XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-16-250-350-68-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 10.36 10.00 82,850 MAX VALUE 18,555.80 1.90 0.18 2.06

Relational linkage 0.19 0.62 0.45 0.44 288.50 0.00 -518.75 0.07 0.16 1.55

Tightness 0.27 0.43 0.35 0.35 88.18 0.00 -261.29 0.03 0.08 3.26

Tuples 145 186 165.70 166.00 41,425 MAX VALUE 1,277.32 7.09 0.04 3.26

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

Value table constraints 8 21 12.50 12.50 500 MAX VALUE 99.94 2.93 0.23 2.26

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	10.36	10.00	82,850	MAX VALUE	18,555.80	1.90	0.18	2.06
Relational linkage	0.19	0.62	0.45	0.44	288.50	0.00	-518.75	0.07	0.16	1.55
Tightness	0.27	0.43	0.35	0.35	88.18	0.00	-261.29	0.03	0.08	3.26
Tuples	145	186	165.70	166.00	41,425	MAX VALUE	1,277.32	7.09	0.04	3.26
Values	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00
Value table constraints	8	21	12.50	12.50	500	MAX VALUE	99.94	2.93	0.23	2.26
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: 16
Number of leaves: 7
Tree depth: 5
CIR: 0.02
Independent Cluster Pairs: 2
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/Tree1.json

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

Cluster constraints 13 99 53.19 49.50 851 8.41e+25 59.69 32.80 0.62 2.69

Variables per cluster 9 25 16.44 17.00 263 9.21e+18 43.67 5.93 0.36 2.19

Separator constraints 0 89 37.56 30.00 601 0 None 31.74 0.84 2.60

Separator variables 0 23 13.94 13.50 223 0 None 6.57 0.47 2.19

Clusters per var 1 14 6.58 7.00 263 6.94e+27 64.11 3.80 0.58 2.38

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	13	99	53.19	49.50	851	8.41e+25	59.69	32.80	0.62	2.69
Variables per cluster	9	25	16.44	17.00	263	9.21e+18	43.67	5.93	0.36	2.19
Separator constraints	0	89	37.56	30.00	601	0	None	31.74	0.84	2.60
Separator variables	0	23	13.94	13.50	223	0	None	6.57	0.47	2.19
Clusters per var	1	14	6.58	7.00	263	6.94e+27	64.11	3.80	0.58	2.38

Dual tree decomposition

Number of clusters: 38
Number of leaves: 18
Tree depth: 5
CIR: 0.10
Independent Cluster Pairs: 64
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/DualTree1.json

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

Cluster constraints 65 873 269.76 194.50 10,251 MAX VALUE 203.70 201.93 0.75 3.56

Variables per cluster 16 134 42.89 31.00 1,630 MAX VALUE 136.00 28.99 0.68 3.31

Separator constraints 0 507 189.58 160.50 7,204 0 None 120.42 0.64 3.60

Separator variables 0 97 36.32 28.00 1,380 0 None 22.03 0.61 3.28

Clusters per variable 1 10 6.52 7.00 1,630 MAX VALUE 435.19 2.53 0.39 2.05

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	65	873	269.76	194.50	10,251	MAX VALUE	203.70	201.93	0.75	3.56
Variables per cluster	16	134	42.89	31.00	1,630	MAX VALUE	136.00	28.99	0.68	3.31
Separator constraints	0	507	189.58	160.50	7,204	0	None	120.42	0.64	3.60
Separator variables	0	97	36.32	28.00	1,380	0	None	22.03	0.61	3.28
Clusters per variable	1	10	6.52	7.00	1,630	MAX VALUE	435.19	2.53	0.39	2.05

Primal graph

Density: 32.05%
MCB compute time (ms): 5
MCB cycles: 274
Triangles: 318
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/Primal1.json

