XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-40-135-650-65-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 4 26 13.95 14.00 150,630 MAX VALUE 28,195.10 3.01 0.22 2.52

Relational linkage 0.10 0.45 0.25 0.25 405.90 0.00 -2,223.72 0.05 0.19 2.04

Tightness 0.63 0.69 0.65 0.65 87.93 0.00 -57.90 0.01 0.02 3.99

Tuples 503 599 557.89 558.00 75,315 MAX VALUE 853.68 18.99 0.03 3.99

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 6.50 270 1.84e+32 74.29 2.07 0.31 1.98

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	13.95	14.00	150,630	MAX VALUE	28,195.10	3.01	0.22	2.52
Relational linkage	0.10	0.45	0.25	0.25	405.90	0.00	-2,223.72	0.05	0.19	2.04
Tightness	0.63	0.69	0.65	0.65	87.93	0.00	-57.90	0.01	0.02	3.99
Tuples	503	599	557.89	558.00	75,315	MAX VALUE	853.68	18.99	0.03	3.99
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	6.50	270	1.84e+32	74.29	2.07	0.31	1.98
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: 25
Number of leaves: 13
Tree depth: 5
CIR: 0.18
Independent Cluster Pairs: 49
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/Tree1.json

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

Cluster constraints 2 22 11.28 9.00 282 3.89e+24 56.62 5.91 0.52 2.59

Variables per cluster 3 15 8.88 8.00 222 5.09e+22 52.28 3.79 0.43 2.05

Separator constraints 0 18 5.88 3.00 147 0 None 5.70 0.97 2.27

Separator variables 0 14 7.28 6.00 182 0 None 3.81 0.52 2.16

Clusters per var 1 15 5.55 3.50 222 8.14e+21 50.45 4.58 0.82 2.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	22	11.28	9.00	282	3.89e+24	56.62	5.91	0.52	2.59
Variables per cluster	3	15	8.88	8.00	222	5.09e+22	52.28	3.79	0.43	2.05
Separator constraints	0	18	5.88	3.00	147	0	None	5.70	0.97	2.27
Separator variables	0	14	7.28	6.00	182	0	None	3.81	0.52	2.16
Clusters per var	1	15	5.55	3.50	222	8.14e+21	50.45	4.58	0.82	2.25

Dual tree decomposition

Number of clusters: 38
Number of leaves: 14
Tree depth: 5
CIR: 0.29
Independent Cluster Pairs: 195
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/DualTree1.json

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

Cluster constraints 7 170 61.50 50.50 2,337 MAX VALUE 147.93 41.30 0.67 3.46

Variables per cluster 5 58 20.32 15.50 772 MAX VALUE 108.00 12.93 0.64 3.03

Separator constraints 0 102 38.82 31.50 1,475 0 None 25.78 0.66 3.19

Separator variables 0 45 16.76 13.50 637 0 None 9.96 0.59 2.93

Clusters per variable 1 10 5.72 6.00 772 MAX VALUE 209.36 2.81 0.49 2.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	170	61.50	50.50	2,337	MAX VALUE	147.93	41.30	0.67	3.46
Variables per cluster	5	58	20.32	15.50	772	MAX VALUE	108.00	12.93	0.64	3.03
Separator constraints	0	102	38.82	31.50	1,475	0	None	25.78	0.66	3.19
Separator variables	0	45	16.76	13.50	637	0	None	9.96	0.59	2.93
Clusters per variable	1	10	5.72	6.00	772	MAX VALUE	209.36	2.81	0.49	2.17

Primal graph

Density: 17.31%
MCB compute time (ms): 3
MCB cycles: 106
Triangles: 41
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/Primal1.json

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

Clustering coefficient 0.00 0.40 0.15 0.14 5.93 0.00 None 0.09 0.60 2.84

Degree 2 12 6.75 6.50 270 1.84e+32 74.29 2.07 0.31 1.98

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.63 4.00 385 MAX VALUE 135.66 0.50 0.14 0.71

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.40	0.15	0.14	5.93	0.00	None	0.09	0.60	2.84
Degree	2	12	6.75	6.50	270	1.84e+32	74.29	2.07	0.31	1.98
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.63	4.00	385	MAX VALUE	135.66	0.50	0.14	0.71

Triangulated primal graph

Density: 38.59%
MCB compute time (ms): 5
MCB cycles: 320
Triangles: 1,299

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

Clustering coefficient 0.55 1.00 0.81 0.79 32.30 0.00 -9.35 0.16 0.20 2.82

Degree 2 29 15.05 15.50 602 MAX VALUE 99.26 8.77 0.58 2.91

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 960 MAX VALUE 351.56 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.55	1.00	0.81	0.79	32.30	0.00	-9.35	0.16	0.20	2.82
Degree	2	29	15.05	15.50	602	MAX VALUE	99.26	8.77	0.58	2.91
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	960	MAX VALUE	351.56	0.00	0.00	0.00

Dual graph

Density: 9.53%
MCB compute time (ms): 116
MCB cycles: 829
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/Dual1.json

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

Clustering coefficient 0.43 0.75 0.50 0.49 67.62 0.00 -93.78 0.04 0.09 3.70

Degree 4 20 12.77 13.00 1,724 MAX VALUE 340.60 2.67 0.21 2.31

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.21 3.00 2,659 MAX VALUE 959.26 0.45 0.14 0.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.75	0.50	0.49	67.62	0.00	-93.78	0.04	0.09	3.70
Degree	4	20	12.77	13.00	1,724	MAX VALUE	340.60	2.67	0.21	2.31
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.21	3.00	2,659	MAX VALUE	959.26	0.45	0.14	0.55

Minimal dual graph

Density: 2.54%
MCB compute time (ms): 31
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 0.83 0.00 None 0.04 6.90 0.12

Degree 2 5 3.41 3.00 460 MAX VALUE 162.94 0.65 0.19 0.98

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.80 7.00 653 MAX VALUE 182.69 1.07 0.16 1.42

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	0.83	0.00	None	0.04	6.90	0.12
Degree	2	5	3.41	3.00	460	MAX VALUE	162.94	0.65	0.19	0.98
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.80	7.00	653	MAX VALUE	182.69	1.07	0.16	1.42

Triangulated dual graph

Density: 41.17%
Triangles: 65,821

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

Clustering coefficient 0.70 1.00 0.82 0.80 111.02 0.00 -27.25 0.09 0.11 4.44

Degree 4 91 55.17 68.00 7,448 MAX VALUE 509.26 29.76 0.54 3.88

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	0.70	1.00	0.82	0.80	111.02	0.00	-27.25	0.09	0.11	4.44
Degree	4	91	55.17	68.00	7,448	MAX VALUE	509.26	29.76	0.54	3.88
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.24%

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

Clustering coefficient 0.51 1.00 0.78 0.71 105.24 0.00 -36.61 0.16 0.21 3.22

Degree 2 49 16.40 7.00 2,214 MAX VALUE 298.75 16.86 1.03 2.99

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	0.51	1.00	0.78	0.71	105.24	0.00	-36.61	0.16	0.21	3.22
Degree	2	49	16.40	7.00	2,214	MAX VALUE	298.75	16.86	1.03	2.99
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.77%
MCB compute time (ms): 23
MCB cycles: 96
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-65-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 167.87 2.23 0.72 0.96

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 7.19 8.00 690 MAX VALUE 188.34 1.02 0.14 0.73

XCSP 2.1 Benchmarks