XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-84-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 4 22 12.57 13.00 113,100 MAX VALUE 22,590.30 2.50 0.20 2.33

Relational linkage 0.16 0.56 0.36 0.36 359.24 0.00 -1,039.33 0.06 0.17 1.84

Tightness 0.45 0.55 0.50 0.50 89.52 0.00 -125.85 0.02 0.04 3.65

Tuples 282 342 314.17 314.00 56,550 MAX VALUE 1,034.87 11.24 0.04 3.65

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

Value table constraints 4 14 9.00 9.50 360 2.28e+37 86.02 2.53 0.28 2.17

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	12.57	13.00	113,100	MAX VALUE	22,590.30	2.50	0.20	2.33
Relational linkage	0.16	0.56	0.36	0.36	359.24	0.00	-1,039.33	0.06	0.17	1.84
Tightness	0.45	0.55	0.50	0.50	89.52	0.00	-125.85	0.02	0.04	3.65
Tuples	282	342	314.17	314.00	56,550	MAX VALUE	1,034.87	11.24	0.04	3.65
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	14	9.00	9.50	360	2.28e+37	86.02	2.53	0.28	2.17
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: 21
Number of leaves: 9
Tree depth: 5
CIR: 0.09
Independent Cluster Pairs: 17
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/Tree1.json

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

Cluster constraints 5 55 25.14 16.00 528 6.43e+26 61.73 17.50 0.70 2.49

Variables per cluster 5 20 11.90 9.00 250 3.60e+21 49.64 5.43 0.46 2.28

Separator constraints 0 49 16.57 8.00 348 0 None 16.15 0.97 2.69

Separator variables 0 19 10.00 8.00 210 0 None 5.59 0.56 2.38

Clusters per var 1 14 6.25 6.50 250 2.99e+25 58.66 4.31 0.69 2.37

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	55	25.14	16.00	528	6.43e+26	61.73	17.50	0.70	2.49
Variables per cluster	5	20	11.90	9.00	250	3.60e+21	49.64	5.43	0.46	2.28
Separator constraints	0	49	16.57	8.00	348	0	None	16.15	0.97	2.69
Separator variables	0	19	10.00	8.00	210	0	None	5.59	0.56	2.38
Clusters per var	1	14	6.25	6.50	250	2.99e+25	58.66	4.31	0.69	2.37

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 137
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/DualTree1.json

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

Cluster constraints 20 359 122.13 100.00 4,641 MAX VALUE 174.84 79.67 0.65 3.56

Variables per cluster 9 85 28.61 22.50 1,087 MAX VALUE 121.16 18.13 0.63 3.11

Separator constraints 0 200 80.87 72.50 3,073 0 None 46.96 0.58 3.56

Separator variables 0 60 23.87 19.50 907 0 None 13.74 0.58 3.17

Clusters per variable 1 11 6.04 7.00 1,087 MAX VALUE 294.08 2.68 0.44 2.18

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	20	359	122.13	100.00	4,641	MAX VALUE	174.84	79.67	0.65	3.56
Variables per cluster	9	85	28.61	22.50	1,087	MAX VALUE	121.16	18.13	0.63	3.11
Separator constraints	0	200	80.87	72.50	3,073	0	None	46.96	0.58	3.56
Separator variables	0	60	23.87	19.50	907	0	None	13.74	0.58	3.17
Clusters per variable	1	11	6.04	7.00	1,087	MAX VALUE	294.08	2.68	0.44	2.18

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 228
Triangles: 113
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/Primal1.json

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

Clustering coefficient 0.10 0.67 0.23 0.22 9.22 0.00 -61.44 0.09 0.41 3.13

Degree 4 14 9.00 9.50 360 2.28e+37 86.02 2.53 0.28 2.17

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.55 4.00 809 MAX VALUE 286.38 0.51 0.14 0.71

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.10	0.67	0.23	0.22	9.22	0.00	-61.44	0.09	0.41	3.13
Degree	4	14	9.00	9.50	360	2.28e+37	86.02	2.53	0.28	2.17
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.55	4.00	809	MAX VALUE	286.38	0.51	0.14	0.71

Triangulated primal graph

Density: 51.28%
MCB compute time (ms): 13
MCB cycles: 382
Triangles: 2,413

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

Clustering coefficient 0.65 1.00 0.84 0.81 33.64 0.00 -7.26 0.11 0.13 3.13

Degree 4 32 20.00 24.50 800 MAX VALUE 112.64 9.56 0.48 2.88

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,146 MAX VALUE 419.67 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.65	1.00	0.84	0.81	33.64	0.00	-7.26	0.11	0.13	3.13
Degree	4	32	20.00	24.50	800	MAX VALUE	112.64	9.56	0.48	2.88
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,146	MAX VALUE	419.67	0.00	0.00	0.00

Dual graph

Density: 9.73%
MCB compute time (ms): 360
MCB cycles: 1,773
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/Dual1.json

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

Clustering coefficient 0.43 0.68 0.51 0.49 91.02 0.00 -123.15 0.04 0.07 4.10

Degree 8 24 17.42 18.00 3,136 MAX VALUE 510.95 3.27 0.19 2.52

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.24 3.00 5,749 MAX VALUE 2,070.70 0.45 0.14 0.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.68	0.51	0.49	91.02	0.00	-123.15	0.04	0.07	4.10
Degree	8	24	17.42	18.00	3,136	MAX VALUE	510.95	3.27	0.19	2.52
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.24	3.00	5,749	MAX VALUE	2,070.70	0.45	0.14	0.58

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 86
MCB cycles: 141

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 5 3.56 3.00 640 MAX VALUE 224.70 0.72 0.20 1.05

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.72 7.00 947 MAX VALUE 266.16 1.16 0.17 1.50

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	5	3.56	3.00	640	MAX VALUE	224.70	0.72	0.20	1.05
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.72	7.00	947	MAX VALUE	266.16	1.16	0.17	1.50

Triangulated dual graph

Density: 45.28%
Triangles: 186,949

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

Clustering coefficient 0.68 1.00 0.83 0.81 149.37 0.00 -34.60 0.09 0.11 4.63

Degree 8 128 81.04 85.00 14,588 MAX VALUE 754.89 40.17 0.50 3.89

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	0.68	1.00	0.83	0.81	149.37	0.00	-34.60	0.09	0.11	4.63
Degree	8	128	81.04	85.00	14,588	MAX VALUE	754.89	40.17	0.50	3.89
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.49%

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

Clustering coefficient 0.49 1.00 0.79 0.75 142.87 0.00 -44.96 0.15 0.19 3.28

Degree 2 63 20.57 7.00 3,702 MAX VALUE 420.83 22.67 1.10 3.03

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	0.49	1.00	0.79	0.75	142.87	0.00	-44.96	0.15	0.19	3.28
Degree	2	63	20.57	7.00	3,702	MAX VALUE	420.83	22.67	1.10	3.03
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 46
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-84-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 14 3.27 2.00 720 MAX VALUE 210.79 2.91 0.89 0.87

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.52 6.00 920 MAX VALUE 263.28 0.88 0.13 0.58

XCSP 2.1 Benchmarks