XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-16-250-350-16-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 10.38 10.00 83,032 MAX VALUE 18,569.80 1.92 0.19 2.07

Relational linkage 0.19 0.62 0.44 0.44 284.31 0.00 -528.44 0.07 0.16 1.55

Tightness 0.27 0.44 0.35 0.35 87.83 0.00 -262.56 0.03 0.09 3.40

Tuples 144 188 166.06 165.50 41,516 MAX VALUE 1,277.79 8.12 0.05 3.40

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

Value table constraints 9 18 12.50 12.00 500 MAX VALUE 100.31 2.39 0.19 2.15

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	10.38	10.00	83,032	MAX VALUE	18,569.80	1.92	0.19	2.07
Relational linkage	0.19	0.62	0.44	0.44	284.31	0.00	-528.44	0.07	0.16	1.55
Tightness	0.27	0.44	0.35	0.35	87.83	0.00	-262.56	0.03	0.09	3.40
Tuples	144	188	166.06	165.50	41,516	MAX VALUE	1,277.79	8.12	0.05	3.40
Values	16	16	16.00	16.00	640	MAX VALUE	110.90	0.00	0.00	0.00
Value table constraints	9	18	12.50	12.00	500	MAX VALUE	100.31	2.39	0.19	2.15
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: 7
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/Tree1.json

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

Cluster constraints 19 108 49.87 42.00 748 3.77e+24 56.59 26.22 0.53 2.62

Variables per cluster 10 26 16.27 16.00 244 7.33e+17 41.14 4.97 0.31 2.43

Separator constraints 0 81 33.20 31.00 498 0 None 22.81 0.69 2.62

Separator variables 0 23 13.60 14.00 204 0 None 5.58 0.41 2.43

Clusters per var 1 13 6.10 7.00 244 4.13e+26 61.29 3.57 0.59 2.38

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	19	108	49.87	42.00	748	3.77e+24	56.59	26.22	0.53	2.62
Variables per cluster	10	26	16.27	16.00	244	7.33e+17	41.14	4.97	0.31	2.43
Separator constraints	0	81	33.20	31.00	498	0	None	22.81	0.69	2.62
Separator variables	0	23	13.60	14.00	204	0	None	5.58	0.41	2.43
Clusters per var	1	13	6.10	7.00	244	4.13e+26	61.29	3.57	0.59	2.38

Dual tree decomposition

Number of clusters: 38
Number of leaves: 18
Tree depth: 5
CIR: 0.12
Independent Cluster Pairs: 79
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/DualTree1.json

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

Cluster constraints 73 860 269.89 202.50 10,256 MAX VALUE 204.63 194.30 0.72 3.60

Variables per cluster 17 133 43.47 31.50 1,652 MAX VALUE 136.57 29.57 0.68 3.33

Separator constraints 0 502 191.24 156.00 7,267 0 None 116.20 0.61 3.60

Separator variables 0 100 36.89 29.50 1,402 0 None 22.65 0.61 3.25

Clusters per variable 1 10 6.61 7.50 1,652 MAX VALUE 438.57 2.57 0.39 2.11

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	73	860	269.89	202.50	10,256	MAX VALUE	204.63	194.30	0.72	3.60
Variables per cluster	17	133	43.47	31.50	1,652	MAX VALUE	136.57	29.57	0.68	3.33
Separator constraints	0	502	191.24	156.00	7,267	0	None	116.20	0.61	3.60
Separator variables	0	100	36.89	29.50	1,402	0	None	22.65	0.61	3.25
Clusters per variable	1	10	6.61	7.50	1,652	MAX VALUE	438.57	2.57	0.39	2.11

Primal graph

Density: 32.05%
MCB compute time (ms): 5
MCB cycles: 281
Triangles: 311
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/Primal1.json

