XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-16-250-350-31-ext
Number of variables: 40
Number of constraints: 250
Satisfiable: True
Timestamp: 2025-07-20 22:09:22
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 250

General features

Coarse blocks: 8,000
Value tables: 40

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

Arity 2 2 2.00 2.00 500 MAX VALUE 173.29 0.00 0.00 0.00

Coarse blocks size 4 16 10.40 10.00 83,186 MAX VALUE 18,590.90 1.89 0.18 2.05

Relational linkage 0.25 0.69 0.46 0.44 291.31 0.00 -512.51 0.07 0.16 1.58

Tightness 0.27 0.43 0.35 0.35 87.53 0.00 -263.29 0.03 0.08 3.37

Tuples 146 188 166.37 167.00 41,593 MAX VALUE 1,278.30 7.59 0.05 3.37

Values 16 16 16.00 16.00 640 MAX VALUE 110.90 0.00 0.00 0.00

Value table constraints 6 18 12.50 13.00 500 MAX VALUE 99.73 2.99 0.24 2.37

Value table partitions 16 16 16.00 16.00 640 MAX VALUE 110.90 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	500	MAX VALUE	173.29	0.00	0.00	0.00
Coarse blocks size	4	16	10.40	10.00	83,186	MAX VALUE	18,590.90	1.89	0.18	2.05
Relational linkage	0.25	0.69	0.46	0.44	291.31	0.00	-512.51	0.07	0.16	1.58
Tightness	0.27	0.43	0.35	0.35	87.53	0.00	-263.29	0.03	0.08	3.37
Tuples	146	188	166.37	167.00	41,593	MAX VALUE	1,278.30	7.59	0.05	3.37
Values	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00
Value table constraints	6	18	12.50	13.00	500	MAX VALUE	99.73	2.99	0.24	2.37
Value table partitions	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00

Tree decomposition

Number of clusters: 17
Number of leaves: 9
Tree depth: 3
CIR: 0.01
Independent Cluster Pairs: 1
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/Tree1.json

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

Cluster constraints 11 108 44.24 31.00 752 1.46e+26 60.24 31.54 0.71 2.59

Variables per cluster 7 24 13.82 12.00 235 6.63e+18 43.34 5.52 0.40 2.31

Separator constraints 0 92 29.53 20.00 502 0 None 27.84 0.94 2.83

Separator variables 0 22 11.47 10.00 195 0 None 5.68 0.50 2.31

Clusters per var 1 13 5.88 7.00 235 1.63e+25 58.05 3.66 0.62 2.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	11	108	44.24	31.00	752	1.46e+26	60.24	31.54	0.71	2.59
Variables per cluster	7	24	13.82	12.00	235	6.63e+18	43.34	5.52	0.40	2.31
Separator constraints	0	92	29.53	20.00	502	0	None	27.84	0.94	2.83
Separator variables	0	22	11.47	10.00	195	0	None	5.68	0.50	2.31
Clusters per var	1	13	5.88	7.00	235	1.63e+25	58.05	3.66	0.62	2.23

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.13
Independent Cluster Pairs: 85
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/DualTree1.json

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

Cluster constraints 69 825 268.26 213.00 10,194 MAX VALUE 204.37 189.70 0.71 3.64

Variables per cluster 16 126 42.92 31.00 1,631 MAX VALUE 136.05 28.92 0.67 3.30

Separator constraints 0 471 187.90 167.00 7,140 0 None 111.91 0.60 3.56

Separator variables 0 97 36.34 28.50 1,381 0 None 22.14 0.61 3.32

Clusters per variable 1 11 6.52 7.00 1,631 MAX VALUE 435.32 2.57 0.39 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	69	825	268.26	213.00	10,194	MAX VALUE	204.37	189.70	0.71	3.64
Variables per cluster	16	126	42.92	31.00	1,631	MAX VALUE	136.05	28.92	0.67	3.30
Separator constraints	0	471	187.90	167.00	7,140	0	None	111.91	0.60	3.56
Separator variables	0	97	36.34	28.50	1,381	0	None	22.14	0.61	3.32
Clusters per variable	1	11	6.52	7.00	1,631	MAX VALUE	435.32	2.57	0.39	2.15

