XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-16-250-350-50-ext
Number of variables: 40
Number of constraints: 250
Satisfiable: True
Timestamp: 2025-07-20 22:09:22
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 83,342 MAX VALUE 18,601.30 1.91 0.18 2.06

Relational linkage 0.19 0.62 0.45 0.44 288.81 0.00 -520.18 0.08 0.18 1.64

Tightness 0.26 0.43 0.35 0.35 87.22 0.00 -264.11 0.03 0.08 3.30

Tuples 147 189 166.68 167.00 41,671 MAX VALUE 1,278.78 7.34 0.04 3.30

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

Value table constraints 8 19 12.50 12.00 500 MAX VALUE 100.11 2.70 0.22 2.28

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	83,342	MAX VALUE	18,601.30	1.91	0.18	2.06
Relational linkage	0.19	0.62	0.45	0.44	288.81	0.00	-520.18	0.08	0.18	1.64
Tightness	0.26	0.43	0.35	0.35	87.22	0.00	-264.11	0.03	0.08	3.30
Tuples	147	189	166.68	167.00	41,671	MAX VALUE	1,278.78	7.34	0.04	3.30
Values	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00
Value table constraints	8	19	12.50	12.00	500	MAX VALUE	100.11	2.70	0.22	2.28
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: 15
Number of leaves: 9
Tree depth: 3
CIR: 0.01
Independent Cluster Pairs: 1
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/Tree1.json

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

Cluster constraints 16 114 47.40 33.00 711 5.83e+23 54.72 31.97 0.67 2.62

Variables per cluster 9 26 15.07 13.00 226 1.67e+17 39.66 5.78 0.38 2.21

Separator constraints 0 102 30.73 16.00 461 0 None 27.79 0.90 2.52

Separator variables 0 25 12.40 11.00 186 0 None 5.99 0.48 2.30

Clusters per var 1 10 5.65 6.50 226 1.60e+25 58.03 3.17 0.56 2.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	114	47.40	33.00	711	5.83e+23	54.72	31.97	0.67	2.62
Variables per cluster	9	26	15.07	13.00	226	1.67e+17	39.66	5.78	0.38	2.21
Separator constraints	0	102	30.73	16.00	461	0	None	27.79	0.90	2.52
Separator variables	0	25	12.40	11.00	186	0	None	5.99	0.48	2.30
Clusters per var	1	10	5.65	6.50	226	1.60e+25	58.03	3.17	0.56	2.02

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.11
Independent Cluster Pairs: 75
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/DualTree1.json

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

Cluster constraints 72 785 259.92 203.00 9,877 MAX VALUE 203.82 173.50 0.67 3.56

Variables per cluster 17 128 42.32 31.50 1,608 MAX VALUE 135.95 27.47 0.65 3.42

Separator constraints 0 444 180.42 166.00 6,856 0 None 99.97 0.55 3.60

Separator variables 0 95 35.74 29.00 1,358 0 None 20.69 0.58 3.31

Clusters per variable 1 10 6.43 7.00 1,608 MAX VALUE 431.47 2.55 0.40 2.07

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	72	785	259.92	203.00	9,877	MAX VALUE	203.82	173.50	0.67	3.56
Variables per cluster	17	128	42.32	31.50	1,608	MAX VALUE	135.95	27.47	0.65	3.42
Separator constraints	0	444	180.42	166.00	6,856	0	None	99.97	0.55	3.60
Separator variables	0	95	35.74	29.00	1,358	0	None	20.69	0.58	3.31
Clusters per variable	1	10	6.43	7.00	1,608	MAX VALUE	431.47	2.55	0.40	2.07

Primal graph

Density: 32.05%
MCB compute time (ms): 6
MCB cycles: 239
Triangles: 322
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/Primal1.json

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

Clustering coefficient 0.19 0.44 0.32 0.32 12.80 0.00 -46.05 0.05 0.16 3.40

Degree 8 19 12.50 12.00 500 MAX VALUE 100.11 2.70 0.22 2.28

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.10 3.00 742 MAX VALUE 269.76 0.31 0.10 0.34

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.19	0.44	0.32	0.32	12.80	0.00	-46.05	0.05	0.16	3.40
Degree	8	19	12.50	12.00	500	MAX VALUE	100.11	2.70	0.22	2.28
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.10	3.00	742	MAX VALUE	269.76	0.31	0.10	0.34

Triangulated primal graph

Density: 65.51%
MCB compute time (ms): 19
MCB cycles: 483
Triangles: 3,929

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

Clustering coefficient 0.74 1.00 0.87 0.85 34.80 0.00 -5.76 0.09 0.10 3.09

Degree 8 34 25.55 30.50 1,022 MAX VALUE 125.61 9.32 0.36 2.43

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,449 MAX VALUE 530.63 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.74	1.00	0.87	0.85	34.80	0.00	-5.76	0.09	0.10	3.09
Degree	8	34	25.55	30.50	1,022	MAX VALUE	125.61	9.32	0.36	2.43
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,449	MAX VALUE	530.63	0.00	0.00	0.00

Dual graph

Density: 9.71%
MCB compute time (ms): 841
MCB cycles: 3,614
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/Dual1.json

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

Clustering coefficient 0.47 0.60 0.51 0.50 126.36 0.00 -170.75 0.02 0.04 4.67

Degree 16 35 24.17 24.00 6,042 MAX VALUE 793.12 3.85 0.16 2.71

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.10 3.00 11,199 MAX VALUE 4,073.09 0.30 0.10 0.32

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.60	0.51	0.50	126.36	0.00	-170.75	0.02	0.04	4.67
Degree	16	35	24.17	24.00	6,042	MAX VALUE	793.12	3.85	0.16	2.71
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.10	3.00	11,199	MAX VALUE	4,073.09	0.30	0.10	0.32

Minimal dual graph

Density: 1.48%
MCB compute time (ms): 226
MCB cycles: 211

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.03 9.43 0.07

Degree 2 6 3.68 4.00 920 MAX VALUE 320.11 0.78 0.21 1.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.79 7.00 1,433 MAX VALUE 400.82 1.16 0.17 1.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.03	9.43	0.07
Degree	2	6	3.68	4.00	920	MAX VALUE	320.11	0.78	0.21	1.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.79	7.00	1,433	MAX VALUE	400.82	1.16	0.17	1.54

Triangulated dual graph

Density: 50.90%
Triangles: 629,688

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

Clustering coefficient 0.74 1.00 0.84 0.79 210.18 0.00 -44.52 0.08 0.10 4.93

Degree 16 182 126.74 164.00 31,684 MAX VALUE 1,168.85 56.87 0.45 3.87

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	0.74	1.00	0.84	0.79	210.18	0.00	-44.52	0.08	0.10	4.93
Degree	16	182	126.74	164.00	31,684	MAX VALUE	1,168.85	56.87	0.45	3.87
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.19%

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

Clustering coefficient 0.54 1.00 0.81 0.76 202.91 0.00 -55.95 0.14 0.17 3.58

Degree 2 89 27.86 8.00 6,964 MAX VALUE 625.44 32.32 1.16 3.26

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	0.54	1.00	0.81	0.76	202.91	0.00	-55.95	0.14	0.17	3.58
Degree	2	89	27.86	8.00	6,964	MAX VALUE	625.44	32.32	1.16	3.26
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.19%
MCB compute time (ms): 80
MCB cycles: 211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-50-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 19 3.45 2.00 1,000 MAX VALUE 273.39 3.76 1.09 0.72

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.02 6.00 1,270 MAX VALUE 378.64 0.19 0.03 0.05

XCSP 2.1 Benchmarks