XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-17-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:24
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 180

General features

Coarse blocks: 9,000
Value tables: 40

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

Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Coarse blocks size 4 22 12.45 12.00 112,026 MAX VALUE 22,501.20 2.48 0.20 2.33

Relational linkage 0.16 0.52 0.35 0.36 351.72 0.00 -1,061.58 0.06 0.18 1.85

Tightness 0.45 0.55 0.50 0.50 90.38 0.00 -124.15 0.02 0.04 3.75

Tuples 281 343 311.18 311.50 56,013 MAX VALUE 1,033.13 12.38 0.04 3.75

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 5 14 9.00 9.00 360 3.71e+37 86.51 2.27 0.25 2.09

Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 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	360	MAX VALUE	124.77	0.00	0.00	0.00
Coarse blocks size	4	22	12.45	12.00	112,026	MAX VALUE	22,501.20	2.48	0.20	2.33
Relational linkage	0.16	0.52	0.35	0.36	351.72	0.00	-1,061.58	0.06	0.18	1.85
Tightness	0.45	0.55	0.50	0.50	90.38	0.00	-124.15	0.02	0.04	3.75
Tuples	281	343	311.18	311.50	56,013	MAX VALUE	1,033.13	12.38	0.04	3.75
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	5	14	9.00	9.00	360	3.71e+37	86.51	2.27	0.25	2.09
Value table partitions	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 20
Number of leaves: 10
Tree depth: 4
CIR: 0.08
Independent Cluster Pairs: 13
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/Tree1.json

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

Cluster constraints 8 53 21.85 18.00 437 1.80e+25 58.15 13.91 0.64 2.72

Variables per cluster 6 21 11.40 10.50 228 2.55e+20 46.99 4.80 0.42 2.28

Separator constraints 0 47 12.85 8.00 257 0 None 12.30 0.96 2.69

Separator variables 0 19 9.40 8.00 188 0 None 4.78 0.51 2.28

Clusters per var 1 13 5.70 6.50 228 1.29e+24 55.52 3.82 0.67 2.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	8	53	21.85	18.00	437	1.80e+25	58.15	13.91	0.64	2.72
Variables per cluster	6	21	11.40	10.50	228	2.55e+20	46.99	4.80	0.42	2.28
Separator constraints	0	47	12.85	8.00	257	0	None	12.30	0.96	2.69
Separator variables	0	19	9.40	8.00	188	0	None	4.78	0.51	2.28
Clusters per var	1	13	5.70	6.50	228	1.29e+24	55.52	3.82	0.67	2.28

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 138
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/DualTree1.json

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

Cluster constraints 21 367 123.95 99.00 4,710 MAX VALUE 175.59 80.92 0.65 3.53

Variables per cluster 9 86 29.08 21.50 1,105 MAX VALUE 121.70 18.70 0.64 3.25

Separator constraints 0 214 83.34 77.00 3,167 0 None 49.03 0.59 3.60

Separator variables 0 65 24.34 19.50 925 0 None 14.28 0.59 3.27

Clusters per variable 1 10 6.14 7.00 1,105 MAX VALUE 296.09 2.75 0.45 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	21	367	123.95	99.00	4,710	MAX VALUE	175.59	80.92	0.65	3.53
Variables per cluster	9	86	29.08	21.50	1,105	MAX VALUE	121.70	18.70	0.64	3.25
Separator constraints	0	214	83.34	77.00	3,167	0	None	49.03	0.59	3.60
Separator variables	0	65	24.34	19.50	925	0	None	14.28	0.59	3.27
Clusters per variable	1	10	6.14	7.00	1,105	MAX VALUE	296.09	2.75	0.45	2.15

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 168
Triangles: 125
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/Primal1.json

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

Clustering coefficient 0.00 0.60 0.25 0.23 9.85 0.00 None 0.10 0.39 3.10

Degree 5 14 9.00 9.00 360 3.71e+37 86.51 2.27 0.25 2.09

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.37 3.00 566 MAX VALUE 202.34 0.49 0.15 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.60	0.25	0.23	9.85	0.00	None	0.10	0.39	3.10
Degree	5	14	9.00	9.00	360	3.71e+37	86.51	2.27	0.25	2.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.37	3.00	566	MAX VALUE	202.34	0.49	0.15	0.69

Triangulated primal graph

Density: 51.03%
MCB compute time (ms): 7
MCB cycles: 392
Triangles: 2,348

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

Clustering coefficient 0.64 1.00 0.83 0.82 33.39 0.00 -7.61 0.12 0.14 3.04

Degree 5 32 19.90 25.50 796 MAX VALUE 113.00 9.48 0.48 2.79

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,176 MAX VALUE 430.66 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.64	1.00	0.83	0.82	33.39	0.00	-7.61	0.12	0.14	3.04
Degree	5	32	19.90	25.50	796	MAX VALUE	113.00	9.48	0.48	2.79
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,176	MAX VALUE	430.66	0.00	0.00	0.00

Dual graph

Density: 9.58%
MCB compute time (ms): 357
MCB cycles: 1,584
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/Dual1.json

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

Clustering coefficient 0.44 0.62 0.50 0.50 90.35 0.00 -124.34 0.03 0.06 4.05

Degree 8 24 17.14 17.00 3,086 MAX VALUE 508.37 3.11 0.18 2.51

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.15 3.00 4,995 MAX VALUE 1,809.53 0.38 0.12 0.44

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.62	0.50	0.50	90.35	0.00	-124.34	0.03	0.06	4.05
Degree	8	24	17.14	17.00	3,086	MAX VALUE	508.37	3.11	0.18	2.51
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.15	3.00	4,995	MAX VALUE	1,809.53	0.38	0.12	0.44

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 77
MCB cycles: 141

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

Clustering coefficient 0.00 0.17 0.00 0.00 0.43 0.00 None 0.02 7.86 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 224.47 0.73 0.21 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.74 7.00 951 MAX VALUE 266.42 1.25 0.18 1.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.17	0.00	0.00	0.43	0.00	None	0.02	7.86	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	224.47	0.73	0.21	1.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.74	7.00	951	MAX VALUE	266.42	1.25	0.18	1.61

Triangulated dual graph

Density: 46.47%
Triangles: 198,028

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

Clustering coefficient 0.69 1.00 0.84 0.81 150.35 0.00 -33.37 0.09 0.11 4.65

Degree 8 134 83.19 103.00 14,974 MAX VALUE 759.61 40.98 0.49 4.09

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	0.69	1.00	0.84	0.81	150.35	0.00	-33.37	0.09	0.11	4.65
Degree	8	134	83.19	103.00	14,974	MAX VALUE	759.61	40.98	0.49	4.09
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.69%

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

Clustering coefficient 0.47 1.00 0.80 0.75 143.29 0.00 -44.48 0.16 0.20 3.33

Degree 2 64 20.93 7.00 3,768 MAX VALUE 422.60 22.95 1.10 3.06

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	0.47	1.00	0.80	0.75	143.29	0.00	-44.48	0.16	0.20	3.33
Degree	2	64	20.93	7.00	3,768	MAX VALUE	422.60	22.95	1.10	3.06
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 46
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-17-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 14 3.27 2.00 720 MAX VALUE 211.27 2.87 0.88 0.85

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.48 6.00 914 MAX VALUE 262.42 0.86 0.13 0.55

XCSP 2.1 Benchmarks