XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-80-103-800-76-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 3 32 16.06 16.00 262,146 MAX VALUE 44,886.20 3.57 0.22 2.69

Relational linkage 0.04 0.26 0.15 0.15 454.23 0.00 -5,840.94 0.03 0.20 2.27

Tightness 0.79 0.81 0.80 0.80 82.32 0.00 -23.09 0.01 0.01 4.13

Tuples 1,189 1,373 1,285.10 1,287.00 132,365 MAX VALUE 737.30 33.31 0.03 4.13

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 4.79e+26 61.43 1.87 0.35 1.90

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	3	32	16.06	16.00	262,146	MAX VALUE	44,886.20	3.57	0.22	2.69
Relational linkage	0.04	0.26	0.15	0.15	454.23	0.00	-5,840.94	0.03	0.20	2.27
Tightness	0.79	0.81	0.80	0.80	82.32	0.00	-23.09	0.01	0.01	4.13
Tuples	1,189	1,373	1,285.10	1,287.00	132,365	MAX VALUE	737.30	33.31	0.03	4.13
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	4.79e+26	61.43	1.87	0.35	1.90
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: 27
Number of leaves: 11
Tree depth: 5
CIR: 0.34
Independent Cluster Pairs: 110
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/Tree1.json

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

Cluster constraints 1 13 6.07 4.00 164 2.84e+18 42.49 3.73 0.61 2.26

Variables per cluster 2 14 6.70 6.00 181 6.13e+20 47.86 3.35 0.50 2.29

Separator constraints 0 9 2.26 1.00 61 0 None 2.73 1.21 1.81

Separator variables 0 12 5.22 5.00 141 0 None 3.20 0.61 2.29

Clusters per var 1 15 4.53 4.00 181 1.20e+19 43.93 3.84 0.85 2.04

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	13	6.07	4.00	164	2.84e+18	42.49	3.73	0.61	2.26
Variables per cluster	2	14	6.70	6.00	181	6.13e+20	47.86	3.35	0.50	2.29
Separator constraints	0	9	2.26	1.00	61	0	None	2.73	1.21	1.81
Separator variables	0	12	5.22	5.00	141	0	None	3.20	0.61	2.29
Clusters per var	1	15	4.53	4.00	181	1.20e+19	43.93	3.84	0.85	2.04

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 6
CIR: 0.41
Independent Cluster Pairs: 271
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/DualTree1.json

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

Cluster constraints 7 70 31.37 30.50 1,192 MAX VALUE 123.56 18.61 0.59 3.19

Variables per cluster 5 36 13.76 12.00 523 MAX VALUE 94.71 7.51 0.55 2.73

Separator constraints 0 46 17.89 15.50 680 0 None 11.51 0.64 3.14

Separator variables 0 25 11.05 10.00 420 0 None 5.76 0.52 2.69

Clusters per variable 1 11 5.08 5.00 523 MAX VALUE 144.44 2.78 0.55 2.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	70	31.37	30.50	1,192	MAX VALUE	123.56	18.61	0.59	3.19
Variables per cluster	5	36	13.76	12.00	523	MAX VALUE	94.71	7.51	0.55	2.73
Separator constraints	0	46	17.89	15.50	680	0	None	11.51	0.64	3.14
Separator variables	0	25	11.05	10.00	420	0	None	5.76	0.52	2.69
Clusters per variable	1	11	5.08	5.00	523	MAX VALUE	144.44	2.78	0.55	2.23

Primal graph

Density: 13.21%
MCB compute time (ms): 2
MCB cycles: 65
Triangles: 22
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/Primal1.json

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

Clustering coefficient 0.00 0.50 None 0.11 None None None None None 2.60

Degree 1 11 5.15 5.00 206 4.79e+26 61.43 2.06 0.40 2.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.86 4.00 251 4.24e+37 86.64 0.74 0.19 1.08

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.50	None	0.11	None	None	None	None	None	2.60
Degree	1	11	5.15	5.00	206	4.79e+26	61.43	2.06	0.40	2.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.86	4.00	251	4.24e+37	86.64	0.74	0.19	1.08

Triangulated primal graph

Density: 29.74%
MCB compute time (ms): 3
MCB cycles: 211
Triangles: 800

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

Clustering coefficient 0.46 1.00 None 0.78 None None None None None 3.22

Degree 1 27 11.60 9.50 464 6.76e+36 84.80 7.93 0.68 2.79

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 633 MAX VALUE 231.81 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	1.00	None	0.78	None	None	None	None	None	3.22
Degree	1	27	11.60	9.50	464	6.76e+36	84.80	7.93	0.68	2.79
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	633	MAX VALUE	231.81	0.00	0.00	0.00

Dual graph

Density: 9.75%
MCB compute time (ms): 35
MCB cycles: 442
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/Dual1.json

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

Clustering coefficient 0.40 1.00 0.51 0.48 52.06 0.00 -71.49 0.09 0.18 3.27

Degree 4 16 9.94 10.00 1,024 MAX VALUE 232.40 2.74 0.28 2.37

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.21 3.00 1,421 MAX VALUE 511.39 0.53 0.16 0.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	1.00	0.51	0.48	52.06	0.00	-71.49	0.09	0.18	3.27
Degree	4	16	9.94	10.00	1,024	MAX VALUE	232.40	2.74	0.28	2.37
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.21	3.00	1,421	MAX VALUE	511.39	0.53	0.16	0.55

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 118.58 0.62 0.19 0.94

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.92 7.00 443 MAX VALUE 122.69 1.24 0.18 1.60

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	118.58	0.62	0.19	0.94
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.92	7.00	443	MAX VALUE	122.69	1.24	0.18	1.60

Triangulated dual graph

Density: 31.73%
Triangles: 16,445

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

Clustering coefficient 0.60 1.00 0.79 0.78 81.52 0.00 -25.36 0.13 0.16 3.91

Degree 4 60 32.37 28.00 3,334 MAX VALUE 333.05 19.03 0.59 3.53

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	0.60	1.00	0.79	0.78	81.52	0.00	-25.36	0.13	0.16	3.91
Degree	4	60	32.37	28.00	3,334	MAX VALUE	333.05	19.03	0.59	3.53
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.84%

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

Clustering coefficient 0.47 1.00 0.76 0.67 77.88 0.00 -32.15 0.19 0.26 3.00

Degree 2 36 12.08 6.00 1,244 MAX VALUE 208.66 11.43 0.95 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	0.47	1.00	0.76	0.67	77.88	0.00	-32.15	0.19	0.26	3.00
Degree	2	36	12.08	6.00	1,244	MAX VALUE	208.66	11.43	0.95	2.86
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-2-40-80-103-800-76-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.8/normalized-rand-2-40-80-103-800-76-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 0.76

Degree 1 11 2.88 2.00 412 MAX VALUE 132.83 1.78 0.62 1.11

Eccentricity None None None None None None None None None None

MCB cycle size 6 12 7.72 8.00 494 MAX VALUE 129.62 1.49 0.19 1.09

XCSP 2.1 Benchmarks