XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-30-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:27
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 20 12.41 12.00 111,660 MAX VALUE 22,472.10 2.48 0.20 2.33

Relational linkage 0.16 0.60 0.36 0.36 356.32 0.00 -1,050.22 0.07 0.19 1.92

Tightness 0.46 0.57 0.50 0.50 90.67 0.00 -123.56 0.02 0.04 3.69

Tuples 269 336 310.17 312.00 55,830 MAX VALUE 1,032.54 12.30 0.04 3.69

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

Value table constraints 2 17 9.00 9.00 360 1.19e+37 85.37 2.92 0.32 2.32

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	20	12.41	12.00	111,660	MAX VALUE	22,472.10	2.48	0.20	2.33
Relational linkage	0.16	0.60	0.36	0.36	356.32	0.00	-1,050.22	0.07	0.19	1.92
Tightness	0.46	0.57	0.50	0.50	90.67	0.00	-123.56	0.02	0.04	3.69
Tuples	269	336	310.17	312.00	55,830	MAX VALUE	1,032.54	12.30	0.04	3.69
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	2	17	9.00	9.00	360	1.19e+37	85.37	2.92	0.32	2.32
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: 19
Number of leaves: 11
Tree depth: 3
CIR: 0.15
Independent Cluster Pairs: 23
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/Tree1.json

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

Cluster constraints 2 64 20.63 15.00 392 1.24e+22 50.87 16.78 0.81 2.73

Variables per cluster 3 22 10.32 9.00 196 2.05e+18 42.16 4.95 0.48 2.45

Separator constraints 0 46 11.16 7.00 212 0 None 12.91 1.16 2.65

Separator variables 0 18 8.21 7.00 156 0 None 4.55 0.55 2.45

Clusters per var 1 13 4.90 5.50 196 1.11e+22 50.76 3.26 0.67 2.05

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	64	20.63	15.00	392	1.24e+22	50.87	16.78	0.81	2.73
Variables per cluster	3	22	10.32	9.00	196	2.05e+18	42.16	4.95	0.48	2.45
Separator constraints	0	46	11.16	7.00	212	0	None	12.91	1.16	2.65
Separator variables	0	18	8.21	7.00	156	0	None	4.55	0.55	2.45
Clusters per var	1	13	4.90	5.50	196	1.11e+22	50.76	3.26	0.67	2.05

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 6
CIR: 0.20
Independent Cluster Pairs: 131
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/DualTree1.json

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

Cluster constraints 21 382 126.34 99.50 4,801 MAX VALUE 174.17 89.87 0.71 3.64

Variables per cluster 8 84 28.89 22.00 1,098 MAX VALUE 120.88 19.09 0.66 3.21

Separator constraints 0 202 83.97 75.00 3,191 0 None 53.68 0.64 3.55

Separator variables 0 65 24.16 20.00 918 0 None 14.59 0.60 3.28

Clusters per variable 1 12 6.10 7.00 1,098 MAX VALUE 296.60 2.69 0.44 2.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	21	382	126.34	99.50	4,801	MAX VALUE	174.17	89.87	0.71	3.64
Variables per cluster	8	84	28.89	22.00	1,098	MAX VALUE	120.88	19.09	0.66	3.21
Separator constraints	0	202	83.97	75.00	3,191	0	None	53.68	0.64	3.55
Separator variables	0	65	24.16	20.00	918	0	None	14.59	0.60	3.28
Clusters per variable	1	12	6.10	7.00	1,098	MAX VALUE	296.60	2.69	0.44	2.25

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 151
Triangles: 133
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/Primal1.json

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

Clustering coefficient 0.00 0.48 0.23 0.24 9.23 0.00 None 0.10 0.44 3.34

Degree 2 17 9.00 9.00 360 1.19e+37 85.37 2.92 0.32 2.32

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.25 3.00 491 MAX VALUE 176.82 0.43 0.13 0.56

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.48	0.23	0.24	9.23	0.00	None	0.10	0.44	3.34
Degree	2	17	9.00	9.00	360	1.19e+37	85.37	2.92	0.32	2.32
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.25	3.00	491	MAX VALUE	176.82	0.43	0.13	0.56

Triangulated primal graph

Density: 49.62%
MCB compute time (ms): 12
MCB cycles: 362
Triangles: 2,299

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

Clustering coefficient 0.61 1.00 0.85 0.83 33.83 0.00 -7.07 0.11 0.14 2.88

Degree 2 33 19.35 25.50 774 MAX VALUE 110.34 9.76 0.50 2.62

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,086 MAX VALUE 397.70 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.61	1.00	0.85	0.83	33.83	0.00	-7.07	0.11	0.14	2.88
Degree	2	33	19.35	25.50	774	MAX VALUE	110.34	9.76	0.50	2.62
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,086	MAX VALUE	397.70	0.00	0.00	0.00

Dual graph

Density: 9.99%
MCB compute time (ms): 256
MCB cycles: 1,685
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/Dual1.json

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

Clustering coefficient 0.45 0.78 0.51 0.50 91.86 0.00 -121.53 0.04 0.07 4.33

Degree 7 27 17.89 18.00 3,220 MAX VALUE 514.01 4.12 0.23 2.78

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.17 3.00 5,336 MAX VALUE 1,931.16 0.39 0.12 0.47

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.78	0.51	0.50	91.86	0.00	-121.53	0.04	0.07	4.33
Degree	7	27	17.89	18.00	3,220	MAX VALUE	514.01	4.12	0.23	2.78
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.17	3.00	5,336	MAX VALUE	1,931.16	0.39	0.12	0.47

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 72
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 3.00 640 MAX VALUE 224.28 0.75 0.21 1.11

Eccentricity None None None None None None None None None None

MCB cycle size 4 10 6.64 7.00 936 MAX VALUE 264.43 1.22 0.18 1.60

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	3.00	640	MAX VALUE	224.28	0.75	0.21	1.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	10	6.64	7.00	936	MAX VALUE	264.43	1.22	0.18	1.60

Triangulated dual graph

Density: 46.96%
Triangles: 201,413

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

Clustering coefficient 0.68 1.00 0.83 0.82 150.29 0.00 -33.44 0.09 0.10 4.68

Degree 7 137 84.07 103.00 15,132 MAX VALUE 761.75 40.77 0.48 4.08

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	0.68	1.00	0.83	0.82	150.29	0.00	-33.44	0.09	0.10	4.68
Degree	7	137	84.07	103.00	15,132	MAX VALUE	761.75	40.77	0.48	4.08
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.28%

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

Clustering coefficient 0.48 1.00 0.79 0.75 142.40 0.00 -45.84 0.16 0.20 3.32

Degree 2 64 20.20 7.00 3,636 MAX VALUE 419.93 21.95 1.09 3.14

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	0.79	0.75	142.40	0.00	-45.84	0.16	0.20	3.32
Degree	2	64	20.20	7.00	3,636	MAX VALUE	419.93	21.95	1.09	3.14
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-2-40-25-180-500-30-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-30-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 17 3.27 2.00 720 MAX VALUE 210.14 2.97 0.91 0.87

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.43 6.00 906 MAX VALUE 261.27 0.82 0.13 0.52

XCSP 2.1 Benchmarks