XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-180-84-900-18-ext
Number of variables: 40
Number of constraints: 84
Satisfiable: True
Timestamp: 2025-07-20 22:09:38
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 84

General features

Coarse blocks: 29,340
Value tables: 35

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 3 36 17.95 18.00 526,715 MAX VALUE 83,945.70 4.04 0.22 2.81

Relational linkage 0.02 0.14 0.08 0.08 482.30 0.00 -16,322.10 0.02 0.20 2.43

Tightness 0.90 0.91 0.90 0.90 75.62 0.00 -8.83 0.00 0.00 4.22

Tuples 3,059 3,368 3,232.44 3,235.00 271,525 MAX VALUE 678.79 54.43 0.02 4.22

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

Value table constraints 2 10 4.66 4.00 163 1.34e+22 50.95 1.96 0.42 1.85

Value table partitions 180 180 180.00 180.00 6,300 MAX VALUE 181.75 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	168	1.93e+25	58.22	0.00	0.00	0.00
Coarse blocks size	3	36	17.95	18.00	526,715	MAX VALUE	83,945.70	4.04	0.22	2.81
Relational linkage	0.02	0.14	0.08	0.08	482.30	0.00	-16,322.10	0.02	0.20	2.43
Tightness	0.90	0.91	0.90	0.90	75.62	0.00	-8.83	0.00	0.00	4.22
Tuples	3,059	3,368	3,232.44	3,235.00	271,525	MAX VALUE	678.79	54.43	0.02	4.22
Values	180	180	180.00	180.00	7,200	MAX VALUE	207.72	0.00	0.00	0.00
Value table constraints	2	10	4.66	4.00	163	1.34e+22	50.95	1.96	0.42	1.85
Value table partitions	180	180	180.00	180.00	6,300	MAX VALUE	181.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 31
Number of leaves: 12
Tree depth: 5
CIR: 0.56
Independent Cluster Pairs: 243
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/Tree1.json

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

Cluster constraints 1 9 4.16 4.00 129 3.82e+16 38.18 2.33 0.56 1.82

Variables per cluster 2 10 4.84 4.00 150 6.74e+19 45.66 2.20 0.45 1.99

Separator constraints 0 7 1.45 1.00 45 0 None 1.76 1.21 1.59

Separator variables 0 9 3.55 3.00 110 0 None 2.09 0.59 2.03

Clusters per var 1 13 3.75 2.00 150 1.49e+16 37.24 3.46 0.92 1.94

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	9	4.16	4.00	129	3.82e+16	38.18	2.33	0.56	1.82
Variables per cluster	2	10	4.84	4.00	150	6.74e+19	45.66	2.20	0.45	1.99
Separator constraints	0	7	1.45	1.00	45	0	None	1.76	1.21	1.59
Separator variables	0	9	3.55	3.00	110	0	None	2.09	0.59	2.03
Clusters per var	1	13	3.75	2.00	150	1.49e+16	37.24	3.46	0.92	1.94

Dual tree decomposition

Number of clusters: 38
Number of leaves: 11
Tree depth: 7
CIR: 0.56
Independent Cluster Pairs: 370
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/DualTree1.json

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

Cluster constraints 4 60 20.11 12.00 764 MAX VALUE 102.94 15.56 0.77 3.03

Variables per cluster 4 25 9.97 8.00 379 4.77e+35 82.15 5.59 0.56 2.58

Separator constraints 0 34 10.50 7.00 399 0 None 9.11 0.87 2.90

Separator variables 0 19 7.76 7.00 295 0 None 4.37 0.56 2.52

Clusters per variable 1 10 4.51 4.00 379 MAX VALUE 108.61 2.64 0.59 2.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	60	20.11	12.00	764	MAX VALUE	102.94	15.56	0.77	3.03
Variables per cluster	4	25	9.97	8.00	379	4.77e+35	82.15	5.59	0.56	2.58
Separator constraints	0	34	10.50	7.00	399	0	None	9.11	0.87	2.90
Separator variables	0	19	7.76	7.00	295	0	None	4.37	0.56	2.52
Clusters per variable	1	10	4.51	4.00	379	MAX VALUE	108.61	2.64	0.59	2.16

