XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-16-250-350-61-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 83,056 MAX VALUE 18,574.00 1.92 0.18 2.07

Relational linkage 0.19 0.62 0.45 0.44 288.50 0.00 -519.16 0.07 0.16 1.56

Tightness 0.28 0.45 0.35 0.35 87.78 0.00 -262.57 0.03 0.09 3.36

Tuples 142 185 166.11 167.00 41,528 MAX VALUE 1,277.89 7.74 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 7 21 12.50 12.00 500 MAX VALUE 99.59 3.40 0.27 2.35

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	83,056	MAX VALUE	18,574.00	1.92	0.18	2.07
Relational linkage	0.19	0.62	0.45	0.44	288.50	0.00	-519.16	0.07	0.16	1.56
Tightness	0.28	0.45	0.35	0.35	87.78	0.00	-262.57	0.03	0.09	3.36
Tuples	142	185	166.11	167.00	41,528	MAX VALUE	1,277.89	7.74	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	7	21	12.50	12.00	500	MAX VALUE	99.59	3.40	0.27	2.35
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: 9
Tree depth: 3
CIR: 0.01
Independent Cluster Pairs: 1
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/Tree1.json

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

Cluster constraints 11 111 46.88 34.00 750 1.50e+25 57.97 31.15 0.66 2.60

Variables per cluster 8 25 14.62 12.50 234 1.47e+18 41.83 5.53 0.38 2.22

Separator constraints 0 91 31.25 22.00 500 0 None 27.36 0.88 2.69

Separator variables 0 23 12.12 10.50 194 0 None 5.76 0.48 2.22

Clusters per var 1 12 5.85 7.00 234 2.12e+25 58.32 3.55 0.61 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	11	111	46.88	34.00	750	1.50e+25	57.97	31.15	0.66	2.60
Variables per cluster	8	25	14.62	12.50	234	1.47e+18	41.83	5.53	0.38	2.22
Separator constraints	0	91	31.25	22.00	500	0	None	27.36	0.88	2.69
Separator variables	0	23	12.12	10.50	194	0	None	5.76	0.48	2.22
Clusters per var	1	12	5.85	7.00	234	2.12e+25	58.32	3.55	0.61	2.21

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.12
Independent Cluster Pairs: 82
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/DualTree1.json

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

Cluster constraints 42 902 274.58 210.00 10,434 MAX VALUE 203.22 214.53 0.78 3.56

Variables per cluster 13 132 43.24 32.50 1,643 MAX VALUE 135.79 30.25 0.70 3.28

Separator constraints 0 515 192.84 163.00 7,328 0 None 127.69 0.66 3.64

Separator variables 0 104 36.66 29.00 1,393 0 None 23.16 0.63 3.37

Clusters per variable 1 11 6.57 7.00 1,643 MAX VALUE 437.72 2.55 0.39 2.13

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	42	902	274.58	210.00	10,434	MAX VALUE	203.22	214.53	0.78	3.56
Variables per cluster	13	132	43.24	32.50	1,643	MAX VALUE	135.79	30.25	0.70	3.28
Separator constraints	0	515	192.84	163.00	7,328	0	None	127.69	0.66	3.64
Separator variables	0	104	36.66	29.00	1,393	0	None	23.16	0.63	3.37
Clusters per variable	1	11	6.57	7.00	1,643	MAX VALUE	437.72	2.55	0.39	2.13

Primal graph

Density: 32.05%
MCB compute time (ms): 7
MCB cycles: 247
Triangles: 331
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/Primal1.json

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

Clustering coefficient 0.11 0.56 0.31 0.32 12.56 0.00 -47.73 0.08 0.25 3.25

Degree 7 21 12.50 12.00 500 MAX VALUE 99.59 3.40 0.27 2.35

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.13 3.00 772 MAX VALUE 280.27 0.33 0.11 0.38

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.11	0.56	0.31	0.32	12.56	0.00	-47.73	0.08	0.25	3.25
Degree	7	21	12.50	12.00	500	MAX VALUE	99.59	3.40	0.27	2.35
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.13	3.00	772	MAX VALUE	280.27	0.33	0.11	0.38

Triangulated primal graph

Density: 63.33%
MCB compute time (ms): 27
MCB cycles: 458
Triangles: 3,645

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

Clustering coefficient 0.70 1.00 0.86 0.85 34.52 0.00 -6.13 0.09 0.11 3.09

Degree 7 35 24.70 30.00 988 MAX VALUE 123.96 9.41 0.38 2.63

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,374 MAX VALUE 503.16 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	0.86	0.85	34.52	0.00	-6.13	0.09	0.11	3.09
Degree	7	35	24.70	30.00	988	MAX VALUE	123.96	9.41	0.38	2.63
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,374	MAX VALUE	503.16	0.00	0.00	0.00

Dual graph

Density: 9.98%
MCB compute time (ms): 2,510
MCB cycles: 3,077
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/Dual1.json

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

Clustering coefficient 0.45 0.64 0.51 0.50 127.97 0.00 -167.76 0.03 0.05 4.76

Degree 12 40 24.85 24.00 6,212 MAX VALUE 798.13 4.98 0.20 2.95

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.04 3.00 9,347 MAX VALUE 3,413.80 0.19 0.06 0.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.64	0.51	0.50	127.97	0.00	-167.76	0.03	0.05	4.76
Degree	12	40	24.85	24.00	6,212	MAX VALUE	798.13	4.98	0.20	2.95
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.04	3.00	9,347	MAX VALUE	3,413.80	0.19	0.06	0.16

Minimal dual graph

Density: 1.48%
MCB compute time (ms): 332
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 320.22 0.78 0.21 1.12

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.83 7.00 1,441 MAX VALUE 402.32 1.11 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	320.22	0.78	0.21	1.12
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.83	7.00	1,441	MAX VALUE	402.32	1.11	0.16	1.46

Triangulated dual graph

Density: 54.81%
Triangles: 744,100

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

Clustering coefficient 0.75 1.00 0.85 0.84 213.71 0.00 -40.05 0.07 0.08 5.00

Degree 12 198 136.49 161.00 34,122 MAX VALUE 1,186.86 59.01 0.43 4.03

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	0.75	1.00	0.85	0.84	213.71	0.00	-40.05	0.07	0.08	5.00
Degree	12	198	136.49	161.00	34,122	MAX VALUE	1,186.86	59.01	0.43	4.03
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.16%

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

Clustering coefficient 0.48 1.00 0.81 0.76 203.53 0.00 -55.53 0.15 0.18 3.53

Degree 2 89 27.79 8.00 6,948 MAX VALUE 625.72 32.16 1.16 3.30

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	0.48	1.00	0.81	0.76	203.53	0.00	-55.53	0.15	0.18	3.53
Degree	2	89	27.79	8.00	6,948	MAX VALUE	625.72	32.16	1.16	3.30
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.19%
MCB compute time (ms): 119
MCB cycles: 211
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.35/normalized-rand-2-40-16-250-350-61-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 272.88 3.83 1.11 0.73

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.11 6.00 1,290 MAX VALUE 381.51 0.46 0.08 0.22

XCSP 2.1 Benchmarks