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

Clustering coefficient 0.14 0.47 0.30 0.31 12.11 0.00 -49.03 0.07 0.23 3.52

Degree 8 21 12.50 12.50 500 MAX VALUE 99.94 2.93 0.23 2.26

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.19 3.00 873 MAX VALUE 315.69 0.39 0.12 0.48

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.14	0.47	0.30	0.31	12.11	0.00	-49.03	0.07	0.23	3.52
Degree	8	21	12.50	12.50	500	MAX VALUE	99.94	2.93	0.23	2.26
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.19	3.00	873	MAX VALUE	315.69	0.39	0.12	0.48

Triangulated primal graph

Density: 67.05%
MCB compute time (ms): 18
MCB cycles: 494
Triangles: 4,088

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

Clustering coefficient 0.70 1.00 0.87 0.86 34.79 0.00 -5.75 0.08 0.09 3.21

Degree 8 37 26.15 30.00 1,046 MAX VALUE 126.91 9.00 0.34 2.74

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,482 MAX VALUE 542.71 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.70	1.00	0.87	0.86	34.79	0.00	-5.75	0.08	0.09	3.21
Degree	8	37	26.15	30.00	1,046	MAX VALUE	126.91	9.00	0.34	2.74
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,482	MAX VALUE	542.71	0.00	0.00	0.00

Dual graph

Density: 9.79%
MCB compute time (ms): 820
MCB cycles: 4,482
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/Dual1.json

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

Clustering coefficient 0.47 0.61 0.51 0.50 126.43 0.00 -170.63 0.02 0.04 4.62

Degree 15 37 24.38 24.00 6,094 MAX VALUE 794.41 4.31 0.18 2.81

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.25 3.00 14,566 MAX VALUE 5,243.93 0.45 0.14 0.59

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.61	0.51	0.50	126.43	0.00	-170.63	0.02	0.04	4.62
Degree	15	37	24.38	24.00	6,094	MAX VALUE	794.41	4.31	0.18	2.81
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.25	3.00	14,566	MAX VALUE	5,243.93	0.45	0.14	0.59

Minimal dual graph

Density: 1.48%
MCB compute time (ms): 291
MCB cycles: 211

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

Clustering coefficient 0.00 0.17 0.00 0.00 0.37 0.00 None 0.01 9.37 0.07

Degree 2 6 3.68 4.00 920 MAX VALUE 319.98 0.81 0.22 1.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.74 7.00 1,423 MAX VALUE 399.26 1.16 0.17 1.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.37	0.00	None	0.01	9.37	0.07
Degree	2	6	3.68	4.00	920	MAX VALUE	319.98	0.81	0.22	1.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.74	7.00	1,423	MAX VALUE	399.26	1.16	0.17	1.55

Triangulated dual graph

Density: 53.10%
Triangles: 694,688

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

Clustering coefficient 0.76 1.00 0.85 0.82 212.34 0.00 -41.77 0.08 0.09 4.85

Degree 15 190 132.21 167.00 33,052 MAX VALUE 1,178.83 58.33 0.44 3.90

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	0.76	1.00	0.85	0.82	212.34	0.00	-41.77	0.08	0.09	4.85
Degree	15	190	132.21	167.00	33,052	MAX VALUE	1,178.83	58.33	0.44	3.90
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.36%

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

Clustering coefficient 0.45 1.00 0.81 0.78 203.35 0.00 -55.56 0.14 0.18 3.58

Degree 2 90 28.30 7.00 7,074 MAX VALUE 628.22 32.58 1.15 3.24

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	0.45	1.00	0.81	0.78	203.35	0.00	-55.56	0.14	0.18	3.58
Degree	2	90	28.30	7.00	7,074	MAX VALUE	628.22	32.58	1.15	3.24
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.19%
MCB compute time (ms): 124
MCB cycles: 211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-68-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 21 3.45 2.00 1,000 MAX VALUE 273.22 3.78 1.10 0.71

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.10 6.00 1,288 MAX VALUE 381.23 0.44 0.07 0.20

XCSP 2.1 Benchmarks