XCSP2 Benchmark Database

Instance: normalized-composed-75-1-40-3-ext
Number of variables: 83
Number of constraints: 662
Satisfiable: True
Timestamp: 2025-07-27 21:32:47
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 83
Number of constraints: 662

General features

Coarse blocks: 13,236
Value tables: 83

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

Arity 2 2 2.00 2.00 1,324 MAX VALUE 458.86 0.00 0.00 0.00

Coarse blocks size 1 10 8.40 9.00 111,140 MAX VALUE 27,886.00 1.41 0.17 1.58

Relational linkage 0.10 0.80 0.61 0.60 500.40 0.00 -464.43 0.15 0.25 1.45

Tightness 0.05 0.65 0.16 0.15 106.30 0.00 -1,267.58 0.09 0.58 0.37

Tuples 35 95 83.94 85.00 55,570 MAX VALUE 2,925.96 9.38 0.11 0.37

Values 10 10 10.00 10.00 830 MAX VALUE 191.12 0.00 0.00 0.00

Value table constraints 7 24 15.95 16.00 1,324 MAX VALUE 227.22 3.79 0.24 2.69

Value table partitions 10 10 10.00 10.00 830 MAX VALUE 191.12 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	1,324	MAX VALUE	458.86	0.00	0.00	0.00
Coarse blocks size	1	10	8.40	9.00	111,140	MAX VALUE	27,886.00	1.41	0.17	1.58
Relational linkage	0.10	0.80	0.61	0.60	500.40	0.00	-464.43	0.15	0.25	1.45
Tightness	0.05	0.65	0.16	0.15	106.30	0.00	-1,267.58	0.09	0.58	0.37
Tuples	35	95	83.94	85.00	55,570	MAX VALUE	2,925.96	9.38	0.11	0.37
Values	10	10	10.00	10.00	830	MAX VALUE	191.12	0.00	0.00	0.00
Value table constraints	7	24	15.95	16.00	1,324	MAX VALUE	227.22	3.79	0.24	2.69
Value table partitions	10	10	10.00	10.00	830	MAX VALUE	191.12	0.00	0.00	0.00

Tree decomposition

Number of clusters: 35
Number of leaves: 15
Tree depth: 8
CIR: 0.04
Independent Cluster Pairs: 23
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Tree1.json

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

Cluster constraints 11 279 97.00 40.00 3,395 MAX VALUE 141.93 96.46 0.99 3.44

Variables per cluster 8 49 24.83 20.00 869 MAX VALUE 106.38 14.51 0.58 2.82

Separator constraints 0 270 78.09 26.00 2,733 0 None 92.10 1.18 3.40

Separator variables 0 48 22.46 17.00 786 0 None 14.43 0.64 2.89

Clusters per var 1 25 10.47 12.00 869 MAX VALUE 161.76 6.67 0.64 2.78

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	11	279	97.00	40.00	3,395	MAX VALUE	141.93	96.46	0.99	3.44
Variables per cluster	8	49	24.83	20.00	869	MAX VALUE	106.38	14.51	0.58	2.82
Separator constraints	0	270	78.09	26.00	2,733	0	None	92.10	1.18	3.40
Separator variables	0	48	22.46	17.00	786	0	None	14.43	0.64	2.89
Clusters per var	1	25	10.47	12.00	869	MAX VALUE	161.76	6.67	0.64	2.78

Dual tree decomposition

Number of clusters: 81
Number of leaves: 38
Tree depth: 6
CIR: 0.23
Independent Cluster Pairs: 740
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/DualTree1.json

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

Cluster constraints 75 2,934 535.43 333.00 43,370 MAX VALUE 480.28 551.75 1.03 4.36

Variables per cluster 17 343 67.05 40.00 5,431 MAX VALUE 316.86 64.85 0.97 3.89

Separator constraints 0 1,700 405.88 294.00 32,876 0 None 345.88 0.85 4.32

Separator variables 0 259 58.88 38.00 4,769 0 None 50.65 0.86 3.86

Clusters per variable 1 12 8.20 10.00 5,431 MAX VALUE 1,303.46 3.09 0.38 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	75	2,934	535.43	333.00	43,370	MAX VALUE	480.28	551.75	1.03	4.36
Variables per cluster	17	343	67.05	40.00	5,431	MAX VALUE	316.86	64.85	0.97	3.89
Separator constraints	0	1,700	405.88	294.00	32,876	0	None	345.88	0.85	4.32
Separator variables	0	259	58.88	38.00	4,769	0	None	50.65	0.86	3.86
Clusters per variable	1	12	8.20	10.00	5,431	MAX VALUE	1,303.46	3.09	0.38	2.15

Primal graph

Density: 19.45%
MCB compute time (ms): None
MCB cycles: None
Triangles: 707
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Primal1.json

