAX VALUE	175.26	83.57	0.67	3.53
Variables per cluster	9	87	29.32	23.00	1,114	MAX VALUE	121.95	18.75	0.64	3.24
Separator constraints	0	204	84.47	72.00	3,210	0	None	49.45	0.59	3.60
Separator variables	0	61	24.58	21.00	934	0	None	14.18	0.58	3.16
Clusters per variable	1	11	6.19	7.00	1,114	MAX VALUE	299.92	2.62	0.42	2.15

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 147
Triangles: 118
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/Primal1.json

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

Clustering coefficient 0.07 0.36 0.22 0.21 8.97 0.00 -61.77 0.06 0.29 3.23

Degree 4 13 9.00 9.00 360 3.65e+37 86.49 2.25 0.25 2.02

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.29 3.00 483 MAX VALUE 173.51 0.47 0.14 0.62

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.07	0.36	0.22	0.21	8.97	0.00	-61.77	0.06	0.29	3.23
Degree	4	13	9.00	9.00	360	3.65e+37	86.49	2.25	0.25	2.02
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.29	3.00	483	MAX VALUE	173.51	0.47	0.14	0.62

Triangulated primal graph

Density: 53.72%
MCB compute time (ms): 9
MCB cycles: 415
Triangles: 2,619

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

Clustering coefficient 0.67 1.00 0.84 0.81 33.67 0.00 -7.21 0.11 0.13 3.16

Degree 4 32 20.95 27.00 838 MAX VALUE 115.36 9.52 0.45 2.65

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,245 MAX VALUE 455.92 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.67	1.00	0.84	0.81	33.67	0.00	-7.21	0.11	0.13	3.16
Degree	4	32	20.95	27.00	838	MAX VALUE	115.36	9.52	0.45	2.65
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,245	MAX VALUE	455.92	0.00	0.00	0.00

Dual graph

Density: 9.57%
MCB compute time (ms): 205
MCB cycles: 2,523
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/Dual1.json

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

Clustering coefficient 0.45 0.67 0.50 0.49 89.90 0.00 -125.19 0.03 0.05 3.93

Degree 8 24 17.12 17.00 3,082 MAX VALUE 508.04 3.11 0.18 2.46

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.54 3.00 8,928 MAX VALUE 3,151.14 0.63 0.18 0.89

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.67	0.50	0.49	89.90	0.00	-125.19	0.03	0.05	3.93
Degree	8	24	17.12	17.00	3,082	MAX VALUE	508.04	3.11	0.18	2.46
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.54	3.00	8,928	MAX VALUE	3,151.14	0.63	0.18	0.89

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 69
MCB cycles: 142

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

Clustering coefficient 0.00 0.17 0.00 0.00 0.37 0.00 None 0.02 7.94 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 224.90 0.69 0.19 1.03

Eccentricity None None None None None None None None None None

MCB cycle size 3 10 6.89 7.00 978 MAX VALUE 271.80 1.14 0.17 1.47

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.37	0.00	None	0.02	7.94	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	224.90	0.69	0.19	1.03
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	10	6.89	7.00	978	MAX VALUE	271.80	1.14	0.17	1.47

Triangulated dual graph

Density: 47.28%
Triangles: 202,234

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

Clustering coefficient 0.70 1.00 0.83 0.81 149.99 0.00 -33.83 0.09 0.11 4.65

Degree 8 132 84.63 94.00 15,234 MAX VALUE 764.82 40.32 0.48 3.92

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	0.70	1.00	0.83	0.81	149.99	0.00	-33.83	0.09	0.11	4.65
Degree	8	132	84.63	94.00	15,234	MAX VALUE	764.82	40.32	0.48	3.92
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.09%

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

Clustering coefficient 0.53 1.00 0.80 0.75 144.46 0.00 -42.85 0.15 0.19 3.27

Degree 2 66 21.63 7.00 3,894 MAX VALUE 426.16 23.70 1.10 3.10

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	0.53	1.00	0.80	0.75	144.46	0.00	-42.85	0.15	0.19	3.27
Degree	2	66	21.63	7.00	3,894	MAX VALUE	426.16	23.70	1.10	3.10
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 45
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-11-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 13 3.27 2.00 720 MAX VALUE 211.26 2.86 0.88 0.84

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 6.51 6.00 918 MAX VALUE 262.93 0.90 0.14 0.59

XCSP 2.1 Benchmarks