XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-180-84-900-65-ext
Number of variables: 40
Number of constraints: 84
Satisfiable: True
Timestamp: 2025-07-20 22:09:40
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 84

General features

Coarse blocks: 29,700
Value tables: 37

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 2 36 18.00 18.00 534,711 MAX VALUE 85,068.30 4.02 0.22 2.81

Relational linkage 0.01 0.14 0.08 0.08 513.14 0.00 -17,211.00 0.02 0.20 2.43

Tightness 0.89 0.91 0.90 0.90 75.60 0.00 -8.85 0.00 0.00 4.14

Tuples 3,071 3,411 3,240.36 3,237.50 272,190 MAX VALUE 679.00 55.11 0.02 4.14

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

Value table constraints 2 7 4.46 4.00 165 1.34e+23 53.25 1.43 0.32 1.71

Value table partitions 180 180 180.00 180.00 6,660 MAX VALUE 192.14 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	2	36	18.00	18.00	534,711	MAX VALUE	85,068.30	4.02	0.22	2.81
Relational linkage	0.01	0.14	0.08	0.08	513.14	0.00	-17,211.00	0.02	0.20	2.43
Tightness	0.89	0.91	0.90	0.90	75.60	0.00	-8.85	0.00	0.00	4.14
Tuples	3,071	3,411	3,240.36	3,237.50	272,190	MAX VALUE	679.00	55.11	0.02	4.14
Values	180	180	180.00	180.00	7,200	MAX VALUE	207.72	0.00	0.00	0.00
Value table constraints	2	7	4.46	4.00	165	1.34e+23	53.25	1.43	0.32	1.71
Value table partitions	180	180	180.00	180.00	6,660	MAX VALUE	192.14	0.00	0.00	0.00

Tree decomposition

Number of clusters: 30
Number of leaves: 14
Tree depth: 5
CIR: 0.49
Independent Cluster Pairs: 198
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/Tree1.json

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

Cluster constraints 1 7 3.53 3.00 106 3.69e+14 33.54 1.75 0.49 1.84

Variables per cluster 2 11 5.47 5.00 164 3.61e+20 47.33 2.70 0.49 2.13

Separator constraints 0 3 0.73 0.00 22 0 None 0.96 1.31 1.11

Separator variables 0 10 4.13 4.00 124 0 None 2.62 0.63 2.19

Clusters per var 1 13 4.10 2.00 164 5.11e+16 38.47 3.80 0.93 2.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	7	3.53	3.00	106	3.69e+14	33.54	1.75	0.49	1.84
Variables per cluster	2	11	5.47	5.00	164	3.61e+20	47.33	2.70	0.49	2.13
Separator constraints	0	3	0.73	0.00	22	0	None	0.96	1.31	1.11
Separator variables	0	10	4.13	4.00	124	0	None	2.62	0.63	2.19
Clusters per var	1	13	4.10	2.00	164	5.11e+16	38.47	3.80	0.93	2.02

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 6
CIR: 0.50
Independent Cluster Pairs: 336
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/DualTree1.json

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

Cluster constraints 3 35 18.11 18.00 688 MAX VALUE 103.87 8.61 0.48 3.06

Variables per cluster 3 25 10.50 9.00 399 5.55e+36 84.61 5.34 0.51 2.59

Separator constraints 0 22 9.61 10.50 365 0 None 5.38 0.56 2.78

Separator variables 0 18 8.29 7.50 315 0 None 4.19 0.51 2.64

Clusters per variable 1 11 4.75 4.50 399 MAX VALUE 110.95 2.79 0.59 2.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	35	18.11	18.00	688	MAX VALUE	103.87	8.61	0.48	3.06
Variables per cluster	3	25	10.50	9.00	399	5.55e+36	84.61	5.34	0.51	2.59
Separator constraints	0	22	9.61	10.50	365	0	None	5.38	0.56	2.78
Separator variables	0	18	8.29	7.50	315	0	None	4.19	0.51	2.64
Clusters per variable	1	11	4.75	4.50	399	MAX VALUE	110.95	2.79	0.59	2.23

Primal graph

Density: 10.77%
MCB compute time (ms): 1
MCB cycles: 46
Triangles: 10
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 None 0.07 None None None None None 1.97

Degree 1 7 4.20 4.00 168 1.34e+23 53.25 1.65 0.39 1.85

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 4.09 4.00 188 6.09e+27 63.98 0.75 0.18 1.11

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	None	0.07	None	None	None	None	None	1.97
Degree	1	7	4.20	4.00	168	1.34e+23	53.25	1.65	0.39	1.85
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	4.09	4.00	188	6.09e+27	63.98	0.75	0.18	1.11

Triangulated primal graph

Density: 22.95%
MCB compute time (ms): 2
MCB cycles: 147
Triangles: 462

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

Clustering coefficient 0.33 1.00 None None None None None None None 3.03

Degree 1 22 8.95 6.00 358 3.96e+31 72.76 6.93 0.77 2.72

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 441 MAX VALUE 161.50 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.33	1.00	None	None	None	None	None	None	None	3.03
Degree	1	22	8.95	6.00	358	3.96e+31	72.76	6.93	0.77	2.72
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	441	MAX VALUE	161.50	0.00	0.00	0.00

Dual graph

Density: 9.27%
MCB compute time (ms): 15
MCB cycles: 276
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/Dual1.json

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

Clustering coefficient 0.33 1.00 0.50 0.47 42.25 0.00 -59.34 0.11 0.23 2.83

Degree 2 12 7.69 8.00 646 MAX VALUE 167.95 1.94 0.25 2.01

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.41 3.00 940 MAX VALUE 332.46 0.77 0.23 0.81

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.33	1.00	0.50	0.47	42.25	0.00	-59.34	0.11	0.23	2.83
Degree	2	12	7.69	8.00	646	MAX VALUE	167.95	1.94	0.25	2.01
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.41	3.00	940	MAX VALUE	332.46	0.77	0.23	0.81

Minimal dual graph

Density: 3.67%
MCB compute time (ms): 5
MCB cycles: 45

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

Clustering coefficient 0.00 0.33 None 0.00 None None None None None 0.24

Degree 1 4 3.05 3.00 256 MAX VALUE 91.50 0.63 0.21 0.95

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.78 7.00 305 7.36e+36 84.89 1.46 0.22 1.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	None	0.00	None	None	None	None	None	0.24
Degree	1	4	3.05	3.00	256	MAX VALUE	91.50	0.63	0.21	0.95
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.78	7.00	305	7.36e+36	84.89	1.46	0.22	1.66

Triangulated dual graph

Density: 27.40%
Triangles: 6,387

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

Clustering coefficient 0.49 1.00 0.78 0.76 65.27 0.00 -22.55 0.14 0.18 3.76

Degree 2 52 22.74 21.00 1,910 MAX VALUE 240.85 13.93 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	0.49	1.00	0.78	0.76	65.27	0.00	-22.55	0.14	0.18	3.76
Degree	2	52	22.74	21.00	1,910	MAX VALUE	240.85	13.93	0.61	3.47
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.22%

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 2.96

Degree 1 30 10.14 5.00 852 MAX VALUE 158.45 9.21 0.91 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	2.96
Degree	1	30	10.14	5.00	852	MAX VALUE	158.45	9.21	0.91	2.68
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-2-40-180-84-900-65-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-65-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 1.00

Degree 1 7 2.71 2.00 336 MAX VALUE 111.47 1.39 0.51 1.12

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 8.09 8.00 364 MAX VALUE 93.38 1.40 0.17 1.03

XCSP 2.1 Benchmarks