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

Clustering coefficient 0.17 0.47 0.31 0.31 12.36 0.00 -47.58 0.05 0.17 3.48

Degree 9 18 12.50 12.00 500 MAX VALUE 100.31 2.39 0.19 2.15

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.16 3.00 889 MAX VALUE 321.94 0.37 0.12 0.45

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.17	0.47	0.31	0.31	12.36	0.00	-47.58	0.05	0.17	3.48
Degree	9	18	12.50	12.00	500	MAX VALUE	100.31	2.39	0.19	2.15
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.16	3.00	889	MAX VALUE	321.94	0.37	0.12	0.45

Triangulated primal graph

Density: 67.82%
MCB compute time (ms): 26
MCB cycles: 493
Triangles: 4,119

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

Clustering coefficient 0.71 1.00 0.87 0.86 34.64 0.00 -5.95 0.09 0.10 3.24

Degree 9 37 26.45 31.00 1,058 MAX VALUE 127.84 8.82 0.33 2.80

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,479 MAX VALUE 541.62 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.71	1.00	0.87	0.86	34.64	0.00	-5.95	0.09	0.10	3.24
Degree	9	37	26.45	31.00	1,058	MAX VALUE	127.84	8.82	0.33	2.80
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,479	MAX VALUE	541.62	0.00	0.00	0.00

Dual graph

Density: 9.60%
MCB compute time (ms): 1,260
MCB cycles: 3,227
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/Dual1.json

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

Clustering coefficient 0.47 0.56 0.50 0.50 125.45 0.00 -172.49 0.01 0.03 4.47

Degree 16 33 23.91 24.00 5,978 MAX VALUE 791.02 3.39 0.14 2.60

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.05 3.00 9,828 MAX VALUE 3,587.51 0.21 0.07 0.19

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.56	0.50	0.50	125.45	0.00	-172.49	0.01	0.03	4.47
Degree	16	33	23.91	24.00	5,978	MAX VALUE	791.02	3.39	0.14	2.60
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.05	3.00	9,828	MAX VALUE	3,587.51	0.21	0.07	0.19

Minimal dual graph

Density: 1.48%
MCB compute time (ms): 178
MCB cycles: 216

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

Clustering coefficient 0.00 0.17 0.00 0.00 0.63 0.00 None 0.02 7.33 0.12

Degree 2 6 3.68 4.00 920 MAX VALUE 319.87 0.82 0.22 1.16

Eccentricity None None None None None None None None None None

MCB cycle size 3 10 6.63 7.00 1,432 MAX VALUE 404.73 1.17 0.18 1.53

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.63	0.00	None	0.02	7.33	0.12
Degree	2	6	3.68	4.00	920	MAX VALUE	319.87	0.82	0.22	1.16
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	10	6.63	7.00	1,432	MAX VALUE	404.73	1.17	0.18	1.53

Triangulated dual graph

Density: 53.94%
Triangles: 717,406

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

Clustering coefficient 0.74 1.00 0.85 0.83 212.98 0.00 -41.00 0.07 0.09 4.81

Degree 16 198 134.30 166.00 33,576 MAX VALUE 1,183.65 58.60 0.44 4.02

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	0.85	0.83	212.98	0.00	-41.00	0.07	0.09	4.81
Degree	16	198	134.30	166.00	33,576	MAX VALUE	1,183.65	58.60	0.44	4.02
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 10.85%

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

Clustering coefficient 0.54 1.00 0.81 0.78 201.97 0.00 -57.60 0.15 0.18 3.51

Degree 2 90 27.02 8.00 6,754 MAX VALUE 620.97 31.25 1.16 3.35

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	0.78	201.97	0.00	-57.60	0.15	0.18	3.51
Degree	2	90	27.02	8.00	6,754	MAX VALUE	620.97	31.25	1.16	3.35
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.19%
MCB compute time (ms): 79
MCB cycles: 211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-16-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 273.59 3.73 1.08 0.70

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.09 6.00 1,284 MAX VALUE 380.65 0.40 0.07 0.18

XCSP 2.1 Benchmarks