Primal graph

Density: 10.77%
MCB compute time (ms): 1
MCB cycles: 46
Triangles: 14
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/Primal1.json

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

Clustering coefficient 0.00 0.67 None 0.11 None None None None None 2.52

Degree 1 10 4.20 4.00 168 1.34e+22 50.95 2.19 0.52 1.99

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.87 4.00 178 5.26e+26 61.53 0.68 0.18 1.01

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.67	None	0.11	None	None	None	None	None	2.52
Degree	1	10	4.20	4.00	168	1.34e+22	50.95	2.19	0.52	1.99
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.87	4.00	178	5.26e+26	61.53	0.68	0.18	1.01

Triangulated primal graph

Density: 19.87%
MCB compute time (ms): 2
MCB cycles: 124
Triangles: 328

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

Clustering coefficient 0.42 1.00 None 0.71 None None None None None 3.29

Degree 1 21 7.75 5.00 310 1.17e+29 66.93 6.14 0.79 2.57

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 372 MAX VALUE 136.23 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.42	1.00	None	0.71	None	None	None	None	None	3.29
Degree	1	21	7.75	5.00	310	1.17e+29	66.93	6.14	0.79	2.57
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	372	MAX VALUE	136.23	0.00	0.00	0.00

Dual graph

Density: 10.47%
MCB compute time (ms): 18
MCB cycles: 329
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/Dual1.json

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

Clustering coefficient 0.33 1.00 0.54 0.50 45.18 0.00 -54.55 0.14 0.27 3.30

Degree 3 17 8.69 8.00 730 MAX VALUE 175.38 3.19 0.37 2.50

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.41 3.00 1,122 MAX VALUE 396.29 0.79 0.23 0.75

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.33	1.00	0.54	0.50	45.18	0.00	-54.55	0.14	0.27	3.30
Degree	3	17	8.69	8.00	730	MAX VALUE	175.38	3.19	0.37	2.50
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.41	3.00	1,122	MAX VALUE	396.29	0.79	0.23	0.75

Minimal dual graph

Density: 3.67%
MCB compute time (ms): 6
MCB cycles: 45

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 0.32

Degree 1 4 3.05 3.00 256 MAX VALUE 91.38 0.65 0.21 0.98

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 7.00 7.00 315 5.33e+37 86.87 1.19 0.17 1.57

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	0.32
Degree	1	4	3.05	3.00	256	MAX VALUE	91.38	0.65	0.21	0.98
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	7.00	7.00	315	5.33e+37	86.87	1.19	0.17	1.57

Triangulated dual graph

Density: 26.76%
Triangles: 6,346

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

Clustering coefficient 0.58 1.00 0.78 0.75 65.11 0.00 -22.55 0.13 0.17 3.86

Degree 3 45 22.21 17.50 1,866 MAX VALUE 236.96 14.24 0.64 3.44

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	0.58	1.00	0.78	0.75	65.11	0.00	-22.55	0.13	0.17	3.86
Degree	3	45	22.21	17.50	1,866	MAX VALUE	236.96	14.24	0.64	3.44
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.42%

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

Clustering coefficient 0.33 1.00 None 0.67 None None None None None 2.84

Degree 1 29 9.48 5.00 796 MAX VALUE 152.72 8.93 0.94 2.68

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	0.33	1.00	None	0.67	None	None	None	None	None	2.84
Degree	1	29	9.48	5.00	796	MAX VALUE	152.72	8.93	0.94	2.68
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.20%
MCB compute time (ms): 7
MCB cycles: 45
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-18-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 1.05

Degree 1 10 2.71 2.00 336 MAX VALUE 109.17 1.62 0.60 1.17

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.73 8.00 348 MAX VALUE 91.33 1.37 0.18 1.01

XCSP 2.1 Benchmarks