Primal graph

Density: 32.05%
MCB compute time (ms): 4
MCB cycles: 329
Triangles: 326
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/Primal1.json

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

Clustering coefficient 0.22 0.50 0.33 0.32 13.38 0.00 -44.52 0.07 0.20 3.35

Degree 6 18 12.50 13.00 500 MAX VALUE 99.73 2.99 0.24 2.37

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.23 3.00 1,062 MAX VALUE 383.02 0.42 0.13 0.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.22	0.50	0.33	0.32	13.38	0.00	-44.52	0.07	0.20	3.35
Degree	6	18	12.50	13.00	500	MAX VALUE	99.73	2.99	0.24	2.37
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.23	3.00	1,062	MAX VALUE	383.02	0.42	0.13	0.54

Triangulated primal graph

Density: 60.38%
MCB compute time (ms): 12
MCB cycles: 453
Triangles: 3,319

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

Clustering coefficient 0.66 1.00 0.86 0.83 34.35 0.00 -6.36 0.10 0.12 3.06

Degree 6 35 23.55 29.00 942 MAX VALUE 121.44 9.54 0.41 2.71

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,359 MAX VALUE 497.67 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.66	1.00	0.86	0.83	34.35	0.00	-6.36	0.10	0.12	3.06
Degree	6	35	23.55	29.00	942	MAX VALUE	121.44	9.54	0.41	2.71
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,359	MAX VALUE	497.67	0.00	0.00	0.00

Dual graph

Density: 9.81%
MCB compute time (ms): 789
MCB cycles: 3,889
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/Dual1.json

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

Clustering coefficient 0.48 0.65 0.51 0.50 127.74 0.00 -168.19 0.03 0.05 4.59

Degree 15 33 24.43 24.00 6,108 MAX VALUE 796.20 3.58 0.15 2.67

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.09 3.00 12,009 MAX VALUE 4,370.44 0.29 0.09 0.30

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.65	0.51	0.50	127.74	0.00	-168.19	0.03	0.05	4.59
Degree	15	33	24.43	24.00	6,108	MAX VALUE	796.20	3.58	0.15	2.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.09	3.00	12,009	MAX VALUE	4,370.44	0.29	0.09	0.30

Minimal dual graph

Density: 1.48%
MCB compute time (ms): 225
MCB cycles: 211

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 3.68 4.00 920 MAX VALUE 319.93 0.81 0.22 1.14

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.74 7.00 1,423 MAX VALUE 398.59 1.27 0.19 1.63

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	3.68	4.00	920	MAX VALUE	319.93	0.81	0.22	1.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.74	7.00	1,423	MAX VALUE	398.59	1.27	0.19	1.63

Triangulated dual graph

Density: 52.58%
Triangles: 677,350

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

Clustering coefficient 0.71 1.00 0.85 0.84 211.99 0.00 -42.29 0.08 0.09 4.94

Degree 15 199 130.92 151.00 32,730 MAX VALUE 1,176.69 57.70 0.44 4.14

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	0.71	1.00	0.85	0.84	211.99	0.00	-42.29	0.08	0.09	4.94
Degree	15	199	130.92	151.00	32,730	MAX VALUE	1,176.69	57.70	0.44	4.14
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.39%

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

Clustering coefficient 0.47 1.00 0.81 0.76 203.59 0.00 -55.23 0.14 0.18 3.49

Degree 2 90 28.37 9.00 7,092 MAX VALUE 629.88 32.67 1.15 3.24

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	0.47	1.00	0.81	0.76	203.59	0.00	-55.23	0.14	0.18	3.49
Degree	2	90	28.37	9.00	7,092	MAX VALUE	629.88	32.67	1.15	3.24
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.19%
MCB compute time (ms): 79
MCB cycles: 211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-31-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 18 3.45 2.00 1,000 MAX VALUE 273.01 3.79 1.10 0.73

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.02 6.00 1,270 MAX VALUE 378.64 0.19 0.03 0.05

XCSP 2.1 Benchmarks