XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-16-ext
Number of variables: 40
Number of constraints: 180
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: 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 12.46 12.00 112,132 MAX VALUE 22,504.60 2.53 0.20 2.34

Relational linkage 0.12 0.56 0.35 0.36 353.36 0.00 -1,057.52 0.06 0.18 1.87

Tightness 0.46 0.56 0.50 0.50 90.29 0.00 -124.32 0.02 0.04 3.77

Tuples 278 338 311.48 312.00 56,066 MAX VALUE 1,033.29 12.61 0.04 3.77

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

Value table constraints 3 13 9.00 9.00 360 2.21e+37 85.99 2.49 0.28 2.11

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	12.46	12.00	112,132	MAX VALUE	22,504.60	2.53	0.20	2.34
Relational linkage	0.12	0.56	0.35	0.36	353.36	0.00	-1,057.52	0.06	0.18	1.87
Tightness	0.46	0.56	0.50	0.50	90.29	0.00	-124.32	0.02	0.04	3.77
Tuples	278	338	311.48	312.00	56,066	MAX VALUE	1,033.29	12.61	0.04	3.77
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	3	13	9.00	9.00	360	2.21e+37	85.99	2.49	0.28	2.11
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: 0.08
Independent Cluster Pairs: 17
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-ext/Tree1.json

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

Cluster constraints 3 44 22.27 20.50 490 2.01e+27 62.87 13.75 0.62 2.84

Variables per cluster 4 19 11.77 10.50 259 3.99e+22 52.04 4.96 0.42 2.40

Separator constraints 0 38 14.09 10.00 310 0 None 13.03 0.92 2.71

Separator variables 0 18 9.95 8.50 219 0 None 5.18 0.52 2.50

Clusters per var 1 16 6.47 6.00 259 1.95e+25 58.23 4.81 0.74 2.43

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	44	22.27	20.50	490	2.01e+27	62.87	13.75	0.62	2.84
Variables per cluster	4	19	11.77	10.50	259	3.99e+22	52.04	4.96	0.42	2.40
Separator constraints	0	38	14.09	10.00	310	0	None	13.03	0.92	2.71
Separator variables	0	18	9.95	8.50	219	0	None	5.18	0.52	2.50
Clusters per var	1	16	6.47	6.00	259	1.95e+25	58.23	4.81	0.74	2.43

Dual tree decomposition

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

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

Cluster constraints 19 344 123.00 108.50 4,674 MAX VALUE 174.19 81.96 0.67 3.53

Variables per cluster 8 86 28.92 23.00 1,099 MAX VALUE 121.17 18.84 0.65 3.23

Separator constraints 0 186 81.84 78.00 3,110 0 None 48.62 0.59 3.46

Separator variables 0 64 24.18 21.00 919 0 None 14.38 0.59 3.16

Clusters per variable 1 11 6.11 7.00 1,099 MAX VALUE 295.20 2.75 0.45 2.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	19	344	123.00	108.50	4,674	MAX VALUE	174.19	81.96	0.67	3.53
Variables per cluster	8	86	28.92	23.00	1,099	MAX VALUE	121.17	18.84	0.65	3.23
Separator constraints	0	186	81.84	78.00	3,110	0	None	48.62	0.59	3.46
Separator variables	0	64	24.18	21.00	919	0	None	14.38	0.59	3.16
Clusters per variable	1	11	6.11	7.00	1,099	MAX VALUE	295.20	2.75	0.45	2.24

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 145
Triangles: 115
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-ext/Primal1.json

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

Clustering coefficient 0.00 0.40 0.21 0.20 8.28 0.00 None 0.08 0.39 3.23

Degree 3 13 9.00 9.00 360 2.21e+37 85.99 2.49 0.28 2.11

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.32 3.00 481 MAX VALUE 172.53 0.47 0.14 0.62

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.40	0.21	0.20	8.28	0.00	None	0.08	0.39	3.23
Degree	3	13	9.00	9.00	360	2.21e+37	85.99	2.49	0.28	2.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.32	3.00	481	MAX VALUE	172.53	0.47	0.14	0.62

Triangulated primal graph

Density: 50.00%
MCB compute time (ms): 11
MCB cycles: 357
Triangles: 2,245

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

Clustering coefficient 0.59 1.00 0.83 0.81 33.20 0.00 -7.87 0.12 0.14 3.04

Degree 3 33 19.50 23.00 780 MAX VALUE 111.69 9.48 0.49 2.95

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,071 MAX VALUE 392.20 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.59	1.00	0.83	0.81	33.20	0.00	-7.87	0.12	0.14	3.04
Degree	3	33	19.50	23.00	780	MAX VALUE	111.69	9.48	0.49	2.95
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,071	MAX VALUE	392.20	0.00	0.00	0.00

Dual graph

Density: 9.71%
MCB compute time (ms): 274
MCB cycles: 1,805
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-ext/Dual1.json

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

Clustering coefficient 0.44 0.71 0.50 0.50 90.38 0.00 -124.30 0.03 0.06 4.05

Degree 7 24 17.38 17.00 3,128 MAX VALUE 510.29 3.29 0.19 2.54

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.28 3.00 5,920 MAX VALUE 2,125.37 0.50 0.15 0.65

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.71	0.50	0.50	90.38	0.00	-124.30	0.03	0.06	4.05
Degree	7	24	17.38	17.00	3,128	MAX VALUE	510.29	3.29	0.19	2.54
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.28	3.00	5,920	MAX VALUE	2,125.37	0.50	0.15	0.65

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 67
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 6 3.56 3.00 640 MAX VALUE 224.54 0.73 0.21 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.91 7.00 975 MAX VALUE 270.69 1.11 0.16 1.45

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	3.56	3.00	640	MAX VALUE	224.54	0.73	0.21	1.08
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.91	7.00	975	MAX VALUE	270.69	1.11	0.16	1.45

Triangulated dual graph

Density: 46.57%
Triangles: 198,516

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

Clustering coefficient 0.71 1.00 0.83 0.82 150.17 0.00 -33.59 0.09 0.11 4.60

Degree 7 130 83.36 96.00 15,004 MAX VALUE 759.87 40.96 0.49 3.83

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	0.71	1.00	0.83	0.82	150.17	0.00	-33.59	0.09	0.11	4.60
Degree	7	130	83.36	96.00	15,004	MAX VALUE	759.87	40.96	0.49	3.83
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 12.01%

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

Clustering coefficient 0.47 1.00 0.80 0.75 144.30 0.00 -43.08 0.15 0.19 3.30

Degree 2 66 21.49 7.00 3,868 MAX VALUE 424.37 23.56 1.10 3.08

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	144.30	0.00	-43.08	0.15	0.19	3.30
Degree	2	66	21.49	7.00	3,868	MAX VALUE	424.37	23.56	1.10	3.08
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 40
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-16-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 13 3.27 2.00 720 MAX VALUE 210.76 2.90 0.89 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.60 6.00 930 MAX VALUE 264.72 0.91 0.14 0.61

XCSP 2.1 Benchmarks