XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-180-84-900-95-ext
Number of variables: 40
Number of constraints: 84
Satisfiable: True
Timestamp: 2025-07-20 22:09:41
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 84

General features

Coarse blocks: 29,520
Value tables: 36

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

Arity 2 2 2.00 2.00 168 1.93e+25 58.22 0.00 0.00 0.00

Coarse blocks size 5 35 17.92 18.00 528,854 MAX VALUE 84,404.60 4.01 0.22 2.81

Relational linkage 0.03 0.14 0.08 0.08 498.06 0.00 -16,766.30 0.02 0.20 2.45

Tightness 0.90 0.91 0.90 0.90 75.64 0.00 -8.81 0.00 0.00 4.12

Tuples 3,050 3,393 3,225.14 3,227.00 270,912 MAX VALUE 678.60 60.42 0.02 4.12

Values 180 180 180.00 180.00 7,200 MAX VALUE 207.72 0.00 0.00 0.00

Value table constraints 2 9 4.56 4.00 164 2.01e+22 51.36 1.86 0.41 1.90

Value table partitions 180 180 180.00 180.00 6,480 MAX VALUE 186.95 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	168	1.93e+25	58.22	0.00	0.00	0.00
Coarse blocks size	5	35	17.92	18.00	528,854	MAX VALUE	84,404.60	4.01	0.22	2.81
Relational linkage	0.03	0.14	0.08	0.08	498.06	0.00	-16,766.30	0.02	0.20	2.45
Tightness	0.90	0.91	0.90	0.90	75.64	0.00	-8.81	0.00	0.00	4.12
Tuples	3,050	3,393	3,225.14	3,227.00	270,912	MAX VALUE	678.60	60.42	0.02	4.12
Values	180	180	180.00	180.00	7,200	MAX VALUE	207.72	0.00	0.00	0.00
Value table constraints	2	9	4.56	4.00	164	2.01e+22	51.36	1.86	0.41	1.90
Value table partitions	180	180	180.00	180.00	6,480	MAX VALUE	186.95	0.00	0.00	0.00

Tree decomposition

Number of clusters: 31
Number of leaves: 15
Tree depth: 6
CIR: 0.54
Independent Cluster Pairs: 237
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Tree1.json

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

Cluster constraints 1 11 4.45 4.00 138 1.50e+17 39.55 2.70 0.61 2.14

Variables per cluster 2 10 5.03 5.00 156 1.67e+20 46.57 2.39 0.47 2.00

Separator constraints 0 8 1.74 1.00 54 0 None 2.17 1.25 1.65

Separator variables 0 9 3.74 3.00 116 0 None 2.31 0.62 2.04

Clusters per var 1 12 3.90 2.50 156 2.46e+16 37.74 3.37 0.87 1.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	11	4.45	4.00	138	1.50e+17	39.55	2.70	0.61	2.14
Variables per cluster	2	10	5.03	5.00	156	1.67e+20	46.57	2.39	0.47	2.00
Separator constraints	0	8	1.74	1.00	54	0	None	2.17	1.25	1.65
Separator variables	0	9	3.74	3.00	116	0	None	2.31	0.62	2.04
Clusters per var	1	12	3.90	2.50	156	2.46e+16	37.74	3.37	0.87	1.88

Dual tree decomposition

Number of clusters: 38
Number of leaves: 11
Tree depth: 7
CIR: 0.55
Independent Cluster Pairs: 364
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/DualTree1.json

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

Cluster constraints 4 53 18.13 15.00 689 MAX VALUE 101.70 12.09 0.67 2.85

Variables per cluster 5 23 9.97 9.00 379 1.54e+36 83.33 4.84 0.49 2.53

Separator constraints 0 26 8.82 7.00 335 0 None 6.39 0.72 2.70

Separator variables 0 17 7.76 7.50 295 0 None 3.75 0.48 2.31

Clusters per variable 1 11 4.51 4.00 379 MAX VALUE 109.47 2.63 0.58 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	53	18.13	15.00	689	MAX VALUE	101.70	12.09	0.67	2.85
Variables per cluster	5	23	9.97	9.00	379	1.54e+36	83.33	4.84	0.49	2.53
Separator constraints	0	26	8.82	7.00	335	0	None	6.39	0.72	2.70
Separator variables	0	17	7.76	7.50	295	0	None	3.75	0.48	2.31
Clusters per variable	1	11	4.51	4.00	379	MAX VALUE	109.47	2.63	0.58	2.21

