XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-8-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 3 21 12.50 12.00 112,542 MAX VALUE 22,542.30 2.51 0.20 2.34

Relational linkage 0.12 0.52 0.36 0.36 356.48 0.00 -1,047.22 0.06 0.17 1.82

Tightness 0.45 0.54 0.50 0.50 89.97 0.00 -124.96 0.02 0.04 3.68

Tuples 289 345 312.62 312.00 56,271 MAX VALUE 1,033.97 11.71 0.04 3.68

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 8.50 360 2.70e+37 86.19 2.65 0.29 2.13

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	21	12.50	12.00	112,542	MAX VALUE	22,542.30	2.51	0.20	2.34
Relational linkage	0.12	0.52	0.36	0.36	356.48	0.00	-1,047.22	0.06	0.17	1.82
Tightness	0.45	0.54	0.50	0.50	89.97	0.00	-124.96	0.02	0.04	3.68
Tuples	289	345	312.62	312.00	56,271	MAX VALUE	1,033.97	11.71	0.04	3.68
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	8.50	360	2.70e+37	86.19	2.65	0.29	2.13
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: 21
Number of leaves: 10
Tree depth: 5
CIR: 0.06
Independent Cluster Pairs: 11
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/Tree1.json

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

Cluster constraints 6 50 22.38 18.00 470 4.07e+26 61.27 13.40 0.60 2.78

Variables per cluster 6 20 12.00 12.00 252 8.76e+21 50.52 4.63 0.39 2.40

Separator constraints 0 39 13.81 9.00 290 0 None 12.21 0.88 2.69

Separator variables 0 19 10.10 10.00 212 0 None 4.83 0.48 2.47

Clusters per var 1 14 6.30 5.50 252 1.52e+25 57.99 4.63 0.74 2.30

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	50	22.38	18.00	470	4.07e+26	61.27	13.40	0.60	2.78
Variables per cluster	6	20	12.00	12.00	252	8.76e+21	50.52	4.63	0.39	2.40
Separator constraints	0	39	13.81	9.00	290	0	None	12.21	0.88	2.69
Separator variables	0	19	10.10	10.00	212	0	None	4.83	0.48	2.47
Clusters per var	1	14	6.30	5.50	252	1.52e+25	57.99	4.63	0.74	2.30

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.22
Independent Cluster Pairs: 146
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/DualTree1.json

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

Cluster constraints 25 369 122.32 97.00 4,648 MAX VALUE 173.41 87.02 0.71 3.53

Variables per cluster 10 84 28.55 23.00 1,085 MAX VALUE 120.94 18.26 0.64 3.17

Separator constraints 0 212 80.74 69.00 3,068 0 None 53.41 0.66 3.42

Separator variables 0 59 23.82 20.00 905 0 None 13.90 0.58 3.14

Clusters per variable 1 11 6.03 7.00 1,085 MAX VALUE 293.07 2.72 0.45 2.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	369	122.32	97.00	4,648	MAX VALUE	173.41	87.02	0.71	3.53
Variables per cluster	10	84	28.55	23.00	1,085	MAX VALUE	120.94	18.26	0.64	3.17
Separator constraints	0	212	80.74	69.00	3,068	0	None	53.41	0.66	3.42
Separator variables	0	59	23.82	20.00	905	0	None	13.90	0.58	3.14
Clusters per variable	1	11	6.03	7.00	1,085	MAX VALUE	293.07	2.72	0.45	2.24

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 144
Triangles: 113
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/Primal1.json

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

Clustering coefficient 0.07 0.40 0.22 0.21 8.65 0.00 -63.87 0.07 0.35 3.18

Degree 5 15 9.00 8.50 360 2.70e+37 86.19 2.65 0.29 2.13

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.28 3.00 472 MAX VALUE 169.71 0.45 0.14 0.59

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.07	0.40	0.22	0.21	8.65	0.00	-63.87	0.07	0.35	3.18
Degree	5	15	9.00	8.50	360	2.70e+37	86.19	2.65	0.29	2.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.28	3.00	472	MAX VALUE	169.71	0.45	0.14	0.59

Triangulated primal graph

Density: 51.54%
MCB compute time (ms): 8
MCB cycles: 382
Triangles: 2,349

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

Clustering coefficient 0.62 1.00 0.83 0.83 33.37 0.00 -7.72 0.13 0.15 3.01

Degree 5 32 20.10 22.50 804 MAX VALUE 113.75 9.39 0.47 2.91

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,146 MAX VALUE 419.67 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.62	1.00	0.83	0.83	33.37	0.00	-7.72	0.13	0.15	3.01
Degree	5	32	20.10	22.50	804	MAX VALUE	113.75	9.39	0.47	2.91
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,146	MAX VALUE	419.67	0.00	0.00	0.00

Dual graph

Density: 9.81%
MCB compute time (ms): 265
MCB cycles: 1,658
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/Dual1.json

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

Clustering coefficient 0.44 0.65 0.51 0.50 90.98 0.00 -123.23 0.04 0.07 4.33

Degree 9 28 17.56 18.00 3,160 MAX VALUE 511.11 3.88 0.22 2.71

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.17 3.00 5,258 MAX VALUE 1,902.23 0.40 0.13 0.48

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.65	0.51	0.50	90.98	0.00	-123.23	0.04	0.07	4.33
Degree	9	28	17.56	18.00	3,160	MAX VALUE	511.11	3.88	0.22	2.71
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.17	3.00	5,258	MAX VALUE	1,902.23	0.40	0.13	0.48

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 82
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 6 3.56 3.00 640 MAX VALUE 224.61 0.72 0.20 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 3 8 6.72 7.00 947 MAX VALUE 266.68 1.03 0.15 1.38

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	6	3.56	3.00	640	MAX VALUE	224.61	0.72	0.20	1.08
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	8	6.72	7.00	947	MAX VALUE	266.68	1.03	0.15	1.38

Triangulated dual graph

Density: 45.24%
Triangles: 185,783

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

Clustering coefficient 0.70 1.00 0.83 0.81 149.32 0.00 -34.71 0.09 0.11 4.65

Degree 9 126 80.98 86.00 14,576 MAX VALUE 754.59 40.05 0.49 3.82

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	0.83	0.81	149.32	0.00	-34.71	0.09	0.11	4.65
Degree	9	126	80.98	86.00	14,576	MAX VALUE	754.59	40.05	0.49	3.82
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.57%

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

Clustering coefficient 0.51 1.00 0.79 0.75 142.45 0.00 -45.57 0.16 0.20 3.34

Degree 2 65 20.71 7.00 3,728 MAX VALUE 423.92 22.39 1.08 3.18

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	0.51	1.00	0.79	0.75	142.45	0.00	-45.57	0.16	0.20	3.34
Degree	2	65	20.71	7.00	3,728	MAX VALUE	423.92	22.39	1.08	3.18
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 39
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-8-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 210.95 2.93 0.89 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.52 6.00 920 MAX VALUE 263.28 0.88 0.13 0.58

XCSP 2.1 Benchmarks