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

Clustering coefficient 0.12 0.40 0.21 0.20 17.36 0.00 -131.82 0.05 0.22 4.00

Degree 7 24 15.95 16.00 1,324 MAX VALUE 227.22 3.79 0.24 2.69

Eccentricity 2 3 2.88 3.00 239 6.92e+37 87.13 0.33 0.11 0.37

MCB cycle size 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	0.12	0.40	0.21	0.20	17.36	0.00	-131.82	0.05	0.22	4.00
Degree	7	24	15.95	16.00	1,324	MAX VALUE	227.22	3.79	0.24	2.69
Eccentricity	2	3	2.88	3.00	239	6.92e+37	87.13	0.33	0.11	0.37
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 57.66%
MCB compute time (ms): None
MCB cycles: None
Triangles: 30,502

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

Clustering coefficient 0.69 1.00 0.88 0.86 72.68 0.00 -11.34 0.08 0.09 3.93

Degree 7 72 47.28 59.00 3,924 MAX VALUE 305.14 21.23 0.45 3.30

Eccentricity 2 3 2.19 2.00 182 6.35e+27 64.02 0.39 0.18 0.49

MCB cycle size 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	0.69	1.00	0.88	0.86	72.68	0.00	-11.34	0.08	0.09	3.93
Degree	7	72	47.28	59.00	3,924	MAX VALUE	305.14	21.23	0.45	3.30
Eccentricity	2	3	2.19	2.00	182	6.35e+27	64.02	0.39	0.18	0.49
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 4.80%
MCB compute time (ms): 205,822
MCB cycles: 11,339
Triangles: 55,460
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Dual1.json

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

Clustering coefficient 0.48 0.65 0.50 0.50 333.67 0.00 -454.04 0.02 0.04 5.36

Degree 16 45 31.70 32.00 20,988 MAX VALUE 2,278.40 5.18 0.16 3.02

Eccentricity 3 4 3.05 3.00 2,022 MAX VALUE 737.64 0.23 0.07 0.21

MCB cycle size 3 5 3.07 3.00 34,862 MAX VALUE 12,700.00 0.26 0.09 0.27

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.65	0.50	0.50	333.67	0.00	-454.04	0.02	0.04	5.36
Degree	16	45	31.70	32.00	20,988	MAX VALUE	2,278.40	5.18	0.16	3.02
Eccentricity	3	4	3.05	3.00	2,022	MAX VALUE	737.64	0.23	0.07	0.21
MCB cycle size	3	5	3.07	3.00	34,862	MAX VALUE	12,700.00	0.26	0.09	0.27

Minimal dual graph

Density: 0.57%
MCB compute time (ms): 7,553
MCB cycles: 581

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 6 3.75 4.00 2,482 MAX VALUE 859.36 0.82 0.22 1.18

Eccentricity 7 10 8.25 8.00 5,460 MAX VALUE 1,394.98 0.60 0.07 0.91

MCB cycle size 4 10 7.42 8.00 4,312 MAX VALUE 1,156.37 1.18 0.16 1.55

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	6	3.75	4.00	2,482	MAX VALUE	859.36	0.82	0.22	1.18
Eccentricity	7	10	8.25	8.00	5,460	MAX VALUE	1,394.98	0.60	0.07	0.91
MCB cycle size	4	10	7.42	8.00	4,312	MAX VALUE	1,156.37	1.18	0.16	1.55

Triangulated dual graph

Density: None%
Triangles: None

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

Clustering coefficient None None None None None None None None None None

Degree None None None None None None None None None None

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	None	None	None	None	None	None	None	None	None	None
Degree	None	None	None	None	None	None	None	None	None	None
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 9.10%

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

Clustering coefficient 0.52 1.00 0.85 0.83 559.91 0.00 -119.18 0.13 0.15 3.97

Degree 2 210 60.15 8.00 39,820 MAX VALUE 1,846.01 81.77 1.36 3.56

Eccentricity 3 5 3.77 4.00 2,493 MAX VALUE 871.26 0.52 0.14 0.76

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.52	1.00	0.85	0.83	559.91	0.00	-119.18	0.13	0.15	3.97
Degree	2	210	60.15	8.00	39,820	MAX VALUE	1,846.01	81.77	1.36	3.56
Eccentricity	3	5	3.77	4.00	2,493	MAX VALUE	871.26	0.52	0.14	0.76

Incidence graph

Density: 0.48%
MCB compute time (ms): 5,265
MCB cycles: 580
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/composed-75-1-40/normalized-composed-75-1-40-3-ext/Incidence1.json

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 24 3.55 2.00 2,648 MAX VALUE 686.09 4.57 1.29 0.65

Eccentricity 5 8 6.36 6.00 4,735 MAX VALUE 1,374.69 0.59 0.09 0.83

MCB cycle size 6 8 6.12 6.00 3,552 MAX VALUE 1,049.58 0.48 0.08 0.23

XCSP2 Benchmarks