Primal graph

Density: 10.77%
MCB compute time (ms): 1
MCB cycles: 47
Triangles: 16
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Primal1.json

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

Clustering coefficient 0.00 0.50 None 0.13 None None None None None 2.50

Degree 1 9 4.20 4.00 168 2.01e+22 51.36 2.06 0.49 2.04

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.98 4.00 187 5.42e+27 63.86 0.84 0.21 1.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.50	None	0.13	None	None	None	None	None	2.50
Degree	1	9	4.20	4.00	168	2.01e+22	51.36	2.06	0.49	2.04
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.98	4.00	187	5.42e+27	63.86	0.84	0.21	1.17

Triangulated primal graph

Density: 20.64%
MCB compute time (ms): 2
MCB cycles: 142
Triangles: 362

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

Clustering coefficient 0.40 1.00 None 0.78 None None None None None 3.00

Degree 1 20 8.05 6.00 322 3.47e+29 68.02 6.16 0.77 2.57

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 426 MAX VALUE 156.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	1.00	None	0.78	None	None	None	None	None	3.00
Degree	1	20	8.05	6.00	322	3.47e+29	68.02	6.16	0.77	2.57
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	426	MAX VALUE	156.00	0.00	0.00	0.00

Dual graph

Density: 10.15%
MCB compute time (ms): 16
MCB cycles: 279
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Dual1.json

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

Clustering coefficient 0.40 1.00 0.54 0.50 45.22 0.00 -53.86 0.13 0.24 3.21

Degree 4 15 8.43 8.00 708 MAX VALUE 174.76 2.58 0.31 2.30

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.21 3.00 896 MAX VALUE 321.94 0.59 0.18 0.51

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	1.00	0.54	0.50	45.22	0.00	-53.86	0.13	0.24	3.21
Degree	4	15	8.43	8.00	708	MAX VALUE	174.76	2.58	0.31	2.30
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.21	3.00	896	MAX VALUE	321.94	0.59	0.18	0.51

Minimal dual graph

Density: 3.67%
MCB compute time (ms): 7
MCB cycles: 45

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 4 3.05 3.00 256 MAX VALUE 92.14 0.55 0.18 0.83

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 7.07 7.00 318 7.34e+37 87.19 1.25 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	4	3.05	3.00	256	MAX VALUE	92.14	0.55	0.18	0.83
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	7.07	7.00	318	7.34e+37	87.19	1.25	0.18	1.56

Triangulated dual graph

Density: 25.27%
Triangles: 5,320

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

Clustering coefficient 0.53 1.00 0.77 0.77 64.81 0.00 -23.28 0.14 0.19 4.02

Degree 4 45 20.98 18.00 1,762 MAX VALUE 236.25 12.70 0.61 3.47

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	0.53	1.00	0.77	0.77	64.81	0.00	-23.28	0.14	0.19	4.02
Degree	4	45	20.98	18.00	1,762	MAX VALUE	236.25	12.70	0.61	3.47
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.91%

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

Clustering coefficient 0.47 1.00 0.74 0.67 62.46 0.00 -27.67 0.19 0.26 2.83

Degree 2 32 10.71 6.00 900 MAX VALUE 163.38 9.69 0.90 2.71

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	0.74	0.67	62.46	0.00	-27.67	0.19	0.26	2.83
Degree	2	32	10.71	6.00	900	MAX VALUE	163.38	9.69	0.90	2.71
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.20%
MCB compute time (ms): 8
MCB cycles: 45
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-95-ext/Incidence1.json

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

Clustering coefficient 0.00 0.00 None 0.00 None None None None None 0.97

Degree 1 9 2.71 2.00 336 MAX VALUE 109.58 1.56 0.58 1.11

Eccentricity None None None None None None None None None None

MCB cycle size 6 12 7.91 8.00 356 MAX VALUE 92.06 1.68 0.21 1.17

XCSP 2.1 Benchmarks