XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-83-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 21 12.57 13.00 113,118 MAX VALUE 22,588.00 2.52 0.20 2.34

Relational linkage 0.16 0.56 0.36 0.36 356.52 0.00 -1,048.27 0.06 0.18 1.88

Tightness 0.45 0.56 0.50 0.50 89.51 0.00 -125.91 0.02 0.04 3.73

Tuples 278 342 314.22 314.00 56,559 MAX VALUE 1,034.87 12.66 0.04 3.73

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

Value table constraints 5 13 9.00 9.00 360 2.56e+37 86.14 2.54 0.28 2.13

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	21	12.57	13.00	113,118	MAX VALUE	22,588.00	2.52	0.20	2.34
Relational linkage	0.16	0.56	0.36	0.36	356.52	0.00	-1,048.27	0.06	0.18	1.88
Tightness	0.45	0.56	0.50	0.50	89.51	0.00	-125.91	0.02	0.04	3.73
Tuples	278	342	314.22	314.00	56,559	MAX VALUE	1,034.87	12.66	0.04	3.73
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	5	13	9.00	9.00	360	2.56e+37	86.14	2.54	0.28	2.13
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: 4
CIR: 0.07
Independent Cluster Pairs: 14
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/Tree1.json

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

Cluster constraints 7 50 21.14 15.00 444 6.32e+25 59.41 14.71 0.70 2.60

Variables per cluster 6 20 10.81 9.00 227 8.78e+20 48.22 4.61 0.43 2.27

Separator constraints 0 43 12.57 9.00 264 0 None 12.71 1.01 2.60

Separator variables 0 19 8.90 8.00 187 0 None 4.59 0.52 2.33

Clusters per var 1 14 5.67 6.00 227 7.25e+23 54.94 4.03 0.71 2.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	50	21.14	15.00	444	6.32e+25	59.41	14.71	0.70	2.60
Variables per cluster	6	20	10.81	9.00	227	8.78e+20	48.22	4.61	0.43	2.27
Separator constraints	0	43	12.57	9.00	264	0	None	12.71	1.01	2.60
Separator variables	0	19	8.90	8.00	187	0	None	4.59	0.52	2.33
Clusters per var	1	14	5.67	6.00	227	7.25e+23	54.94	4.03	0.71	2.28

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.23
Independent Cluster Pairs: 151
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/DualTree1.json

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

Cluster constraints 26 383 122.58 104.50 4,658 MAX VALUE 174.00 84.47 0.69 3.56

Variables per cluster 10 81 28.34 21.00 1,077 MAX VALUE 120.64 18.17 0.64 3.16

Separator constraints 0 205 81.29 69.50 3,089 0 None 52.13 0.64 3.53

Separator variables 0 62 23.61 19.50 897 0 None 13.83 0.59 3.11

Clusters per variable 1 10 5.98 7.00 1,077 MAX VALUE 292.28 2.67 0.45 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	26	383	122.58	104.50	4,658	MAX VALUE	174.00	84.47	0.69	3.56
Variables per cluster	10	81	28.34	21.00	1,077	MAX VALUE	120.64	18.17	0.64	3.16
Separator constraints	0	205	81.29	69.50	3,089	0	None	52.13	0.64	3.53
Separator variables	0	62	23.61	19.50	897	0	None	13.83	0.59	3.11
Clusters per variable	1	10	5.98	7.00	1,077	MAX VALUE	292.28	2.67	0.45	2.15

Primal graph

Density: 23.08%
MCB compute time (ms): 3
MCB cycles: 198
Triangles: 117
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/Primal1.json

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

Clustering coefficient 0.08 0.50 0.23 0.22 9.23 0.00 -60.37 0.07 0.30 3.05

Degree 5 13 9.00 9.00 360 2.56e+37 86.14 2.54 0.28 2.13

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.45 3.00 683 MAX VALUE 243.13 0.50 0.14 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.08	0.50	0.23	0.22	9.23	0.00	-60.37	0.07	0.30	3.05
Degree	5	13	9.00	9.00	360	2.56e+37	86.14	2.54	0.28	2.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.45	3.00	683	MAX VALUE	243.13	0.50	0.14	0.69

Triangulated primal graph

Density: 48.33%
MCB compute time (ms): 15
MCB cycles: 338
Triangles: 2,100

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

Clustering coefficient 0.59 1.00 0.83 0.82 33.19 0.00 -7.92 0.12 0.15 3.04

Degree 5 32 18.85 23.50 754 MAX VALUE 110.42 9.41 0.50 2.84

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,014 MAX VALUE 371.33 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.59	1.00	0.83	0.82	33.19	0.00	-7.92	0.12	0.15	3.04
Degree	5	32	18.85	23.50	754	MAX VALUE	110.42	9.41	0.50	2.84
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,014	MAX VALUE	371.33	0.00	0.00	0.00

Dual graph

Density: 9.74%
MCB compute time (ms): 489
MCB cycles: 1,503
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/Dual1.json

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

Clustering coefficient 0.45 0.62 0.51 0.50 91.31 0.00 -122.49 0.03 0.06 4.15

Degree 9 23 17.43 17.00 3,138 MAX VALUE 510.99 3.30 0.19 2.50

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.09 3.00 4,647 MAX VALUE 1,690.72 0.30 0.10 0.31

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.62	0.51	0.50	91.31	0.00	-122.49	0.03	0.06	4.15
Degree	9	23	17.43	17.00	3,138	MAX VALUE	510.99	3.30	0.19	2.50
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.09	3.00	4,647	MAX VALUE	1,690.72	0.30	0.10	0.31

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 87
MCB cycles: 141

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.04 7.99 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 224.72 0.71 0.20 1.06

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.76 7.00 953 MAX VALUE 267.31 1.11 0.16 1.48

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.04	7.99	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	224.72	0.71	0.20	1.06
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.76	7.00	953	MAX VALUE	267.31	1.11	0.16	1.48

Triangulated dual graph

Density: 44.85%
Triangles: 184,503

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

Clustering coefficient 0.70 1.00 0.83 0.82 149.49 0.00 -34.44 0.09 0.11 4.66

Degree 9 127 80.29 96.00 14,452 MAX VALUE 751.90 40.24 0.50 3.95

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	149.49	0.00	-34.44	0.09	0.11	4.66
Degree	9	127	80.29	96.00	14,452	MAX VALUE	751.90	40.24	0.50	3.95
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.60%

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

Clustering coefficient 0.55 1.00 0.80 0.74 143.23 0.00 -44.46 0.15 0.19 3.29

Degree 2 65 20.76 7.00 3,736 MAX VALUE 421.69 22.73 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	0.55	1.00	0.80	0.74	143.23	0.00	-44.46	0.15	0.19	3.29
Degree	2	65	20.76	7.00	3,736	MAX VALUE	421.69	22.73	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-2-40-25-180-500-83-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-83-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 13 3.27 2.00 720 MAX VALUE 210.90 2.91 0.89 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.45 6.00 910 MAX VALUE 261.84 0.84 0.13 0.54

XCSP 2.1 Benchmarks