XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-80-103-800-62-ext
Number of variables: 40
Number of constraints: 103
Satisfiable: True
Timestamp: 2025-07-20 22:09:37
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 103

General features

Coarse blocks: 16,320
Value tables: 38

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

Arity 2 2 2.00 2.00 206 1.01e+31 71.39 0.00 0.00 0.00

Coarse blocks size 4 30 16.02 16.00 261,415 MAX VALUE 44,839.20 3.58 0.22 2.69

Relational linkage 0.05 0.26 0.15 0.15 457.69 0.00 -5,818.26 0.03 0.20 2.28

Tightness 0.78 0.81 0.80 0.80 82.38 0.00 -23.01 0.01 0.01 4.16

Tuples 1,196 1,382 1,281.33 1,280.00 131,977 MAX VALUE 736.99 36.97 0.03 4.16

Values 80 80 80.00 80.00 3,200 MAX VALUE 175.28 0.00 0.00 0.00

Value table constraints 2 11 5.37 5.00 204 2.33e+26 60.71 2.11 0.39 2.06

Value table partitions 80 80 80.00 80.00 3,040 MAX VALUE 166.52 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	206	1.01e+31	71.39	0.00	0.00	0.00
Coarse blocks size	4	30	16.02	16.00	261,415	MAX VALUE	44,839.20	3.58	0.22	2.69
Relational linkage	0.05	0.26	0.15	0.15	457.69	0.00	-5,818.26	0.03	0.20	2.28
Tightness	0.78	0.81	0.80	0.80	82.38	0.00	-23.01	0.01	0.01	4.16
Tuples	1,196	1,382	1,281.33	1,280.00	131,977	MAX VALUE	736.99	36.97	0.03	4.16
Values	80	80	80.00	80.00	3,200	MAX VALUE	175.28	0.00	0.00	0.00
Value table constraints	2	11	5.37	5.00	204	2.33e+26	60.71	2.11	0.39	2.06
Value table partitions	80	80	80.00	80.00	3,040	MAX VALUE	166.52	0.00	0.00	0.00

Tree decomposition

Number of clusters: 29
Number of leaves: 13
Tree depth: 5
CIR: 0.39
Independent Cluster Pairs: 148
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/Tree1.json

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

Cluster constraints 1 15 6.59 6.00 191 5.71e+20 47.79 4.13 0.63 2.37

Variables per cluster 2 12 6.38 6.00 185 4.63e+21 49.89 3.21 0.50 2.23

Separator constraints 0 12 3.03 2.00 88 0 None 3.48 1.15 1.96

Separator variables 0 11 5.00 4.00 145 0 None 3.17 0.63 2.31

Clusters per var 1 13 4.62 2.00 185 4.00e+18 42.83 4.08 0.88 2.08

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	15	6.59	6.00	191	5.71e+20	47.79	4.13	0.63	2.37
Variables per cluster	2	12	6.38	6.00	185	4.63e+21	49.89	3.21	0.50	2.23
Separator constraints	0	12	3.03	2.00	88	0	None	3.48	1.15	1.96
Separator variables	0	11	5.00	4.00	145	0	None	3.17	0.63	2.31
Clusters per var	1	13	4.62	2.00	185	4.00e+18	42.83	4.08	0.88	2.08

Dual tree decomposition

Number of clusters: 38
Number of leaves: 13
Tree depth: 7
CIR: 0.44
Independent Cluster Pairs: 294
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/DualTree1.json

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

Cluster constraints 3 83 33.29 27.50 1,265 MAX VALUE 123.23 21.53 0.65 3.25

Variables per cluster 3 37 13.89 11.00 528 MAX VALUE 94.01 8.15 0.59 2.80

Separator constraints 0 45 19.34 16.00 735 0 None 13.36 0.69 3.21

Separator variables 0 26 11.18 10.00 425 0 None 6.33 0.57 2.78

Clusters per variable 1 11 5.13 5.00 528 MAX VALUE 146.44 2.81 0.55 2.29

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	83	33.29	27.50	1,265	MAX VALUE	123.23	21.53	0.65	3.25
Variables per cluster	3	37	13.89	11.00	528	MAX VALUE	94.01	8.15	0.59	2.80
Separator constraints	0	45	19.34	16.00	735	0	None	13.36	0.69	3.21
Separator variables	0	26	11.18	10.00	425	0	None	6.33	0.57	2.78
Clusters per variable	1	11	5.13	5.00	528	MAX VALUE	146.44	2.81	0.55	2.29

