XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-40-135-650-41-ext
Number of variables: 40
Number of constraints: 135
Satisfiable: True
Timestamp: 2025-07-20 22:09:32
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 4 26 13.99 14.00 151,080 MAX VALUE 28,230.60 3.00 0.21 2.51

Relational linkage 0.10 0.42 0.26 0.25 411.12 0.00 -2,205.59 0.05 0.19 2.10

Tightness 0.62 0.68 0.65 0.65 87.79 0.00 -58.12 0.01 0.02 3.97

Tuples 517 613 559.56 558.00 75,540 MAX VALUE 854.08 19.75 0.04 3.97

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

Value table constraints 2 12 6.75 7.00 270 5.58e+31 73.10 2.52 0.37 2.19

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	4	26	13.99	14.00	151,080	MAX VALUE	28,230.60	3.00	0.21	2.51
Relational linkage	0.10	0.42	0.26	0.25	411.12	0.00	-2,205.59	0.05	0.19	2.10
Tightness	0.62	0.68	0.65	0.65	87.79	0.00	-58.12	0.01	0.02	3.97
Tuples	517	613	559.56	558.00	75,540	MAX VALUE	854.08	19.75	0.04	3.97
Values	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00
Value table constraints	2	12	6.75	7.00	270	5.58e+31	73.10	2.52	0.37	2.19
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: 4
CIR: 0.23
Independent Cluster Pairs: 59
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/Tree1.json

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

Cluster constraints 2 28 10.71 8.00 257 1.40e+22 50.99 7.55 0.71 2.59

Variables per cluster 3 17 8.17 7.00 196 4.81e+20 47.62 4.03 0.49 2.33

Separator constraints 0 22 5.08 3.00 122 0 None 6.07 1.19 2.27

Separator variables 0 16 6.50 5.50 156 0 None 3.83 0.59 2.38

Clusters per var 1 14 4.90 4.00 196 2.73e+20 47.06 3.85 0.78 2.11

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	28	10.71	8.00	257	1.40e+22	50.99	7.55	0.71	2.59
Variables per cluster	3	17	8.17	7.00	196	4.81e+20	47.62	4.03	0.49	2.33
Separator constraints	0	22	5.08	3.00	122	0	None	6.07	1.19	2.27
Separator variables	0	16	6.50	5.50	156	0	None	3.83	0.59	2.38
Clusters per var	1	14	4.90	4.00	196	2.73e+20	47.06	3.85	0.78	2.11

Dual tree decomposition

Number of clusters: 38
Number of leaves: 13
Tree depth: 6
CIR: 0.29
Independent Cluster Pairs: 195
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/DualTree1.json

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

Cluster constraints 13 203 65.45 53.00 2,487 MAX VALUE 149.68 45.71 0.70 3.46

Variables per cluster 7 59 20.24 16.00 769 MAX VALUE 107.82 13.00 0.64 2.98

Separator constraints 0 113 41.68 38.50 1,584 0 None 28.38 0.68 3.42

Separator variables 0 43 16.68 14.00 634 0 None 10.05 0.60 2.92

Clusters per variable 1 11 5.70 7.00 769 MAX VALUE 209.07 2.82 0.49 2.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	13	203	65.45	53.00	2,487	MAX VALUE	149.68	45.71	0.70	3.46
Variables per cluster	7	59	20.24	16.00	769	MAX VALUE	107.82	13.00	0.64	2.98
Separator constraints	0	113	41.68	38.50	1,584	0	None	28.38	0.68	3.42
Separator variables	0	43	16.68	14.00	634	0	None	10.05	0.60	2.92
Clusters per variable	1	11	5.70	7.00	769	MAX VALUE	209.07	2.82	0.49	2.24

Primal graph

Density: 17.31%
MCB compute time (ms): 3
MCB cycles: 100
Triangles: 54
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/Primal1.json

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

Clustering coefficient 0.00 0.33 0.17 0.17 6.75 0.00 None 0.10 0.58 2.96

Degree 2 12 6.75 7.00 270 5.58e+31 73.10 2.52 0.37 2.19

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.49 3.00 349 MAX VALUE 123.83 0.54 0.15 0.77

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.17	0.17	6.75	0.00	None	0.10	0.58	2.96
Degree	2	12	6.75	7.00	270	5.58e+31	73.10	2.52	0.37	2.19
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.49	3.00	349	MAX VALUE	123.83	0.54	0.15	0.77

Triangulated primal graph

Density: 37.44%
MCB compute time (ms): 5
MCB cycles: 260
Triangles: 1,285

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

Clustering coefficient 0.53 1.00 0.82 0.79 32.77 0.00 -8.68 0.15 0.18 2.73

Degree 2 29 14.60 14.00 584 MAX VALUE 96.49 8.94 0.61 2.83

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 780 MAX VALUE 285.64 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.53	1.00	0.82	0.79	32.77	0.00	-8.68	0.15	0.18	2.73
Degree	2	29	14.60	14.00	584	MAX VALUE	96.49	8.94	0.61	2.83
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	780	MAX VALUE	285.64	0.00	0.00	0.00

Dual graph

Density: 9.98%
MCB compute time (ms): 135
MCB cycles: 853
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/Dual1.json

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

Clustering coefficient 0.43 0.82 0.51 0.49 69.30 0.00 -90.92 0.06 0.13 3.92

Degree 6 21 13.38 14.00 1,806 MAX VALUE 345.59 3.26 0.24 2.52

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.16 3.00 2,695 MAX VALUE 975.53 0.40 0.13 0.46

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.82	0.51	0.49	69.30	0.00	-90.92	0.06	0.13	3.92
Degree	6	21	13.38	14.00	1,806	MAX VALUE	345.59	3.26	0.24	2.52
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.16	3.00	2,695	MAX VALUE	975.53	0.40	0.13	0.46

Minimal dual graph

Density: 2.54%
MCB compute time (ms): 26
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 162.61 0.70 0.21 1.05

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.74 7.00 647 MAX VALUE 181.81 1.06 0.16 1.40

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	162.61	0.70	0.21	1.05
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.74	7.00	647	MAX VALUE	181.81	1.06	0.16	1.40

Triangulated dual graph

Density: 41.11%
Triangles: 65,784

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

Clustering coefficient 0.68 1.00 0.82 0.79 111.08 0.00 -27.18 0.09 0.11 4.46

Degree 6 92 55.08 69.00 7,436 MAX VALUE 508.96 29.72 0.54 3.83

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	0.68	1.00	0.82	0.79	111.08	0.00	-27.18	0.09	0.11	4.46
Degree	6	92	55.08	69.00	7,436	MAX VALUE	508.96	29.72	0.54	3.83
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.25%

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

Clustering coefficient 0.46 1.00 0.78 0.71 104.85 0.00 -37.40 0.17 0.22 3.19

Degree 2 53 16.41 7.00 2,216 MAX VALUE 298.90 16.72 1.02 3.08

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	0.46	1.00	0.78	0.71	104.85	0.00	-37.40	0.17	0.22	3.19
Degree	2	53	16.41	7.00	2,216	MAX VALUE	298.90	16.72	1.02	3.08
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-2-40-40-135-650-41-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-41-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 12 3.09 2.00 540 MAX VALUE 166.67 2.33 0.75 0.98

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 6.92 6.00 664 MAX VALUE 184.60 1.04 0.15 0.74

XCSP 2.1 Benchmarks