XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-0-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 3 21 12.47 12.00 112,200 MAX VALUE 22,517.20 2.48 0.20 2.33

Relational linkage 0.12 0.60 0.36 0.36 356.52 0.00 -1,048.84 0.06 0.18 1.89

Tightness 0.45 0.55 0.50 0.50 90.24 0.00 -124.40 0.02 0.03 3.59

Tuples 282 341 311.67 312.00 56,100 MAX VALUE 1,033.44 10.96 0.04 3.59

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 9.00 360 1.45e+37 85.57 2.69 0.30 2.19

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	12.47	12.00	112,200	MAX VALUE	22,517.20	2.48	0.20	2.33
Relational linkage	0.12	0.60	0.36	0.36	356.52	0.00	-1,048.84	0.06	0.18	1.89
Tightness	0.45	0.55	0.50	0.50	90.24	0.00	-124.40	0.02	0.03	3.59
Tuples	282	341	311.67	312.00	56,100	MAX VALUE	1,033.44	10.96	0.04	3.59
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	9.00	360	1.45e+37	85.57	2.69	0.30	2.19
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: 10
Tree depth: 3
CIR: 0.11
Independent Cluster Pairs: 19
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/Tree1.json

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

Cluster constraints 2 61 21.75 19.50 435 1.65e+24 55.76 15.33 0.70 2.76

Variables per cluster 3 21 10.90 10.00 218 6.52e+19 45.62 4.82 0.44 2.53

Separator constraints 0 41 12.75 9.00 255 0 None 12.80 1.00 2.55

Separator variables 0 18 8.90 9.00 178 0 None 4.69 0.53 2.53

Clusters per var 1 14 5.45 6.00 218 1.92e+23 53.61 3.75 0.69 2.10

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	61	21.75	19.50	435	1.65e+24	55.76	15.33	0.70	2.76
Variables per cluster	3	21	10.90	10.00	218	6.52e+19	45.62	4.82	0.44	2.53
Separator constraints	0	41	12.75	9.00	255	0	None	12.80	1.00	2.55
Separator variables	0	18	8.90	9.00	178	0	None	4.69	0.53	2.53
Clusters per var	1	14	5.45	6.00	218	1.92e+23	53.61	3.75	0.69	2.10

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.19
Independent Cluster Pairs: 127
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/DualTree1.json

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

Cluster constraints 21 338 125.92 104.00 4,785 MAX VALUE 174.97 85.50 0.68 3.60

Variables per cluster 9 81 28.82 22.00 1,095 MAX VALUE 121.16 18.52 0.64 3.31

Separator constraints 0 210 84.21 82.50 3,200 0 None 52.40 0.62 3.60

Separator variables 0 62 24.08 19.50 915 0 None 14.08 0.58 3.26

Clusters per variable 1 10 6.08 7.00 1,095 MAX VALUE 295.20 2.68 0.44 2.14

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	21	338	125.92	104.00	4,785	MAX VALUE	174.97	85.50	0.68	3.60
Variables per cluster	9	81	28.82	22.00	1,095	MAX VALUE	121.16	18.52	0.64	3.31
Separator constraints	0	210	84.21	82.50	3,200	0	None	52.40	0.62	3.60
Separator variables	0	62	24.08	19.50	915	0	None	14.08	0.58	3.26
Clusters per variable	1	10	6.08	7.00	1,095	MAX VALUE	295.20	2.68	0.44	2.14

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 186
Triangles: 122
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/Primal1.json

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

Clustering coefficient 0.00 0.36 0.22 0.22 8.85 0.00 None 0.08 0.37 2.94

Degree 2 15 9.00 9.00 360 1.45e+37 85.57 2.69 0.30 2.19

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.41 3.00 635 MAX VALUE 226.43 0.50 0.15 0.70

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.36	0.22	0.22	8.85	0.00	None	0.08	0.37	2.94
Degree	2	15	9.00	9.00	360	1.45e+37	85.57	2.69	0.30	2.19
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.41	3.00	635	MAX VALUE	226.43	0.50	0.15	0.70

Triangulated primal graph

Density: 49.74%
MCB compute time (ms): 8
MCB cycles: 377
Triangles: 2,253

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

Clustering coefficient 0.60 1.00 0.84 0.81 33.46 0.00 -7.55 0.12 0.14 3.08

Degree 2 33 19.40 25.00 776 MAX VALUE 110.89 9.58 0.49 2.86

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,131 MAX VALUE 414.18 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	0.84	0.81	33.46	0.00	-7.55	0.12	0.14	3.08
Degree	2	33	19.40	25.00	776	MAX VALUE	110.89	9.58	0.49	2.86
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,131	MAX VALUE	414.18	0.00	0.00	0.00

Dual graph

Density: 9.84%
MCB compute time (ms): 289
MCB cycles: 1,761
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/Dual1.json

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

Clustering coefficient 0.46 0.83 0.51 0.50 91.30 0.00 -122.73 0.04 0.08 4.14

Degree 8 27 17.61 18.00 3,170 MAX VALUE 512.55 3.46 0.20 2.59

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.20 3.00 5,635 MAX VALUE 2,034.95 0.42 0.13 0.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.83	0.51	0.50	91.30	0.00	-122.73	0.04	0.08	4.14
Degree	8	27	17.61	18.00	3,170	MAX VALUE	512.55	3.46	0.20	2.59
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.20	3.00	5,635	MAX VALUE	2,034.95	0.42	0.13	0.52

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 81
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 6 3.56 3.00 640 MAX VALUE 224.60 0.73 0.21 1.07

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.72 7.00 948 MAX VALUE 266.47 1.16 0.17 1.55

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	6	3.56	3.00	640	MAX VALUE	224.60	0.73	0.21	1.07
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.72	7.00	948	MAX VALUE	266.47	1.16	0.17	1.55

Triangulated dual graph

Density: 46.06%
Triangles: 192,437

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

Clustering coefficient 0.70 1.00 0.83 0.81 149.75 0.00 -34.17 0.09 0.11 4.62

Degree 8 129 82.44 100.00 14,840 MAX VALUE 758.49 40.22 0.49 3.82

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	149.75	0.00	-34.17	0.09	0.11	4.62
Degree	8	129	82.44	100.00	14,840	MAX VALUE	758.49	40.22	0.49	3.82
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.17%

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

Clustering coefficient 0.51 1.00 0.80 0.76 144.78 0.00 -42.50 0.15 0.19 3.27

Degree 2 66 21.79 7.00 3,922 MAX VALUE 427.35 23.82 1.09 3.07

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	0.76	144.78	0.00	-42.50	0.15	0.19	3.27
Degree	2	66	21.79	7.00	3,922	MAX VALUE	427.35	23.82	1.09	3.07
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 51
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-0-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 210.34 2.93 0.90 0.84

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 6.45 6.00 910 MAX VALUE 261.78 0.87 0.13 0.56

XCSP 2.1 Benchmarks