XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-60-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:28
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 3 22 12.45 12.00 112,066 MAX VALUE 22,508.80 2.47 0.20 2.32

Relational linkage 0.12 0.52 0.36 0.36 356.00 0.00 -1,049.05 0.06 0.17 1.85

Tightness 0.45 0.56 0.50 0.50 90.35 0.00 -124.23 0.02 0.04 3.72

Tuples 277 342 311.29 310.00 56,033 MAX VALUE 1,033.18 12.92 0.04 3.72

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

Value table constraints 5 15 9.00 9.00 360 3.54e+37 86.46 2.38 0.26 2.04

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	3	22	12.45	12.00	112,066	MAX VALUE	22,508.80	2.47	0.20	2.32
Relational linkage	0.12	0.52	0.36	0.36	356.00	0.00	-1,049.05	0.06	0.17	1.85
Tightness	0.45	0.56	0.50	0.50	90.35	0.00	-124.23	0.02	0.04	3.72
Tuples	277	342	311.29	310.00	56,033	MAX VALUE	1,033.18	12.92	0.04	3.72
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	5	15	9.00	9.00	360	3.54e+37	86.46	2.38	0.26	2.04
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: 22
Number of leaves: 10
Tree depth: 5
CIR: 0.03
Independent Cluster Pairs: 7
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/Tree1.json

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

Cluster constraints 6 41 20.86 18.00 459 3.10e+27 63.30 11.47 0.55 2.82

Variables per cluster 6 19 11.45 11.00 252 4.11e+22 52.07 4.35 0.38 2.22

Separator constraints 0 37 12.68 11.00 279 0 None 10.81 0.85 2.63

Separator variables 0 18 9.64 9.50 212 0 None 4.54 0.47 2.31

Clusters per var 1 17 6.30 6.00 252 2.12e+24 56.01 4.96 0.79 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	41	20.86	18.00	459	3.10e+27	63.30	11.47	0.55	2.82
Variables per cluster	6	19	11.45	11.00	252	4.11e+22	52.07	4.35	0.38	2.22
Separator constraints	0	37	12.68	11.00	279	0	None	10.81	0.85	2.63
Separator variables	0	18	9.64	9.50	212	0	None	4.54	0.47	2.31
Clusters per var	1	17	6.30	6.00	252	2.12e+24	56.01	4.96	0.79	2.21

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.20
Independent Cluster Pairs: 131
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/DualTree1.json

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

Cluster constraints 27 354 122.61 93.50 4,659 MAX VALUE 175.22 80.56 0.66 3.40

Variables per cluster 10 84 29.05 21.00 1,104 MAX VALUE 121.66 18.84 0.65 3.12

Separator constraints 0 192 81.74 73.00 3,106 0 None 47.39 0.58 3.53

Separator variables 0 64 24.32 19.00 924 0 None 14.42 0.59 3.14

Clusters per variable 1 10 6.13 7.00 1,104 MAX VALUE 296.63 2.73 0.44 2.20

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	27	354	122.61	93.50	4,659	MAX VALUE	175.22	80.56	0.66	3.40
Variables per cluster	10	84	29.05	21.00	1,104	MAX VALUE	121.66	18.84	0.65	3.12
Separator constraints	0	192	81.74	73.00	3,106	0	None	47.39	0.58	3.53
Separator variables	0	64	24.32	19.00	924	0	None	14.42	0.59	3.14
Clusters per variable	1	10	6.13	7.00	1,104	MAX VALUE	296.63	2.73	0.44	2.20

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 151
Triangles: 111
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/Primal1.json

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

Clustering coefficient 0.10 0.38 0.22 0.21 8.75 0.00 -62.59 0.06 0.29 3.16

Degree 5 15 9.00 9.00 360 3.54e+37 86.46 2.38 0.26 2.04

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.30 3.00 499 MAX VALUE 179.12 0.46 0.14 0.61

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.10	0.38	0.22	0.21	8.75	0.00	-62.59	0.06	0.29	3.16
Degree	5	15	9.00	9.00	360	3.54e+37	86.46	2.38	0.26	2.04
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.30	3.00	499	MAX VALUE	179.12	0.46	0.14	0.61

Triangulated primal graph

Density: 49.10%
MCB compute time (ms): 11
MCB cycles: 369
Triangles: 2,111

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

Clustering coefficient 0.55 1.00 0.83 0.81 33.18 0.00 -8.05 0.14 0.17 3.04

Degree 5 34 19.15 23.00 766 MAX VALUE 111.50 9.48 0.50 2.83

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,107 MAX VALUE 405.39 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.55	1.00	0.83	0.81	33.18	0.00	-8.05	0.14	0.17	3.04
Degree	5	34	19.15	23.00	766	MAX VALUE	111.50	9.48	0.50	2.83
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,107	MAX VALUE	405.39	0.00	0.00	0.00

Dual graph

Density: 9.64%
MCB compute time (ms): 266
MCB cycles: 1,666
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/Dual1.json

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

Clustering coefficient 0.44 0.65 0.50 0.50 90.82 0.00 -123.45 0.03 0.06 4.02

Degree 9 25 17.26 17.00 3,106 MAX VALUE 509.49 3.18 0.18 2.53

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.18 3.00 5,294 MAX VALUE 1,914.86 0.40 0.12 0.48

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.65	0.50	0.50	90.82	0.00	-123.45	0.03	0.06	4.02
Degree	9	25	17.26	17.00	3,106	MAX VALUE	509.49	3.18	0.18	2.53
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.18	3.00	5,294	MAX VALUE	1,914.86	0.40	0.12	0.48

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 79
MCB cycles: 141

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 5 3.56 4.00 640 MAX VALUE 224.48 0.72 0.20 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.72 7.00 948 MAX VALUE 266.59 1.13 0.17 1.53

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	5	3.56	4.00	640	MAX VALUE	224.48	0.72	0.20	1.09
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.72	7.00	948	MAX VALUE	266.59	1.13	0.17	1.53

Triangulated dual graph

Density: 46.62%
Triangles: 199,613

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

Clustering coefficient 0.70 1.00 0.84 0.82 150.35 0.00 -33.35 0.09 0.10 4.61

Degree 9 133 83.44 98.00 15,020 MAX VALUE 760.11 41.09 0.49 3.93

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	0.70	1.00	0.84	0.82	150.35	0.00	-33.35	0.09	0.10	4.61
Degree	9	133	83.44	98.00	15,020	MAX VALUE	760.11	41.09	0.49	3.93
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.61%

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

Clustering coefficient 0.53 1.00 0.80 0.75 143.81 0.00 -43.88 0.16 0.20 3.27

Degree 2 65 20.78 7.00 3,740 MAX VALUE 419.68 22.95 1.10 3.13

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	0.53	1.00	0.80	0.75	143.81	0.00	-43.88	0.16	0.20	3.27
Degree	2	65	20.78	7.00	3,740	MAX VALUE	419.68	22.95	1.10	3.13
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 44
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-60-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 15 3.27 2.00 720 MAX VALUE 211.23 2.88 0.88 0.85

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.51 6.00 918 MAX VALUE 263.00 0.87 0.13 0.57

XCSP 2.1 Benchmarks