XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-180-84-900-16-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: 29,700
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 4 37 18.01 18.00 534,760 MAX VALUE 85,065.70 4.04 0.22 2.81

Relational linkage 0.02 0.14 0.08 0.08 514.01 0.00 -17,199.70 0.02 0.20 2.43

Tightness 0.90 0.90 0.90 0.90 75.60 0.00 -8.85 0.00 0.00 4.19

Tuples 3,146 3,371 3,240.98 3,230.00 272,242 MAX VALUE 679.01 51.64 0.02 4.19

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

Value table constraints 2 9 4.46 4.00 165 9.83e+22 52.94 1.60 0.36 1.81

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	4	37	18.01	18.00	534,760	MAX VALUE	85,065.70	4.04	0.22	2.81
Relational linkage	0.02	0.14	0.08	0.08	514.01	0.00	-17,199.70	0.02	0.20	2.43
Tightness	0.90	0.90	0.90	0.90	75.60	0.00	-8.85	0.00	0.00	4.19
Tuples	3,146	3,371	3,240.98	3,230.00	272,242	MAX VALUE	679.01	51.64	0.02	4.19
Values	180	180	180.00	180.00	7,200	MAX VALUE	207.72	0.00	0.00	0.00
Value table constraints	2	9	4.46	4.00	165	9.83e+22	52.94	1.60	0.36	1.81
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: 6
CIR: 0.52
Independent Cluster Pairs: 210
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-16-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-16-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-16-ext/Tree1.json

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

Cluster constraints 1 8 4.07 4.00 122 2.26e+16 37.66 2.00 0.49 1.93

Variables per cluster 2 10 5.37 5.00 161 3.69e+20 47.36 2.39 0.44 2.01

Separator constraints 0 5 1.27 1.00 38 0 None 1.55 1.22 1.42

Separator variables 0 9 4.03 4.00 121 0 None 2.29 0.57 2.05

Clusters per var 1 15 4.03 2.50 161 2.24e+17 39.95 3.45 0.86 1.91

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	8	4.07	4.00	122	2.26e+16	37.66	2.00	0.49	1.93
Variables per cluster	2	10	5.37	5.00	161	3.69e+20	47.36	2.39	0.44	2.01
Separator constraints	0	5	1.27	1.00	38	0	None	1.55	1.22	1.42
Separator variables	0	9	4.03	4.00	121	0	None	2.29	0.57	2.05
Clusters per var	1	15	4.03	2.50	161	2.24e+17	39.95	3.45	0.86	1.91

Dual tree decomposition

Number of clusters: 38
Number of leaves: 14
Tree depth: 6
CIR: 0.45
Independent Cluster Pairs: 303
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-16-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-16-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-16-ext/DualTree1.json

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

Cluster constraints 4 41 18.45 16.00 701 MAX VALUE 104.09 10.11 0.55 3.00

Variables per cluster 4 25 10.61 9.00 403 9.22e+36 85.11 5.44 0.51 2.61

Separator constraints 0 28 9.68 10.00 368 0 None 6.47 0.67 2.70

Separator variables 0 18 8.39 7.50 319 0 None 4.21 0.50 2.68

Clusters per variable 1 11 4.80 5.00 403 MAX VALUE 111.23 2.89 0.60 2.27

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	41	18.45	16.00	701	MAX VALUE	104.09	10.11	0.55	3.00
Variables per cluster	4	25	10.61	9.00	403	9.22e+36	85.11	5.44	0.51	2.61
Separator constraints	0	28	9.68	10.00	368	0	None	6.47	0.67	2.70
Separator variables	0	18	8.39	7.50	319	0	None	4.21	0.50	2.68
Clusters per variable	1	11	4.80	5.00	403	MAX VALUE	111.23	2.89	0.60	2.27

Primal graph

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

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

Clustering coefficient 0.00 0.67 None 0.00 None None None None None 1.83

Degree 1 9 4.20 4.00 168 9.83e+22 52.94 1.79 0.43 1.94

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 4.19 4.00 197 7.93e+28 66.54 0.76 0.18 1.13

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.67	None	0.00	None	None	None	None	None	1.83
Degree	1	9	4.20	4.00	168	9.83e+22	52.94	1.79	0.43	1.94
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	4.19	4.00	197	7.93e+28	66.54	0.76	0.18	1.13

Triangulated primal graph

Density: 22.44%
MCB compute time (ms): 2
MCB cycles: 136
Triangles: 418

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

Clustering coefficient 0.37 1.00 None 0.71 None None None None None 3.11

Degree 1 24 8.75 6.50 350 5.34e+31 73.06 6.40 0.73 2.60

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 408 MAX VALUE 149.41 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.37	1.00	None	0.71	None	None	None	None	None	3.11
Degree	1	24	8.75	6.50	350	5.34e+31	73.06	6.40	0.73	2.60
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	408	MAX VALUE	149.41	0.00	0.00	0.00

Dual graph

Density: 9.55%
MCB compute time (ms): 23
MCB cycles: 252
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-16-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-16-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-16-ext/Dual1.json

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

Clustering coefficient 0.33 1.00 0.51 0.47 42.86 0.00 -58.46 0.12 0.24 3.04

Degree 3 13 7.93 8.00 666 MAX VALUE 170.26 2.22 0.28 2.13

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.22 3.00 811 MAX VALUE 291.54 0.56 0.17 0.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.33	1.00	0.51	0.47	42.86	0.00	-58.46	0.12	0.24	3.04
Degree	3	13	7.93	8.00	666	MAX VALUE	170.26	2.22	0.28	2.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.22	3.00	811	MAX VALUE	291.54	0.56	0.17	0.54

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 92.02 0.58 0.19 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 7.16 7.00 322 1.38e+38 87.82 1.25 0.17 1.58

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	92.02	0.58	0.19	0.86
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	7.16	7.00	322	1.38e+38	87.82	1.25	0.17	1.58

Triangulated dual graph

Density: 28.17%
Triangles: 6,779

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

Clustering coefficient 0.50 1.00 0.78 0.75 65.54 0.00 -22.19 0.14 0.18 3.81

Degree 3 52 23.38 23.00 1,964 MAX VALUE 243.20 14.32 0.61 3.42

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	0.50	1.00	0.78	0.75	65.54	0.00	-22.19	0.14	0.18	3.81
Degree	3	52	23.38	23.00	1,964	MAX VALUE	243.20	14.32	0.61	3.42
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.90%

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

Clustering coefficient 0.40 1.00 0.74 0.67 62.22 0.00 -28.58 0.21 0.28 2.69

Degree 2 33 9.88 5.50 830 MAX VALUE 158.44 8.94 0.90 2.86

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	0.40	1.00	0.74	0.67	62.22	0.00	-28.58	0.21	0.28	2.69
Degree	2	33	9.88	5.50	830	MAX VALUE	158.44	8.94	0.90	2.86
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-2-40-180-84-900-16-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-16-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.9/normalized-rand-2-40-180-84-900-16-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 0.84

Degree 1 9 2.71 2.00 336 MAX VALUE 111.17 1.45 0.53 1.15

Eccentricity None None None None None None None None None None

MCB cycle size 6 12 8.31 8.00 374 MAX VALUE 94.52 1.52 0.18 1.13

XCSP 2.1 Benchmarks