XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-40-135-650-52-ext
Number of variables: 40
Number of constraints: 135
Satisfiable: True
Timestamp: 2025-07-20 22:09:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 135

General features

Coarse blocks: 10,800
Value tables: 40

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

Arity 2 2 2.00 2.00 270 MAX VALUE 93.57 0.00 0.00 0.00

Coarse blocks size 3 26 14.00 14.00 151,220 MAX VALUE 28,234.60 3.02 0.22 2.52

Relational linkage 0.07 0.42 0.25 0.25 406.48 0.00 -2,226.38 0.05 0.20 2.12

Tightness 0.62 0.68 0.65 0.65 87.74 0.00 -58.19 0.01 0.02 3.89

Tuples 509 603 560.07 561.00 75,610 MAX VALUE 854.21 18.83 0.03 3.89

Values 40 40 40.00 40.00 1,600 MAX VALUE 147.56 0.00 0.00 0.00

Value table constraints 3 11 6.75 7.00 270 1.46e+32 74.06 2.15 0.32 1.96

Value table partitions 40 40 40.00 40.00 1,600 MAX VALUE 147.56 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	270	MAX VALUE	93.57	0.00	0.00	0.00
Coarse blocks size	3	26	14.00	14.00	151,220	MAX VALUE	28,234.60	3.02	0.22	2.52
Relational linkage	0.07	0.42	0.25	0.25	406.48	0.00	-2,226.38	0.05	0.20	2.12
Tightness	0.62	0.68	0.65	0.65	87.74	0.00	-58.19	0.01	0.02	3.89
Tuples	509	603	560.07	561.00	75,610	MAX VALUE	854.21	18.83	0.03	3.89
Values	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00
Value table constraints	3	11	6.75	7.00	270	1.46e+32	74.06	2.15	0.32	1.96
Value table partitions	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00

Tree decomposition

Number of clusters: 24
Number of leaves: 12
Tree depth: 5
CIR: 0.25
Independent Cluster Pairs: 62
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/Tree1.json

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

Cluster constraints 3 31 10.71 8.50 257 5.63e+22 52.38 7.20 0.67 2.44

Variables per cluster 4 17 8.33 7.00 200 1.01e+21 48.37 4.06 0.49 2.24

Separator constraints 0 23 5.08 3.00 122 0 None 5.76 1.13 2.28

Separator variables 0 16 6.67 5.50 160 0 None 3.89 0.58 2.29

Clusters per var 1 11 5.00 3.50 200 1.57e+21 48.81 3.75 0.75 2.10

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	31	10.71	8.50	257	5.63e+22	52.38	7.20	0.67	2.44
Variables per cluster	4	17	8.33	7.00	200	1.01e+21	48.37	4.06	0.49	2.24
Separator constraints	0	23	5.08	3.00	122	0	None	5.76	1.13	2.28
Separator variables	0	16	6.67	5.50	160	0	None	3.89	0.58	2.29
Clusters per var	1	11	5.00	3.50	200	1.57e+21	48.81	3.75	0.75	2.10

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.29
Independent Cluster Pairs: 196
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/DualTree1.json

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

Cluster constraints 6 176 61.79 48.00 2,348 MAX VALUE 148.63 39.78 0.64 3.35

Variables per cluster 5 58 20.21 15.50 768 MAX VALUE 107.90 12.73 0.63 3.02

Separator constraints 0 91 38.92 33.00 1,479 0 None 24.77 0.64 3.30

Separator variables 0 44 16.66 14.00 633 0 None 9.87 0.59 3.00

Clusters per variable 1 11 5.69 6.00 768 MAX VALUE 207.91 2.84 0.50 2.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	176	61.79	48.00	2,348	MAX VALUE	148.63	39.78	0.64	3.35
Variables per cluster	5	58	20.21	15.50	768	MAX VALUE	107.90	12.73	0.63	3.02
Separator constraints	0	91	38.92	33.00	1,479	0	None	24.77	0.64	3.30
Separator variables	0	44	16.66	14.00	633	0	None	9.87	0.59	3.00
Clusters per variable	1	11	5.69	6.00	768	MAX VALUE	207.91	2.84	0.50	2.26