Primal graph

Density: 13.21%
MCB compute time (ms): 2
MCB cycles: 67
Triangles: 29
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/Primal1.json

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

Clustering coefficient 0.00 1.00 None 0.17 None None None None None 2.73

Degree 1 11 5.15 5.00 206 2.33e+26 60.71 2.26 0.44 2.15

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.70 4.00 248 3.86e+37 86.55 0.69 0.19 0.99

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	1.00	None	0.17	None	None	None	None	None	2.73
Degree	1	11	5.15	5.00	206	2.33e+26	60.71	2.26	0.44	2.15
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.70	4.00	248	3.86e+37	86.55	0.69	0.19	0.99

Triangulated primal graph

Density: 27.05%
MCB compute time (ms): 3
MCB cycles: 187
Triangles: 656

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

Clustering coefficient 0.33 1.00 None 0.77 None None None None None 3.14

Degree 1 23 10.55 7.50 422 7.00e+34 80.23 7.53 0.71 2.82

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 561 MAX VALUE 205.44 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	0.77	None	None	None	None	None	3.14
Degree	1	23	10.55	7.50	422	7.00e+34	80.23	7.53	0.71	2.82
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	561	MAX VALUE	205.44	0.00	0.00	0.00

Dual graph

Density: 10.09%
MCB compute time (ms): 46
MCB cycles: 448
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/Dual1.json

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

Clustering coefficient 0.40 1.00 0.52 0.50 53.73 0.00 -68.56 0.10 0.19 3.50

Degree 2 18 10.29 10.00 1,060 MAX VALUE 234.95 3.05 0.30 2.44

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.15 3.00 1,409 MAX VALUE 510.17 0.42 0.13 0.43

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	1.00	0.52	0.50	53.73	0.00	-68.56	0.10	0.19	3.50
Degree	2	18	10.29	10.00	1,060	MAX VALUE	234.95	3.05	0.30	2.44
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.15	3.00	1,409	MAX VALUE	510.17	0.42	0.13	0.43

Minimal dual graph

Density: 3.16%
MCB compute time (ms): 12
MCB cycles: 64

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 5 3.22 3.00 332 MAX VALUE 117.87 0.72 0.22 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.73 7.00 431 MAX VALUE 120.76 1.30 0.19 1.61

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	5	3.22	3.00	332	MAX VALUE	117.87	0.72	0.22	1.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.73	7.00	431	MAX VALUE	120.76	1.30	0.19	1.61

Triangulated dual graph

Density: 33.10%
Triangles: 18,259

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

Clustering coefficient 0.58 1.00 0.80 0.78 82.05 0.00 -24.47 0.11 0.14 4.13

Degree 2 66 33.77 35.00 3,478 MAX VALUE 335.72 19.93 0.59 3.70

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	0.80	0.78	82.05	0.00	-24.47	0.11	0.14	4.13
Degree	2	66	33.77	35.00	3,478	MAX VALUE	335.72	19.93	0.59	3.70
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.63%

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

Clustering coefficient 0.45 1.00 0.75 0.67 77.37 0.00 -32.80 0.19 0.25 2.91

Degree 2 36 11.86 5.00 1,222 MAX VALUE 204.58 11.52 0.97 2.79

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	0.45	1.00	0.75	0.67	77.37	0.00	-32.80	0.19	0.25	2.91
Degree	2	36	11.86	5.00	1,222	MAX VALUE	204.58	11.52	0.97	2.79
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.03%
MCB compute time (ms): 13
MCB cycles: 64
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-62-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 0.51

Degree 1 11 2.88 2.00 412 MAX VALUE 132.10 1.85 0.64 1.10

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.31 8.00 468 MAX VALUE 126.30 1.33 0.18 0.96

XCSP 2.1 Benchmarks