XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-58-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:28
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 5 23 12.49 12.00 112,370 MAX VALUE 22,531.20 2.49 0.20 2.33

Relational linkage 0.20 0.64 0.36 0.36 358.68 0.00 -1,041.70 0.06 0.18 1.87

Tightness 0.44 0.55 0.50 0.50 90.10 0.00 -124.72 0.02 0.04 3.82

Tuples 284 347 312.14 312.00 56,185 MAX VALUE 1,033.65 13.42 0.04 3.82

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

Value table constraints 2 15 9.00 9.50 360 6.07e+36 84.70 3.12 0.35 2.30

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	5	23	12.49	12.00	112,370	MAX VALUE	22,531.20	2.49	0.20	2.33
Relational linkage	0.20	0.64	0.36	0.36	358.68	0.00	-1,041.70	0.06	0.18	1.87
Tightness	0.44	0.55	0.50	0.50	90.10	0.00	-124.72	0.02	0.04	3.82
Tuples	284	347	312.14	312.00	56,185	MAX VALUE	1,033.65	13.42	0.04	3.82
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	2	15	9.00	9.50	360	6.07e+36	84.70	3.12	0.35	2.30
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: 11
Tree depth: 4
CIR: 0.16
Independent Cluster Pairs: 30
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/Tree1.json

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

Cluster constraints 3 55 22.29 15.00 468 7.95e+24 57.34 17.61 0.79 2.65

Variables per cluster 3 20 10.43 9.00 219 1.27e+20 46.29 5.39 0.52 2.52

Separator constraints 0 48 13.71 7.00 288 0 None 14.97 1.09 2.53

Separator variables 0 19 8.52 7.00 179 0 None 5.30 0.62 2.58

Clusters per var 1 12 5.47 5.00 219 7.79e+22 52.71 3.88 0.71 2.18

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	55	22.29	15.00	468	7.95e+24	57.34	17.61	0.79	2.65
Variables per cluster	3	20	10.43	9.00	219	1.27e+20	46.29	5.39	0.52	2.52
Separator constraints	0	48	13.71	7.00	288	0	None	14.97	1.09	2.53
Separator variables	0	19	8.52	7.00	179	0	None	5.30	0.62	2.58
Clusters per var	1	12	5.47	5.00	219	7.79e+22	52.71	3.88	0.71	2.18

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 6
CIR: 0.26
Independent Cluster Pairs: 170
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/DualTree1.json

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

Cluster constraints 17 345 125.39 110.00 4,765 MAX VALUE 173.66 84.42 0.67 3.56

Variables per cluster 7 78 28.21 22.00 1,072 MAX VALUE 119.97 18.16 0.64 3.25

Separator constraints 0 175 82.37 78.00 3,130 0 None 50.59 0.61 3.37

Separator variables 0 59 23.47 20.00 892 0 None 13.93 0.59 3.08

Clusters per variable 1 12 5.96 6.00 1,072 MAX VALUE 292.14 2.70 0.45 2.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	17	345	125.39	110.00	4,765	MAX VALUE	173.66	84.42	0.67	3.56
Variables per cluster	7	78	28.21	22.00	1,072	MAX VALUE	119.97	18.16	0.64	3.25
Separator constraints	0	175	82.37	78.00	3,130	0	None	50.59	0.61	3.37
Separator variables	0	59	23.47	20.00	892	0	None	13.93	0.59	3.08
Clusters per variable	1	12	5.96	6.00	1,072	MAX VALUE	292.14	2.70	0.45	2.26

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 158
Triangles: 147
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 0.28 0.26 11.08 0.00 None 0.14 0.51 3.36

Degree 2 15 9.00 9.50 360 6.07e+36 84.70 3.12 0.35 2.30

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.25 3.00 514 MAX VALUE 185.02 0.45 0.14 0.59

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	0.28	0.26	11.08	0.00	None	0.14	0.51	3.36
Degree	2	15	9.00	9.50	360	6.07e+36	84.70	3.12	0.35	2.30
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.25	3.00	514	MAX VALUE	185.02	0.45	0.14	0.59

Triangulated primal graph

Density: 47.31%
MCB compute time (ms): 11
MCB cycles: 343
Triangles: 2,108

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

Clustering coefficient 0.63 1.00 0.84 0.82 33.61 0.00 -7.38 0.12 0.14 2.91

Degree 2 30 18.45 23.00 738 MAX VALUE 107.57 9.71 0.53 2.89

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,029 MAX VALUE 376.82 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.63	1.00	0.84	0.82	33.61	0.00	-7.38	0.12	0.14	2.91
Degree	2	30	18.45	23.00	738	MAX VALUE	107.57	9.71	0.53	2.89
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,029	MAX VALUE	376.82	0.00	0.00	0.00

Dual graph

Density: 10.15%
MCB compute time (ms): 278
MCB cycles: 1,747
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/Dual1.json

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

Clustering coefficient 0.43 0.86 0.52 0.50 93.08 0.00 -119.43 0.05 0.10 4.29

Degree 6 26 18.17 18.50 3,270 MAX VALUE 517.18 3.87 0.21 2.68

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.12 3.00 5,451 MAX VALUE 1,979.37 0.33 0.11 0.38

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.86	0.52	0.50	93.08	0.00	-119.43	0.05	0.10	4.29
Degree	6	26	18.17	18.50	3,270	MAX VALUE	517.18	3.87	0.21	2.68
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.12	3.00	5,451	MAX VALUE	1,979.37	0.33	0.11	0.38

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 84
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 224.52 0.73 0.21 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.73 7.00 949 MAX VALUE 266.58 1.15 0.17 1.52

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	224.52	0.73	0.21	1.08
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.73	7.00	949	MAX VALUE	266.58	1.15	0.17	1.52

Triangulated dual graph

Density: 44.34%
Triangles: 177,285

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

Clustering coefficient 0.64 1.00 0.83 0.82 148.84 0.00 -35.40 0.10 0.12 4.65

Degree 6 137 79.37 94.50 14,286 MAX VALUE 751.15 39.34 0.50 4.14

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	0.64	1.00	0.83	0.82	148.84	0.00	-35.40	0.10	0.12	4.65
Degree	6	137	79.37	94.50	14,286	MAX VALUE	751.15	39.34	0.50	4.14
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.71%

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

Clustering coefficient 0.50 1.00 0.80 0.72 143.19 0.00 -44.73 0.16 0.20 3.31

Degree 2 68 20.96 7.00 3,772 MAX VALUE 424.30 22.78 1.09 3.16

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	0.50	1.00	0.80	0.72	143.19	0.00	-44.73	0.16	0.20	3.31
Degree	2	68	20.96	7.00	3,772	MAX VALUE	424.30	22.78	1.09	3.16
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 41
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-58-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 15 3.27 2.00 720 MAX VALUE 209.46 3.01 0.92 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 6.33 6.00 892 MAX VALUE 259.19 0.78 0.12 0.46

XCSP 2.1 Benchmarks