XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-40-135-650-76-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 2 25 14.04 14.00 151,638 MAX VALUE 28,267.50 3.01 0.21 2.52

Relational linkage 0.05 0.42 0.25 0.25 406.88 0.00 -2,221.83 0.05 0.19 2.08

Tightness 0.61 0.69 0.65 0.65 87.61 0.00 -58.39 0.01 0.02 3.94

Tuples 504 629 561.62 561.00 75,819 MAX VALUE 854.58 20.25 0.04 3.94

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

Value table constraints 3 13 6.75 7.00 270 1.34e+32 73.98 2.19 0.32 2.00

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	2	25	14.04	14.00	151,638	MAX VALUE	28,267.50	3.01	0.21	2.52
Relational linkage	0.05	0.42	0.25	0.25	406.88	0.00	-2,221.83	0.05	0.19	2.08
Tightness	0.61	0.69	0.65	0.65	87.61	0.00	-58.39	0.01	0.02	3.94
Tuples	504	629	561.62	561.00	75,819	MAX VALUE	854.58	20.25	0.04	3.94
Values	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00
Value table constraints	3	13	6.75	7.00	270	1.34e+32	73.98	2.19	0.32	2.00
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: 11
Tree depth: 5
CIR: 0.22
Independent Cluster Pairs: 55
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/Tree1.json

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

Cluster constraints 3 29 12.38 10.00 297 3.61e+23 54.24 8.59 0.69 2.67

Variables per cluster 4 17 9.08 8.50 218 6.32e+21 50.20 4.27 0.47 2.35

Separator constraints 0 24 6.75 3.00 162 0 None 7.47 1.11 2.30

Separator variables 0 16 7.42 6.50 178 0 None 4.23 0.57 2.41

Clusters per var 1 14 5.45 4.00 218 4.90e+22 52.25 4.03 0.74 2.14

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	29	12.38	10.00	297	3.61e+23	54.24	8.59	0.69	2.67
Variables per cluster	4	17	9.08	8.50	218	6.32e+21	50.20	4.27	0.47	2.35
Separator constraints	0	24	6.75	3.00	162	0	None	7.47	1.11	2.30
Separator variables	0	16	7.42	6.50	178	0	None	4.23	0.57	2.41
Clusters per var	1	14	5.45	4.00	218	4.90e+22	52.25	4.03	0.74	2.14

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 7
CIR: 0.30
Independent Cluster Pairs: 201
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/DualTree1.json

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

Cluster constraints 9 149 59.11 50.00 2,246 MAX VALUE 147.17 35.50 0.60 3.42

Variables per cluster 6 55 19.66 16.00 747 MAX VALUE 107.29 11.72 0.60 3.15

Separator constraints 0 82 36.16 36.00 1,374 0 None 21.54 0.60 3.35

Separator variables 0 39 16.11 14.00 612 0 None 9.01 0.56 3.09

Clusters per variable 1 12 5.53 6.00 747 MAX VALUE 204.76 2.82 0.51 2.29

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	9	149	59.11	50.00	2,246	MAX VALUE	147.17	35.50	0.60	3.42
Variables per cluster	6	55	19.66	16.00	747	MAX VALUE	107.29	11.72	0.60	3.15
Separator constraints	0	82	36.16	36.00	1,374	0	None	21.54	0.60	3.35
Separator variables	0	39	16.11	14.00	612	0	None	9.01	0.56	3.09
Clusters per variable	1	12	5.53	6.00	747	MAX VALUE	204.76	2.82	0.51	2.29

Primal graph

Density: 17.31%
MCB compute time (ms): 3
MCB cycles: 96
Triangles: 50
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/Primal1.json

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

Clustering coefficient 0.00 0.33 0.17 0.18 6.96 0.00 None 0.09 0.53 2.93

Degree 3 13 6.75 7.00 270 1.34e+32 73.98 2.19 0.32 2.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.51 3.00 337 MAX VALUE 119.43 0.54 0.15 0.78

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.17	0.18	6.96	0.00	None	0.09	0.53	2.93
Degree	3	13	6.75	7.00	270	1.34e+32	73.98	2.19	0.32	2.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.51	3.00	337	MAX VALUE	119.43	0.54	0.15	0.78

Triangulated primal graph

Density: 40.26%
MCB compute time (ms): 4
MCB cycles: 327
Triangles: 1,466

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

Clustering coefficient 0.56 1.00 0.81 0.79 32.40 0.00 -8.98 0.13 0.17 2.93

Degree 3 29 15.70 15.00 628 MAX VALUE 100.69 8.88 0.57 2.73

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 981 MAX VALUE 359.25 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.56	1.00	0.81	0.79	32.40	0.00	-8.98	0.13	0.17	2.93
Degree	3	29	15.70	15.00	628	MAX VALUE	100.69	8.88	0.57	2.73
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	981	MAX VALUE	359.25	0.00	0.00	0.00

Dual graph

Density: 9.64%
MCB compute time (ms): 101
MCB cycles: 837
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/Dual1.json

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

Clustering coefficient 0.40 0.69 0.50 0.49 67.63 0.00 -93.95 0.05 0.10 3.70

Degree 5 21 12.92 13.00 1,744 MAX VALUE 341.30 3.04 0.24 2.46

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.21 3.00 2,686 MAX VALUE 968.01 0.48 0.15 0.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.40	0.69	0.50	0.49	67.63	0.00	-93.95	0.05	0.10	3.70
Degree	5	21	12.92	13.00	1,744	MAX VALUE	341.30	3.04	0.24	2.46
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.21	3.00	2,686	MAX VALUE	968.01	0.48	0.15	0.55

Minimal dual graph

Density: 2.54%
MCB compute time (ms): 29
MCB cycles: 96

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

Clustering coefficient 0.00 0.33 0.01 0.00 1.50 0.00 None 0.05 4.90 0.21

Degree 2 5 3.41 3.00 460 MAX VALUE 162.98 0.66 0.19 0.99

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.81 7.00 654 MAX VALUE 181.71 1.42 0.21 1.65

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	1.50	0.00	None	0.05	4.90	0.21
Degree	2	5	3.41	3.00	460	MAX VALUE	162.98	0.66	0.19	0.99
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.81	7.00	654	MAX VALUE	181.71	1.42	0.21	1.65

Triangulated dual graph

Density: 37.76%
Triangles: 54,292

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

Clustering coefficient 0.63 1.00 0.81 0.78 109.57 0.00 -29.29 0.11 0.13 4.39

Degree 5 90 50.59 57.00 6,830 MAX VALUE 498.40 27.95 0.55 3.74

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	0.63	1.00	0.81	0.78	109.57	0.00	-29.29	0.11	0.13	4.39
Degree	5	90	50.59	57.00	6,830	MAX VALUE	498.40	27.95	0.55	3.74
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.85%

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

Clustering coefficient 0.50 1.00 0.77 0.70 104.55 0.00 -37.57 0.17 0.22 3.09

Degree 2 51 15.88 7.00 2,144 MAX VALUE 295.97 16.46 1.04 2.97

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	0.50	1.00	0.77	0.70	104.55	0.00	-37.57	0.17	0.22	3.09
Degree	2	51	15.88	7.00	2,144	MAX VALUE	295.97	16.46	1.04	2.97
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-2-40-40-135-650-76-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-76-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 13 3.09 2.00 540 MAX VALUE 167.55 2.25 0.73 0.99

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.02 6.00 674 MAX VALUE 185.98 1.08 0.15 0.78

XCSP 2.1 Benchmarks