XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-76-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 22 12.47 12.00 112,264 MAX VALUE 22,519.90 2.50 0.20 2.33

Relational linkage 0.16 0.52 0.35 0.36 353.88 0.00 -1,054.59 0.06 0.17 1.83

Tightness 0.45 0.56 0.50 0.50 90.19 0.00 -124.53 0.02 0.04 3.73

Tuples 277 344 311.84 311.00 56,132 MAX VALUE 1,033.51 12.37 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 16 9.00 9.00 360 3.52e+37 86.45 2.38 0.26 2.09

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	22	12.47	12.00	112,264	MAX VALUE	22,519.90	2.50	0.20	2.33
Relational linkage	0.16	0.52	0.35	0.36	353.88	0.00	-1,054.59	0.06	0.17	1.83
Tightness	0.45	0.56	0.50	0.50	90.19	0.00	-124.53	0.02	0.04	3.73
Tuples	277	344	311.84	311.00	56,132	MAX VALUE	1,033.51	12.37	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	16	9.00	9.00	360	3.52e+37	86.45	2.38	0.26	2.09
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: 7
Tree depth: 6
CIR: 0.08
Independent Cluster Pairs: 13
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/Tree1.json

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

Cluster constraints 7 59 27.50 23.00 550 6.48e+26 61.74 16.95 0.62 2.72

Variables per cluster 6 21 12.65 12.00 253 1.76e+21 48.92 5.14 0.41 2.42

Separator constraints 0 50 18.50 14.50 370 0 None 15.97 0.86 2.65

Separator variables 0 19 10.65 10.50 213 0 None 5.36 0.50 2.42

Clusters per var 1 14 6.33 6.50 253 5.25e+26 61.53 3.97 0.63 2.38

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	59	27.50	23.00	550	6.48e+26	61.74	16.95	0.62	2.72
Variables per cluster	6	21	12.65	12.00	253	1.76e+21	48.92	5.14	0.41	2.42
Separator constraints	0	50	18.50	14.50	370	0	None	15.97	0.86	2.65
Separator variables	0	19	10.65	10.50	213	0	None	5.36	0.50	2.42
Clusters per var	1	14	6.33	6.50	253	5.25e+26	61.53	3.97	0.63	2.38

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 137
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/DualTree1.json

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

Cluster constraints 25 362 122.29 100.00 4,647 MAX VALUE 174.92 81.57 0.67 3.48

Variables per cluster 10 83 28.71 20.50 1,091 MAX VALUE 121.36 18.33 0.64 3.19

Separator constraints 0 209 81.42 68.50 3,094 0 None 49.68 0.61 3.49

Separator variables 0 64 23.97 19.00 911 0 None 13.93 0.58 3.15

Clusters per variable 1 10 6.06 7.00 1,091 MAX VALUE 294.31 2.69 0.44 2.06

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	362	122.29	100.00	4,647	MAX VALUE	174.92	81.57	0.67	3.48
Variables per cluster	10	83	28.71	20.50	1,091	MAX VALUE	121.36	18.33	0.64	3.19
Separator constraints	0	209	81.42	68.50	3,094	0	None	49.68	0.61	3.49
Separator variables	0	64	23.97	19.00	911	0	None	13.93	0.58	3.15
Clusters per variable	1	10	6.06	7.00	1,091	MAX VALUE	294.31	2.69	0.44	2.06

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 158
Triangles: 125
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/Primal1.json

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

Clustering coefficient 0.08 0.38 0.25 0.25 9.86 0.00 -57.33 0.06 0.24 2.97

Degree 5 16 9.00 9.00 360 3.52e+37 86.45 2.38 0.26 2.09

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.30 3.00 521 MAX VALUE 187.10 0.46 0.14 0.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.08	0.38	0.25	0.25	9.86	0.00	-57.33	0.06	0.24	2.97
Degree	5	16	9.00	9.00	360	3.52e+37	86.45	2.38	0.26	2.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.30	3.00	521	MAX VALUE	187.10	0.46	0.14	0.61

Triangulated primal graph

Density: 54.23%
MCB compute time (ms): 11
MCB cycles: 401
Triangles: 2,645

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

Clustering coefficient 0.65 1.00 0.84 0.83 33.44 0.00 -7.43 0.10 0.12 3.28

Degree 5 33 21.15 25.00 846 MAX VALUE 116.17 9.19 0.43 2.79

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,203 MAX VALUE 440.54 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.65	1.00	0.84	0.83	33.44	0.00	-7.43	0.10	0.12	3.28
Degree	5	33	21.15	25.00	846	MAX VALUE	116.17	9.19	0.43	2.79
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,203	MAX VALUE	440.54	0.00	0.00	0.00

Dual graph

Density: 9.64%
MCB compute time (ms): 195
MCB cycles: 2,470
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/Dual1.json

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

Clustering coefficient 0.44 0.63 0.50 0.50 90.69 0.00 -123.68 0.03 0.06 4.24

Degree 9 26 17.26 17.00 3,106 MAX VALUE 509.06 3.41 0.20 2.61

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.50 3.00 8,652 MAX VALUE 3,062.10 0.60 0.17 0.85

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.63	0.50	0.50	90.69	0.00	-123.68	0.03	0.06	4.24
Degree	9	26	17.26	17.00	3,106	MAX VALUE	509.06	3.41	0.20	2.61
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.50	3.00	8,652	MAX VALUE	3,062.10	0.60	0.17	0.85

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 75
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 0.50 0.00 None 0.02 7.68 0.08

Degree 2 5 3.56 3.00 640 MAX VALUE 224.35 0.74 0.21 1.10

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.82 7.00 962 MAX VALUE 268.17 1.22 0.18 1.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.50	0.00	None	0.02	7.68	0.08
Degree	2	5	3.56	3.00	640	MAX VALUE	224.35	0.74	0.21	1.10
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.82	7.00	962	MAX VALUE	268.17	1.22	0.18	1.55

Triangulated dual graph

Density: 45.59%
Triangles: 190,752

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

Clustering coefficient 0.72 1.00 0.83 0.80 149.75 0.00 -34.08 0.09 0.11 4.59

Degree 9 126 81.60 102.00 14,688 MAX VALUE 755.82 40.69 0.50 3.69

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	0.72	1.00	0.83	0.80	149.75	0.00	-34.08	0.09	0.11	4.59
Degree	9	126	81.60	102.00	14,688	MAX VALUE	755.82	40.69	0.50	3.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.32%

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

Clustering coefficient 0.52 1.00 0.79 0.75 142.54 0.00 -45.34 0.15 0.19 3.36

Degree 2 65 20.27 7.00 3,648 MAX VALUE 418.63 22.42 1.11 3.06

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	0.52	1.00	0.79	0.75	142.54	0.00	-45.34	0.15	0.19	3.36
Degree	2	65	20.27	7.00	3,648	MAX VALUE	418.63	22.42	1.11	3.06
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 46
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-76-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 16 3.27 2.00 720 MAX VALUE 211.22 2.88 0.88 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.43 6.00 906 MAX VALUE 261.27 0.82 0.13 0.52

XCSP 2.1 Benchmarks