XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-48-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 2 21 12.51 13.00 112,560 MAX VALUE 22,544.20 2.50 0.20 2.33

Relational linkage 0.08 0.56 0.35 0.36 354.44 0.00 -1,053.44 0.06 0.17 1.84

Tightness 0.45 0.56 0.50 0.50 89.95 0.00 -125.01 0.02 0.04 3.78

Tuples 272 341 312.67 313.00 56,280 MAX VALUE 1,033.98 12.70 0.04 3.78

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

Value table constraints 5 17 9.00 9.00 360 2.79e+37 86.22 2.65 0.29 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	2	21	12.51	13.00	112,560	MAX VALUE	22,544.20	2.50	0.20	2.33
Relational linkage	0.08	0.56	0.35	0.36	354.44	0.00	-1,053.44	0.06	0.17	1.84
Tightness	0.45	0.56	0.50	0.50	89.95	0.00	-125.01	0.02	0.04	3.78
Tuples	272	341	312.67	313.00	56,280	MAX VALUE	1,033.98	12.70	0.04	3.78
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	5	17	9.00	9.00	360	2.79e+37	86.22	2.65	0.29	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: 10
Tree depth: 4
CIR: 0.08
Independent Cluster Pairs: 15
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/Tree1.json

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

Cluster constraints 7 54 24.52 18.00 515 1.08e+27 62.24 16.60 0.68 2.69

Variables per cluster 6 20 12.00 11.00 252 6.03e+21 50.15 5.24 0.44 2.11

Separator constraints 0 44 15.95 9.00 335 0 None 15.59 0.98 2.69

Separator variables 0 19 10.10 9.00 212 0 None 5.42 0.54 2.22

Clusters per var 1 17 6.30 5.50 252 2.23e+25 58.36 4.46 0.71 2.29

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	54	24.52	18.00	515	1.08e+27	62.24	16.60	0.68	2.69
Variables per cluster	6	20	12.00	11.00	252	6.03e+21	50.15	5.24	0.44	2.11
Separator constraints	0	44	15.95	9.00	335	0	None	15.59	0.98	2.69
Separator variables	0	19	10.10	9.00	212	0	None	5.42	0.54	2.22
Clusters per var	1	17	6.30	5.50	252	2.23e+25	58.36	4.46	0.71	2.29

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 131
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/DualTree1.json

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

Cluster constraints 30 362 125.39 102.00 4,765 MAX VALUE 175.12 86.74 0.69 3.60

Variables per cluster 11 82 29.11 22.00 1,106 MAX VALUE 121.54 18.97 0.65 3.16

Separator constraints 0 205 83.82 77.50 3,185 0 None 51.47 0.61 3.60

Separator variables 0 64 24.37 20.00 926 0 None 14.53 0.60 3.11

Clusters per variable 1 11 6.14 7.00 1,106 MAX VALUE 297.87 2.68 0.44 2.18

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	30	362	125.39	102.00	4,765	MAX VALUE	175.12	86.74	0.69	3.60
Variables per cluster	11	82	29.11	22.00	1,106	MAX VALUE	121.54	18.97	0.65	3.16
Separator constraints	0	205	83.82	77.50	3,185	0	None	51.47	0.61	3.60
Separator variables	0	64	24.37	20.00	926	0	None	14.53	0.60	3.11
Clusters per variable	1	11	6.14	7.00	1,106	MAX VALUE	297.87	2.68	0.44	2.18

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 153
Triangles: 104
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/Primal1.json

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

Clustering coefficient 0.07 0.47 0.21 0.19 8.54 0.00 -64.24 0.08 0.37 3.21

Degree 5 17 9.00 9.00 360 2.79e+37 86.22 2.65 0.29 2.17

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.38 3.00 517 MAX VALUE 184.77 0.49 0.14 0.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.07	0.47	0.21	0.19	8.54	0.00	-64.24	0.08	0.37	3.21
Degree	5	17	9.00	9.00	360	2.79e+37	86.22	2.65	0.29	2.17
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.38	3.00	517	MAX VALUE	184.77	0.49	0.14	0.66

Triangulated primal graph

Density: 51.54%
MCB compute time (ms): 7
MCB cycles: 458
Triangles: 2,412

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

Clustering coefficient 0.57 1.00 0.84 0.82 33.54 0.00 -7.43 0.12 0.14 3.01

Degree 5 35 20.10 23.50 804 MAX VALUE 113.27 9.56 0.48 2.78

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.00 3.00 1,375 MAX VALUE 503.45 0.05 0.02 0.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.57	1.00	0.84	0.82	33.54	0.00	-7.43	0.12	0.14	3.01
Degree	5	35	20.10	23.50	804	MAX VALUE	113.27	9.56	0.48	2.78
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.00	3.00	1,375	MAX VALUE	503.45	0.05	0.02	0.02

Dual graph

Density: 9.81%
MCB compute time (ms): 216
MCB cycles: 2,340
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/Dual1.json

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

Clustering coefficient 0.44 0.67 0.51 0.50 91.59 0.00 -122.11 0.04 0.08 4.34

Degree 10 29 17.56 17.00 3,160 MAX VALUE 511.72 3.69 0.21 2.67

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.46 3.00 8,105 MAX VALUE 2,876.24 0.58 0.17 0.82

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.67	0.51	0.50	91.59	0.00	-122.11	0.04	0.08	4.34
Degree	10	29	17.56	17.00	3,160	MAX VALUE	511.72	3.69	0.21	2.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.46	3.00	8,105	MAX VALUE	2,876.24	0.58	0.17	0.82

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 5 3.56 3.00 640 MAX VALUE 224.10 0.76 0.21 1.13

Eccentricity None None None None None None None None None None

MCB cycle size 5 9 6.74 7.00 950 MAX VALUE 267.62 0.93 0.14 1.33

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	224.10	0.76	0.21	1.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	5	9	6.74	7.00	950	MAX VALUE	267.62	0.93	0.14	1.33

Triangulated dual graph

Density: 46.85%
Triangles: 199,788

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

Clustering coefficient 0.70 1.00 0.83 0.82 150.03 0.00 -33.74 0.09 0.10 4.66

Degree 10 133 83.87 98.00 15,096 MAX VALUE 762.06 40.56 0.48 3.96

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	0.82	150.03	0.00	-33.74	0.09	0.10	4.66
Degree	10	133	83.87	98.00	15,096	MAX VALUE	762.06	40.56	0.48	3.96
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.72%

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

Clustering coefficient 0.51 1.00 0.80 0.73 143.24 0.00 -44.50 0.16 0.19 3.34

Degree 2 66 20.98 7.00 3,776 MAX VALUE 421.80 23.04 1.10 3.11

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	143.24	0.00	-44.50	0.16	0.19	3.34
Degree	2	66	20.98	7.00	3,776	MAX VALUE	421.80	23.04	1.10	3.11
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 49
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-48-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 17 3.27 2.00 720 MAX VALUE 210.99 2.93 0.89 0.87

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.65 6.00 938 MAX VALUE 265.87 0.94 0.14 0.63

XCSP 2.1 Benchmarks