XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-24-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:27
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 3 21 12.52 13.00 112,700 MAX VALUE 22,555.80 2.50 0.20 2.34

Relational linkage 0.12 0.52 0.36 0.36 356.12 0.00 -1,048.75 0.06 0.17 1.84

Tightness 0.45 0.56 0.50 0.50 89.84 0.00 -125.22 0.02 0.04 3.65

Tuples 278 344 313.06 313.00 56,350 MAX VALUE 1,034.22 12.02 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 5 14 9.00 9.00 360 3.23e+37 86.37 2.48 0.28 2.18

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	3	21	12.52	13.00	112,700	MAX VALUE	22,555.80	2.50	0.20	2.34
Relational linkage	0.12	0.52	0.36	0.36	356.12	0.00	-1,048.75	0.06	0.17	1.84
Tightness	0.45	0.56	0.50	0.50	89.84	0.00	-125.22	0.02	0.04	3.65
Tuples	278	344	313.06	313.00	56,350	MAX VALUE	1,034.22	12.02	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	5	14	9.00	9.00	360	3.23e+37	86.37	2.48	0.28	2.18
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: 22
Number of leaves: 10
Tree depth: 5
CIR: 0.05
Independent Cluster Pairs: 10
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/Tree1.json

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

Cluster constraints 7 46 23.23 21.50 511 2.83e+28 65.51 12.82 0.55 2.69

Variables per cluster 6 19 11.73 11.00 258 7.34e+22 52.65 4.35 0.37 2.12

Separator constraints 0 40 15.05 10.50 331 0 None 12.61 0.84 2.75

Separator variables 0 18 9.91 9.00 218 0 None 4.59 0.46 2.19

Clusters per var 1 15 6.45 6.50 258 1.54e+25 57.99 4.82 0.75 2.31

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	46	23.23	21.50	511	2.83e+28	65.51	12.82	0.55	2.69
Variables per cluster	6	19	11.73	11.00	258	7.34e+22	52.65	4.35	0.37	2.12
Separator constraints	0	40	15.05	10.50	331	0	None	12.61	0.84	2.75
Separator variables	0	18	9.91	9.00	218	0	None	4.59	0.46	2.19
Clusters per var	1	15	6.45	6.50	258	1.54e+25	57.99	4.82	0.75	2.31

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 6
CIR: 0.21
Independent Cluster Pairs: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/DualTree1.json

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

Cluster constraints 20 349 123.61 93.00 4,697 MAX VALUE 174.35 84.61 0.68 3.46

Variables per cluster 9 85 29.13 22.00 1,107 MAX VALUE 121.53 18.98 0.65 3.28

Separator constraints 0 191 82.47 73.00 3,134 0 None 49.93 0.61 3.42

Separator variables 0 63 24.39 20.50 927 0 None 14.49 0.59 3.09

Clusters per variable 1 11 6.15 7.00 1,107 MAX VALUE 297.95 2.70 0.44 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	20	349	123.61	93.00	4,697	MAX VALUE	174.35	84.61	0.68	3.46
Variables per cluster	9	85	29.13	22.00	1,107	MAX VALUE	121.53	18.98	0.65	3.28
Separator constraints	0	191	82.47	73.00	3,134	0	None	49.93	0.61	3.42
Separator variables	0	63	24.39	20.50	927	0	None	14.49	0.59	3.09
Clusters per variable	1	11	6.15	7.00	1,107	MAX VALUE	297.95	2.70	0.44	2.21

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 159
Triangles: 114
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/Primal1.json

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

Clustering coefficient 0.07 0.53 0.23 0.22 9.13 0.00 -61.30 0.08 0.34 3.07

Degree 5 14 9.00 9.00 360 3.23e+37 86.37 2.48 0.28 2.18

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.34 3.00 531 MAX VALUE 190.21 0.47 0.14 0.64

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.07	0.53	0.23	0.22	9.13	0.00	-61.30	0.08	0.34	3.07
Degree	5	14	9.00	9.00	360	3.23e+37	86.37	2.48	0.28	2.18
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.34	3.00	531	MAX VALUE	190.21	0.47	0.14	0.64

Triangulated primal graph

Density: 49.87%
MCB compute time (ms): 12
MCB cycles: 355
Triangles: 2,172

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

Clustering coefficient 0.60 1.00 0.83 0.82 33.04 0.00 -8.15 0.13 0.16 3.08

Degree 5 32 19.45 23.00 778 MAX VALUE 112.50 9.29 0.48 2.78

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,065 MAX VALUE 390.01 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.60	1.00	0.83	0.82	33.04	0.00	-8.15	0.13	0.16	3.08
Degree	5	32	19.45	23.00	778	MAX VALUE	112.50	9.29	0.48	2.78
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,065	MAX VALUE	390.01	0.00	0.00	0.00

Dual graph

Density: 9.70%
MCB compute time (ms): 320
MCB cycles: 1,858
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/Dual1.json

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

Clustering coefficient 0.43 0.63 0.51 0.50 91.24 0.00 -122.58 0.03 0.06 4.27

Degree 8 26 17.37 17.00 3,126 MAX VALUE 510.29 3.35 0.19 2.59

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.28 3.00 6,100 MAX VALUE 2,191.38 0.47 0.14 0.63

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.63	0.51	0.50	91.24	0.00	-122.58	0.03	0.06	4.27
Degree	8	26	17.37	17.00	3,126	MAX VALUE	510.29	3.35	0.19	2.59
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.28	3.00	6,100	MAX VALUE	2,191.38	0.47	0.14	0.63

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 77
MCB cycles: 141

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 223.90 0.79 0.22 1.13

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.66 7.00 939 MAX VALUE 265.20 1.10 0.16 1.48

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	223.90	0.79	0.22	1.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.66	7.00	939	MAX VALUE	265.20	1.10	0.16	1.48

Triangulated dual graph

Density: 47.11%
Triangles: 202,305

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

Clustering coefficient 0.69 1.00 0.84 0.82 150.32 0.00 -33.40 0.09 0.10 4.70

Degree 8 135 84.32 92.00 15,178 MAX VALUE 762.81 40.82 0.48 3.94

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	0.69	1.00	0.84	0.82	150.32	0.00	-33.40	0.09	0.10	4.70
Degree	8	135	84.32	92.00	15,178	MAX VALUE	762.81	40.82	0.48	3.94
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.48%

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

Clustering coefficient 0.51 1.00 0.80 0.73 143.54 0.00 -43.97 0.15 0.19 3.31

Degree 2 65 20.56 7.00 3,700 MAX VALUE 417.24 22.86 1.11 3.01

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	0.51	1.00	0.80	0.73	143.54	0.00	-43.97	0.15	0.19	3.31
Degree	2	65	20.56	7.00	3,700	MAX VALUE	417.24	22.86	1.11	3.01
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 44
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-24-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 211.13 2.90 0.89 0.87

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.51 6.00 918 MAX VALUE 263.00 0.87 0.13 0.57

XCSP 2.1 Benchmarks