XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-16-250-350-87-ext
Number of variables: 40
Number of constraints: 250
Satisfiable: True
Timestamp: 2025-07-20 22:09:23
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 250

General features

Coarse blocks: 8,000
Value tables: 40

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

Arity 2 2 2.00 2.00 500 MAX VALUE 173.29 0.00 0.00 0.00

Coarse blocks size 3 16 10.42 10.00 83,322 MAX VALUE 18,603.10 1.90 0.18 2.06

Relational linkage 0.19 0.69 0.46 0.44 291.56 0.00 -512.62 0.08 0.17 1.60

Tightness 0.27 0.43 0.35 0.35 87.26 0.00 -264.03 0.03 0.08 3.36

Tuples 146 188 166.64 166.50 41,661 MAX VALUE 1,278.71 7.51 0.05 3.36

Values 16 16 16.00 16.00 640 MAX VALUE 110.90 0.00 0.00 0.00

Value table constraints 4 18 12.50 13.00 500 MAX VALUE 99.03 3.45 0.28 2.33

Value table partitions 16 16 16.00 16.00 640 MAX VALUE 110.90 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	500	MAX VALUE	173.29	0.00	0.00	0.00
Coarse blocks size	3	16	10.42	10.00	83,322	MAX VALUE	18,603.10	1.90	0.18	2.06
Relational linkage	0.19	0.69	0.46	0.44	291.56	0.00	-512.62	0.08	0.17	1.60
Tightness	0.27	0.43	0.35	0.35	87.26	0.00	-264.03	0.03	0.08	3.36
Tuples	146	188	166.64	166.50	41,661	MAX VALUE	1,278.71	7.51	0.05	3.36
Values	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00
Value table constraints	4	18	12.50	13.00	500	MAX VALUE	99.03	3.45	0.28	2.33
Value table partitions	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00

Tree decomposition

Number of clusters: 17
Number of leaves: 9
Tree depth: 4
CIR: 0.07
Independent Cluster Pairs: 9
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/Tree1.json

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

Cluster constraints 6 110 52.18 41.00 887 3.07e+26 60.99 37.72 0.72 2.75

Variables per cluster 5 24 15.00 14.00 255 1.19e+19 43.92 6.90 0.46 2.07

Separator constraints 0 97 37.47 23.00 637 0 None 35.59 0.95 2.75

Separator variables 0 23 12.65 11.00 215 0 None 7.25 0.57 2.20

Clusters per var 1 12 6.38 7.50 255 3.78e+26 61.20 3.84 0.60 2.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	110	52.18	41.00	887	3.07e+26	60.99	37.72	0.72	2.75
Variables per cluster	5	24	15.00	14.00	255	1.19e+19	43.92	6.90	0.46	2.07
Separator constraints	0	97	37.47	23.00	637	0	None	35.59	0.95	2.75
Separator variables	0	23	12.65	11.00	215	0	None	7.25	0.57	2.20
Clusters per var	1	12	6.38	7.50	255	3.78e+26	61.20	3.84	0.60	2.16

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.12
Independent Cluster Pairs: 79
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/DualTree1.json

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

Cluster constraints 50 883 273.66 205.50 10,399 MAX VALUE 204.05 202.25 0.74 3.60

Variables per cluster 14 131 42.74 30.00 1,624 MAX VALUE 135.62 29.07 0.68 3.32

Separator constraints 0 491 191.74 158.50 7,286 0 None 118.98 0.62 3.56

Separator variables 0 97 36.16 28.00 1,374 0 None 22.14 0.61 3.32

Clusters per variable 1 11 6.50 7.00 1,624 MAX VALUE 434.62 2.53 0.39 2.14

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	50	883	273.66	205.50	10,399	MAX VALUE	204.05	202.25	0.74	3.60
Variables per cluster	14	131	42.74	30.00	1,624	MAX VALUE	135.62	29.07	0.68	3.32
Separator constraints	0	491	191.74	158.50	7,286	0	None	118.98	0.62	3.56
Separator variables	0	97	36.16	28.00	1,374	0	None	22.14	0.61	3.32
Clusters per variable	1	11	6.50	7.00	1,624	MAX VALUE	434.62	2.53	0.39	2.14