Primal graph

Density: 17.31%
MCB compute time (ms): 3
MCB cycles: 98
Triangles: 49
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/Primal1.json

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

Clustering coefficient 0.00 0.67 0.19 0.18 7.46 0.00 None 0.12 0.66 2.87

Degree 3 11 6.75 7.00 270 1.46e+32 74.06 2.15 0.32 1.96

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.51 4.00 344 MAX VALUE 122.05 0.50 0.14 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.67	0.19	0.18	7.46	0.00	None	0.12	0.66	2.87
Degree	3	11	6.75	7.00	270	1.46e+32	74.06	2.15	0.32	1.96
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.51	4.00	344	MAX VALUE	122.05	0.50	0.14	0.69

Triangulated primal graph

Density: 37.95%
MCB compute time (ms): 5
MCB cycles: 301
Triangles: 1,315

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

Clustering coefficient 0.62 1.00 0.81 0.80 32.53 0.00 -8.86 0.14 0.17 2.84

Degree 3 26 14.80 15.00 592 MAX VALUE 97.85 8.87 0.60 2.54

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 903 MAX VALUE 330.68 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.62	1.00	0.81	0.80	32.53	0.00	-8.86	0.14	0.17	2.84
Degree	3	26	14.80	15.00	592	MAX VALUE	97.85	8.87	0.60	2.54
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	903	MAX VALUE	330.68	0.00	0.00	0.00

Dual graph

Density: 9.61%
MCB compute time (ms): 140
MCB cycles: 816
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/Dual1.json

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

Clustering coefficient 0.33 0.70 0.50 0.49 68.10 0.00 -93.02 0.05 0.10 3.68

Degree 4 19 12.87 13.00 1,738 MAX VALUE 341.39 2.81 0.22 2.37

Eccentricity None None None None None None None None None None

MCB cycle size 3 6 3.18 3.00 2,592 MAX VALUE 936.88 0.43 0.14 0.50

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.33	0.70	0.50	0.49	68.10	0.00	-93.02	0.05	0.10	3.68
Degree	4	19	12.87	13.00	1,738	MAX VALUE	341.39	2.81	0.22	2.37
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	6	3.18	3.00	2,592	MAX VALUE	936.88	0.43	0.14	0.50

Minimal dual graph

Density: 2.54%
MCB compute time (ms): 33
MCB cycles: 96

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 3.41 3.00 460 MAX VALUE 163.35 0.60 0.18 0.91

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.89 7.00 661 MAX VALUE 184.12 1.00 0.15 1.37

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	3.41	3.00	460	MAX VALUE	163.35	0.60	0.18	0.91
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.89	7.00	661	MAX VALUE	184.12	1.00	0.15	1.37

Triangulated dual graph

Density: 40.38%
Triangles: 63,062

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

Clustering coefficient 0.66 1.00 0.82 0.80 110.84 0.00 -27.55 0.10 0.12 4.41

Degree 4 93 54.10 57.00 7,304 MAX VALUE 506.64 29.37 0.54 3.89

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	0.66	1.00	0.82	0.80	110.84	0.00	-27.55	0.10	0.12	4.41
Degree	4	93	54.10	57.00	7,304	MAX VALUE	506.64	29.37	0.54	3.89
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.87%

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

Clustering coefficient 0.47 1.00 0.79 0.73 106.29 0.00 -35.16 0.16 0.21 3.11

Degree 2 50 17.24 7.00 2,328 MAX VALUE 304.66 17.51 1.02 2.91

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	0.79	0.73	106.29	0.00	-35.16	0.16	0.21	3.11
Degree	2	50	17.24	7.00	2,328	MAX VALUE	304.66	17.51	1.02	2.91
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.77%
MCB compute time (ms): 22
MCB cycles: 96
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-52-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 11 3.09 2.00 540 MAX VALUE 167.63 2.24 0.73 0.99

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 7.00 7.00 672 MAX VALUE 185.82 1.00 0.14 0.69

XCSP 2.1 Benchmarks