XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-90-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:31
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 12.44 12.00 111,932 MAX VALUE 22,496.40 2.48 0.20 2.33

Relational linkage 0.16 0.64 0.36 0.36 356.48 0.00 -1,047.69 0.06 0.17 1.84

Tightness 0.44 0.55 0.50 0.50 90.45 0.00 -124.00 0.02 0.04 3.76

Tuples 283 350 310.92 311.00 55,966 MAX VALUE 1,032.97 12.45 0.04 3.76

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

Value table constraints 3 14 9.00 9.00 360 2.52e+37 86.12 2.47 0.27 2.23

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	12.44	12.00	111,932	MAX VALUE	22,496.40	2.48	0.20	2.33
Relational linkage	0.16	0.64	0.36	0.36	356.48	0.00	-1,047.69	0.06	0.17	1.84
Tightness	0.44	0.55	0.50	0.50	90.45	0.00	-124.00	0.02	0.04	3.76
Tuples	283	350	310.92	311.00	55,966	MAX VALUE	1,032.97	12.45	0.04	3.76
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	3	14	9.00	9.00	360	2.52e+37	86.12	2.47	0.27	2.23
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: 8
Tree depth: 5
CIR: 0.18
Independent Cluster Pairs: 30
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/Tree1.json

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

Cluster constraints 4 60 24.25 15.50 485 2.49e+25 58.48 17.05 0.70 2.86

Variables per cluster 4 21 11.80 9.50 236 3.18e+20 47.21 5.31 0.45 2.53

Separator constraints 0 48 15.25 7.00 305 0 None 15.19 1.00 2.65

Separator variables 0 19 9.80 8.00 196 0 None 5.36 0.55 2.53

Clusters per var 1 12 5.90 6.50 236 2.63e+25 58.53 3.71 0.63 2.30

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	60	24.25	15.50	485	2.49e+25	58.48	17.05	0.70	2.86
Variables per cluster	4	21	11.80	9.50	236	3.18e+20	47.21	5.31	0.45	2.53
Separator constraints	0	48	15.25	7.00	305	0	None	15.19	1.00	2.65
Separator variables	0	19	9.80	8.00	196	0	None	5.36	0.55	2.53
Clusters per var	1	12	5.90	6.50	236	2.63e+25	58.53	3.71	0.63	2.30

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 6
CIR: 0.25
Independent Cluster Pairs: 165
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/DualTree1.json

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

Cluster constraints 25 396 123.95 98.00 4,710 MAX VALUE 174.52 85.22 0.69 3.38

Variables per cluster 9 82 28.79 21.50 1,094 MAX VALUE 121.20 18.48 0.64 3.19

Separator constraints 0 219 82.84 69.50 3,148 0 None 51.84 0.63 3.35

Separator variables 0 62 24.05 19.00 914 0 None 14.05 0.58 3.16

Clusters per variable 1 10 6.08 7.00 1,094 MAX VALUE 296.03 2.64 0.43 2.18

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	396	123.95	98.00	4,710	MAX VALUE	174.52	85.22	0.69	3.38
Variables per cluster	9	82	28.79	21.50	1,094	MAX VALUE	121.20	18.48	0.64	3.19
Separator constraints	0	219	82.84	69.50	3,148	0	None	51.84	0.63	3.35
Separator variables	0	62	24.05	19.00	914	0	None	14.05	0.58	3.16
Clusters per variable	1	10	6.08	7.00	1,094	MAX VALUE	296.03	2.64	0.43	2.18

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 157
Triangles: 123
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/Primal1.json

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

Clustering coefficient 0.14 0.40 0.24 0.22 9.43 0.00 -59.30 0.07 0.28 3.26

Degree 3 14 9.00 9.00 360 2.52e+37 86.12 2.47 0.27 2.23

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.32 3.00 522 MAX VALUE 187.15 0.47 0.14 0.63

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.14	0.40	0.24	0.22	9.43	0.00	-59.30	0.07	0.28	3.26
Degree	3	14	9.00	9.00	360	2.52e+37	86.12	2.47	0.27	2.23
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.32	3.00	522	MAX VALUE	187.15	0.47	0.14	0.63

Triangulated primal graph

Density: 52.05%
MCB compute time (ms): 8
MCB cycles: 426
Triangles: 2,480

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

Clustering coefficient 0.69 1.00 0.84 0.81 33.46 0.00 -7.43 0.10 0.12 3.24

Degree 3 31 20.30 25.00 812 MAX VALUE 113.62 9.38 0.46 2.87

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,278 MAX VALUE 468.01 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.69	1.00	0.84	0.81	33.46	0.00	-7.43	0.10	0.12	3.24
Degree	3	31	20.30	25.00	812	MAX VALUE	113.62	9.38	0.46	2.87
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,278	MAX VALUE	468.01	0.00	0.00	0.00

Dual graph

Density: 9.70%
MCB compute time (ms): 358
MCB cycles: 1,571
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/Dual1.json

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

Clustering coefficient 0.45 0.71 0.50 0.49 90.66 0.00 -123.81 0.03 0.07 4.19

Degree 8 26 17.36 17.00 3,124 MAX VALUE 510.05 3.37 0.19 2.58

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.14 3.00 4,940 MAX VALUE 1,790.77 0.36 0.12 0.42

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.71	0.50	0.49	90.66	0.00	-123.81	0.03	0.07	4.19
Degree	8	26	17.36	17.00	3,124	MAX VALUE	510.05	3.37	0.19	2.58
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.14	3.00	4,940	MAX VALUE	1,790.77	0.36	0.12	0.42

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 0.33 0.01 0.00 0.97 0.00 None 0.03 6.07 0.18

Degree 2 5 3.56 3.00 640 MAX VALUE 224.52 0.73 0.21 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 3 10 6.71 7.00 946 MAX VALUE 265.62 1.26 0.19 1.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	0.97	0.00	None	0.03	6.07	0.18
Degree	2	5	3.56	3.00	640	MAX VALUE	224.52	0.73	0.21	1.08
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	10	6.71	7.00	946	MAX VALUE	265.62	1.26	0.19	1.58

Triangulated dual graph

Density: 45.92%
Triangles: 192,449

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

Clustering coefficient 0.68 1.00 0.83 0.82 149.66 0.00 -34.21 0.09 0.11 4.55

Degree 8 134 82.20 101.00 14,796 MAX VALUE 757.82 40.27 0.49 3.96

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	149.66	0.00	-34.21	0.09	0.11	4.55
Degree	8	134	82.20	101.00	14,796	MAX VALUE	757.82	40.27	0.49	3.96
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.30%

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

Clustering coefficient 0.42 1.00 0.79 0.72 141.62 0.00 -46.75 0.16 0.20 3.34

Degree 2 63 20.22 7.00 3,640 MAX VALUE 420.16 22.05 1.09 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	0.42	1.00	0.79	0.72	141.62	0.00	-46.75	0.16	0.20	3.34
Degree	2	63	20.22	7.00	3,640	MAX VALUE	420.16	22.05	1.09	3.13
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 41
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-90-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 210.89 2.90 0.89 0.88

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