Primal graph

Density: 32.05%
MCB compute time (ms): 5
MCB cycles: 251
Triangles: 336
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/Primal1.json

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

Clustering coefficient 0.18 0.50 0.32 0.32 12.88 0.00 -46.36 0.07 0.23 3.54

Degree 4 18 12.50 13.00 500 MAX VALUE 99.03 3.45 0.28 2.33

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.10 3.00 777 MAX VALUE 282.66 0.29 0.09 0.32

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.18	0.50	0.32	0.32	12.88	0.00	-46.36	0.07	0.23	3.54
Degree	4	18	12.50	13.00	500	MAX VALUE	99.03	3.45	0.28	2.33
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.10	3.00	777	MAX VALUE	282.66	0.29	0.09	0.32

Triangulated primal graph

Density: 62.95%
MCB compute time (ms): 20
MCB cycles: 473
Triangles: 3,723

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

Clustering coefficient 0.75 1.00 0.87 0.84 34.94 0.00 -5.58 0.08 0.09 3.09

Degree 4 34 24.55 29.50 982 MAX VALUE 122.56 9.72 0.40 2.59

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,419 MAX VALUE 519.64 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.75	1.00	0.87	0.84	34.94	0.00	-5.58	0.08	0.09	3.09
Degree	4	34	24.55	29.50	982	MAX VALUE	122.56	9.72	0.40	2.59
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,419	MAX VALUE	519.64	0.00	0.00	0.00

Dual graph

Density: 10.00%
MCB compute time (ms): 1,241
MCB cycles: 3,063
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/Dual1.json

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

Clustering coefficient 0.47 0.74 0.51 0.50 127.86 0.00 -168.21 0.04 0.07 4.69

Degree 13 34 24.90 25.00 6,226 MAX VALUE 799.71 4.27 0.17 2.81

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.04 3.00 9,303 MAX VALUE 3,397.85 0.19 0.06 0.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.74	0.51	0.50	127.86	0.00	-168.21	0.04	0.07	4.69
Degree	13	34	24.90	25.00	6,226	MAX VALUE	799.71	4.27	0.17	2.81
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.04	3.00	9,303	MAX VALUE	3,397.85	0.19	0.06	0.16

Minimal dual graph

Density: 1.48%
MCB compute time (ms): 248
MCB cycles: 211

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 6 3.68 4.00 920 MAX VALUE 319.46 0.84 0.23 1.19

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.80 7.00 1,435 MAX VALUE 401.71 1.07 0.16 1.46

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	6	3.68	4.00	920	MAX VALUE	319.46	0.84	0.23	1.19
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.80	7.00	1,435	MAX VALUE	401.71	1.07	0.16	1.46

Triangulated dual graph

Density: 52.93%
Triangles: 687,403

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

Clustering coefficient 0.72 1.00 0.85 0.82 212.04 0.00 -42.17 0.08 0.09 4.80

Degree 13 197 131.78 167.00 32,946 MAX VALUE 1,177.93 57.97 0.44 4.11

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	0.72	1.00	0.85	0.82	212.04	0.00	-42.17	0.08	0.09	4.80
Degree	13	197	131.78	167.00	32,946	MAX VALUE	1,177.93	57.97	0.44	4.11
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.23%

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

Clustering coefficient 0.46 1.00 0.82 0.78 204.29 0.00 -54.46 0.15 0.18 3.47

Degree 2 87 27.95 7.00 6,988 MAX VALUE 621.31 32.60 1.17 3.17

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	0.82	0.78	204.29	0.00	-54.46	0.15	0.18	3.47
Degree	2	87	27.95	7.00	6,988	MAX VALUE	621.31	32.60	1.17	3.17
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.19%
MCB compute time (ms): 78
MCB cycles: 211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-87-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 18 3.45 2.00 1,000 MAX VALUE 272.31 3.84 1.11 0.72

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.06 6.00 1,278 MAX VALUE 379.79 0.33 0.05 0.13

XCSP 2.1 Benchmarks