XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-31-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:27
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 12.57 13.00 113,112 MAX VALUE 22,581.00 2.55 0.20 2.36

Relational linkage 0.12 0.56 0.36 0.36 356.28 0.00 -1,049.99 0.06 0.18 1.89

Tightness 0.44 0.56 0.50 0.50 89.51 0.00 -125.91 0.02 0.04 3.79

Tuples 275 347 314.20 314.00 56,556 MAX VALUE 1,034.84 13.25 0.04 3.79

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

Value table constraints 4 16 9.00 9.00 360 1.43e+37 85.55 2.86 0.32 2.26

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	12.57	13.00	113,112	MAX VALUE	22,581.00	2.55	0.20	2.36
Relational linkage	0.12	0.56	0.36	0.36	356.28	0.00	-1,049.99	0.06	0.18	1.89
Tightness	0.44	0.56	0.50	0.50	89.51	0.00	-125.91	0.02	0.04	3.79
Tuples	275	347	314.20	314.00	56,556	MAX VALUE	1,034.84	13.25	0.04	3.79
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	16	9.00	9.00	360	1.43e+37	85.55	2.86	0.32	2.26
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: 13
Tree depth: 3
CIR: 0.13
Independent Cluster Pairs: 24
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/Tree1.json

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

Cluster constraints 5 52 17.24 14.00 362 1.49e+24 55.66 11.57 0.67 2.82

Variables per cluster 5 20 9.76 9.00 205 9.52e+19 46.00 4.21 0.43 2.43

Separator constraints 0 33 8.67 6.00 182 0 None 7.95 0.92 2.52

Separator variables 0 17 7.86 7.00 165 0 None 3.94 0.50 2.43

Clusters per var 1 13 5.12 5.00 205 3.69e+21 49.66 3.77 0.74 2.03

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	52	17.24	14.00	362	1.49e+24	55.66	11.57	0.67	2.82
Variables per cluster	5	20	9.76	9.00	205	9.52e+19	46.00	4.21	0.43	2.43
Separator constraints	0	33	8.67	6.00	182	0	None	7.95	0.92	2.52
Separator variables	0	17	7.86	7.00	165	0	None	3.94	0.50	2.43
Clusters per var	1	13	5.12	5.00	205	3.69e+21	49.66	3.77	0.74	2.03

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 143
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/DualTree1.json

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

Cluster constraints 32 338 125.53 111.50 4,770 MAX VALUE 176.18 80.08 0.64 3.49

Variables per cluster 11 82 28.55 22.50 1,085 MAX VALUE 121.19 17.95 0.63 3.01

Separator constraints 0 189 83.32 77.50 3,166 0 None 47.17 0.57 3.49

Separator variables 0 63 23.82 20.00 905 0 None 13.62 0.57 3.06

Clusters per variable 1 10 6.03 7.00 1,085 MAX VALUE 293.90 2.68 0.45 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	32	338	125.53	111.50	4,770	MAX VALUE	176.18	80.08	0.64	3.49
Variables per cluster	11	82	28.55	22.50	1,085	MAX VALUE	121.19	17.95	0.63	3.01
Separator constraints	0	189	83.32	77.50	3,166	0	None	47.17	0.57	3.49
Separator variables	0	63	23.82	20.00	905	0	None	13.62	0.57	3.06
Clusters per variable	1	10	6.03	7.00	1,085	MAX VALUE	293.90	2.68	0.45	2.17

Primal graph

Density: 23.08%
MCB compute time (ms): 3
MCB cycles: 260
Triangles: 114
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/Primal1.json

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

Clustering coefficient 0.05 0.40 0.23 0.21 9.34 0.00 -60.53 0.07 0.32 2.92

Degree 4 16 9.00 9.00 360 1.43e+37 85.55 2.86 0.32 2.26

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.59 4.00 934 MAX VALUE 329.56 0.54 0.15 0.78

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.05	0.40	0.23	0.21	9.34	0.00	-60.53	0.07	0.32	2.92
Degree	4	16	9.00	9.00	360	1.43e+37	85.55	2.86	0.32	2.26
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.59	4.00	934	MAX VALUE	329.56	0.54	0.15	0.78

Triangulated primal graph

Density: 45.51%
MCB compute time (ms): 5
MCB cycles: 347
Triangles: 1,869

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

Clustering coefficient 0.59 1.00 0.83 0.80 33.20 0.00 -8.00 0.14 0.16 2.79

Degree 4 31 17.75 22.00 710 MAX VALUE 106.86 9.49 0.53 2.64

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,041 MAX VALUE 381.22 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	0.80	33.20	0.00	-8.00	0.14	0.16	2.79
Degree	4	31	17.75	22.00	710	MAX VALUE	106.86	9.49	0.53	2.64
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,041	MAX VALUE	381.22	0.00	0.00	0.00

Dual graph

Density: 9.96%
MCB compute time (ms): 340
MCB cycles: 1,580
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/Dual1.json

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

Clustering coefficient 0.45 0.71 0.52 0.50 93.10 0.00 -119.38 0.05 0.09 4.28

Degree 10 25 17.82 18.00 3,208 MAX VALUE 515.15 3.34 0.19 2.56

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.12 3.00 4,922 MAX VALUE 1,788.17 0.32 0.10 0.36

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.71	0.52	0.50	93.10	0.00	-119.38	0.05	0.09	4.28
Degree	10	25	17.82	18.00	3,208	MAX VALUE	515.15	3.34	0.19	2.56
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.12	3.00	4,922	MAX VALUE	1,788.17	0.32	0.10	0.36

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 77
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 223.81 0.79 0.22 1.16

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.68 7.00 942 MAX VALUE 265.41 1.18 0.18 1.56

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	223.81	0.79	0.22	1.16
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.68	7.00	942	MAX VALUE	265.41	1.18	0.18	1.56

Triangulated dual graph

Density: 44.83%
Triangles: 182,145

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

Clustering coefficient 0.70 1.00 0.83 0.80 149.00 0.00 -35.09 0.09 0.11 4.64

Degree 10 126 80.24 98.50 14,444 MAX VALUE 753.46 39.86 0.50 3.86

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	0.80	149.00	0.00	-35.09	0.09	0.11	4.64
Degree	10	126	80.24	98.50	14,444	MAX VALUE	753.46	39.86	0.50	3.86
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.28%

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

Clustering coefficient 0.54 1.00 0.79 0.72 142.39 0.00 -45.66 0.16 0.20 3.31

Degree 2 64 20.19 7.00 3,634 MAX VALUE 416.85 22.25 1.10 3.09

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	0.54	1.00	0.79	0.72	142.39	0.00	-45.66	0.16	0.20	3.31
Degree	2	64	20.19	7.00	3,634	MAX VALUE	416.85	22.25	1.10	3.09
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-2-40-25-180-500-31-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-31-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 210.32 2.96 0.91 0.89

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.48 6.00 914 MAX VALUE 262.42 0.86 0.13 0.55

XCSP 2.1 Benchmarks