XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-40-135-650-34-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 3 25 13.92 14.00 150,356 MAX VALUE 28,171.90 3.00 0.22 2.52

Relational linkage 0.07 0.40 0.25 0.25 404.43 0.00 -2,232.50 0.05 0.19 2.08

Tightness 0.63 0.68 0.65 0.65 88.01 0.00 -57.77 0.01 0.02 3.92

Tuples 517 599 556.87 556.00 75,178 MAX VALUE 853.45 17.20 0.03 3.92

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

Value table constraints 3 12 6.75 6.50 270 1.81e+32 74.28 2.14 0.32 2.05

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	25	13.92	14.00	150,356	MAX VALUE	28,171.90	3.00	0.22	2.52
Relational linkage	0.07	0.40	0.25	0.25	404.43	0.00	-2,232.50	0.05	0.19	2.08
Tightness	0.63	0.68	0.65	0.65	88.01	0.00	-57.77	0.01	0.02	3.92
Tuples	517	599	556.87	556.00	75,178	MAX VALUE	853.45	17.20	0.03	3.92
Values	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00
Value table constraints	3	12	6.75	6.50	270	1.81e+32	74.28	2.14	0.32	2.05
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: 14
Tree depth: 4
CIR: 0.20
Independent Cluster Pairs: 51
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/Tree1.json

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

Cluster constraints 3 29 10.96 9.00 263 9.31e+22 52.89 6.85 0.63 2.50

Variables per cluster 4 16 8.38 7.00 201 1.82e+21 48.95 3.56 0.42 2.21

Separator constraints 0 21 5.33 3.00 128 0 None 5.89 1.10 2.30

Separator variables 0 14 6.71 6.00 161 0 None 3.38 0.50 2.27

Clusters per var 1 14 5.03 4.00 201 5.89e+20 47.82 3.91 0.78 2.12

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	29	10.96	9.00	263	9.31e+22	52.89	6.85	0.63	2.50
Variables per cluster	4	16	8.38	7.00	201	1.82e+21	48.95	3.56	0.42	2.21
Separator constraints	0	21	5.33	3.00	128	0	None	5.89	1.10	2.30
Separator variables	0	14	6.71	6.00	161	0	None	3.38	0.50	2.27
Clusters per var	1	14	5.03	4.00	201	5.89e+20	47.82	3.91	0.78	2.12

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.34
Independent Cluster Pairs: 226
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/DualTree1.json

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

Cluster constraints 17 171 59.87 51.00 2,275 MAX VALUE 148.23 38.70 0.65 3.30

Variables per cluster 8 51 19.71 16.00 749 MAX VALUE 107.87 11.43 0.58 2.92

Separator constraints 0 104 37.03 34.50 1,407 0 None 23.92 0.65 3.28

Separator variables 0 38 16.16 14.00 614 0 None 8.69 0.54 2.90

Clusters per variable 1 11 5.55 6.00 749 MAX VALUE 205.27 2.75 0.49 2.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	17	171	59.87	51.00	2,275	MAX VALUE	148.23	38.70	0.65	3.30
Variables per cluster	8	51	19.71	16.00	749	MAX VALUE	107.87	11.43	0.58	2.92
Separator constraints	0	104	37.03	34.50	1,407	0	None	23.92	0.65	3.28
Separator variables	0	38	16.16	14.00	614	0	None	8.69	0.54	2.90
Clusters per variable	1	11	5.55	6.00	749	MAX VALUE	205.27	2.75	0.49	2.24

Primal graph

Density: 17.31%
MCB compute time (ms): 3
MCB cycles: 103
Triangles: 52
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/Primal1.json

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

Clustering coefficient 0.00 0.38 0.18 0.18 7.03 0.00 None 0.09 0.53 2.95

Degree 3 12 6.75 6.50 270 1.81e+32 74.28 2.14 0.32 2.05

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.52 4.00 363 MAX VALUE 128.69 0.50 0.14 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.38	0.18	0.18	7.03	0.00	None	0.09	0.53	2.95
Degree	3	12	6.75	6.50	270	1.81e+32	74.28	2.14	0.32	2.05
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.52	4.00	363	MAX VALUE	128.69	0.50	0.14	0.69

Triangulated primal graph

Density: 37.95%
MCB compute time (ms): 7
MCB cycles: 270
Triangles: 1,262

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

Clustering coefficient 0.52 1.00 0.81 0.78 32.44 0.00 -9.15 0.16 0.19 2.66

Degree 3 29 14.80 14.50 592 MAX VALUE 98.32 8.73 0.59 2.74

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 810 MAX VALUE 296.62 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.52	1.00	0.81	0.78	32.44	0.00	-9.15	0.16	0.19	2.66
Degree	3	29	14.80	14.50	592	MAX VALUE	98.32	8.73	0.59	2.74
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	810	MAX VALUE	296.62	0.00	0.00	0.00

Dual graph

Density: 9.60%
MCB compute time (ms): 100
MCB cycles: 832
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/Dual1.json

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

Clustering coefficient 0.43 0.67 0.51 0.50 68.26 0.00 -92.52 0.04 0.08 3.86

Degree 7 22 12.86 13.00 1,736 MAX VALUE 341.17 2.98 0.23 2.46

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.21 3.00 2,669 MAX VALUE 962.01 0.48 0.15 0.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.67	0.51	0.50	68.26	0.00	-92.52	0.04	0.08	3.86
Degree	7	22	12.86	13.00	1,736	MAX VALUE	341.17	2.98	0.23	2.46
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.21	3.00	2,669	MAX VALUE	962.01	0.48	0.15	0.55

Minimal dual graph

Density: 2.54%
MCB compute time (ms): 30
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 163.04 0.65 0.19 0.97

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.79 7.00 652 MAX VALUE 182.43 1.13 0.17 1.48

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	163.04	0.65	0.19	0.97
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.79	7.00	652	MAX VALUE	182.43	1.13	0.17	1.48

Triangulated dual graph

Density: 37.61%
Triangles: 53,023

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

Clustering coefficient 0.61 1.00 0.81 0.78 109.22 0.00 -29.82 0.11 0.14 4.25

Degree 7 91 50.40 60.00 6,804 MAX VALUE 499.53 27.34 0.54 3.84

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	0.61	1.00	0.81	0.78	109.22	0.00	-29.82	0.11	0.14	4.25
Degree	7	91	50.40	60.00	6,804	MAX VALUE	499.53	27.34	0.54	3.84
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.63%

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

Clustering coefficient 0.49 1.00 0.79 0.75 106.78 0.00 -34.52 0.16 0.21 3.08

Degree 2 51 16.92 7.00 2,284 MAX VALUE 300.37 17.50 1.03 2.92

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	0.49	1.00	0.79	0.75	106.78	0.00	-34.52	0.16	0.21	3.08
Degree	2	51	16.92	7.00	2,284	MAX VALUE	300.37	17.50	1.03	2.92
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.77%
MCB compute time (ms): 24
MCB cycles: 96
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-34-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 167.85 2.24 0.73 1.01

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.98 6.00 670 MAX VALUE 185.53 1.00 0.14 0.69

XCSP 2.1 Benchmarks