XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-46-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 4 21 12.44 12.00 111,978 MAX VALUE 22,498.60 2.48 0.20 2.33

Relational linkage 0.16 0.52 0.35 0.36 351.80 0.00 -1,060.51 0.06 0.17 1.82

Tightness 0.46 0.56 0.50 0.50 90.42 0.00 -124.05 0.02 0.04 3.65

Tuples 273 339 311.05 311.50 55,989 MAX VALUE 1,033.07 11.41 0.04 3.65

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

Value table constraints 5 14 9.00 8.00 360 3.43e+37 86.43 2.45 0.27 2.14

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	21	12.44	12.00	111,978	MAX VALUE	22,498.60	2.48	0.20	2.33
Relational linkage	0.16	0.52	0.35	0.36	351.80	0.00	-1,060.51	0.06	0.17	1.82
Tightness	0.46	0.56	0.50	0.50	90.42	0.00	-124.05	0.02	0.04	3.65
Tuples	273	339	311.05	311.50	55,989	MAX VALUE	1,033.07	11.41	0.04	3.65
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	5	14	9.00	8.00	360	3.43e+37	86.43	2.45	0.27	2.14
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: 10
Tree depth: 3
CIR: 0.09
Independent Cluster Pairs: 15
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/Tree1.json

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

Cluster constraints 6 53 21.80 15.00 436 9.94e+24 57.56 13.91 0.64 2.62

Variables per cluster 6 21 11.40 10.00 228 2.81e+20 47.09 4.63 0.41 2.22

Separator constraints 0 39 12.80 6.50 256 0 None 12.06 0.94 2.60

Separator variables 0 18 9.40 7.50 188 0 None 4.61 0.49 2.22

Clusters per var 1 13 5.70 7.00 228 7.00e+23 54.91 3.94 0.69 2.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	6	53	21.80	15.00	436	9.94e+24	57.56	13.91	0.64	2.62
Variables per cluster	6	21	11.40	10.00	228	2.81e+20	47.09	4.63	0.41	2.22
Separator constraints	0	39	12.80	6.50	256	0	None	12.06	0.94	2.60
Separator variables	0	18	9.40	7.50	188	0	None	4.61	0.49	2.22
Clusters per var	1	13	5.70	7.00	228	7.00e+23	54.91	3.94	0.69	2.16

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.19
Independent Cluster Pairs: 124
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/DualTree1.json

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

Cluster constraints 30 340 121.18 95.00 4,605 MAX VALUE 174.86 78.57 0.65 3.37

Variables per cluster 11 81 28.76 23.00 1,093 MAX VALUE 121.51 18.10 0.63 3.07

Separator constraints 0 191 80.13 69.00 3,045 0 None 45.96 0.57 3.40

Separator variables 0 63 24.03 20.50 913 0 None 13.70 0.57 2.96

Clusters per variable 1 10 6.07 7.00 1,093 MAX VALUE 295.11 2.70 0.44 2.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	30	340	121.18	95.00	4,605	MAX VALUE	174.86	78.57	0.65	3.37
Variables per cluster	11	81	28.76	23.00	1,093	MAX VALUE	121.51	18.10	0.63	3.07
Separator constraints	0	191	80.13	69.00	3,045	0	None	45.96	0.57	3.40
Separator variables	0	63	24.03	20.50	913	0	None	13.70	0.57	2.96
Clusters per variable	1	10	6.07	7.00	1,093	MAX VALUE	295.11	2.70	0.44	2.21

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 144
Triangles: 115
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-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 8.68 0.00 -63.88 0.08 0.35 3.35

Degree 5 14 9.00 8.00 360 3.43e+37 86.43 2.45 0.27 2.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.32 3.00 478 MAX VALUE 171.43 0.47 0.14 0.63

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.07	0.40	0.22	0.21	8.68	0.00	-63.88	0.08	0.35	3.35
Degree	5	14	9.00	8.00	360	3.43e+37	86.43	2.45	0.27	2.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.32	3.00	478	MAX VALUE	171.43	0.47	0.14	0.63

Triangulated primal graph

Density: 51.03%
MCB compute time (ms): 11
MCB cycles: 359
Triangles: 2,332

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

Clustering coefficient 0.63 1.00 0.83 0.80 33.36 0.00 -7.66 0.12 0.14 3.04

Degree 5 32 19.90 26.00 796 MAX VALUE 113.03 9.51 0.48 2.57

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,077 MAX VALUE 394.40 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.63	1.00	0.83	0.80	33.36	0.00	-7.66	0.12	0.14	3.04
Degree	5	32	19.90	26.00	796	MAX VALUE	113.03	9.51	0.48	2.57
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,077	MAX VALUE	394.40	0.00	0.00	0.00

Dual graph

Density: 9.68%
MCB compute time (ms): 394
MCB cycles: 1,660
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/Dual1.json

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

Clustering coefficient 0.44 0.61 0.50 0.50 90.81 0.00 -123.44 0.03 0.06 4.14

Degree 10 26 17.33 17.00 3,120 MAX VALUE 509.80 3.47 0.20 2.59

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.20 3.00 5,315 MAX VALUE 1,918.78 0.43 0.13 0.53

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.61	0.50	0.50	90.81	0.00	-123.44	0.03	0.06	4.14
Degree	10	26	17.33	17.00	3,120	MAX VALUE	509.80	3.47	0.20	2.59
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.20	3.00	5,315	MAX VALUE	1,918.78	0.43	0.13	0.53

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 0.33 0.00 0.00 0.83 0.00 None 0.04 7.99 0.10

Degree 2 5 3.56 3.00 640 MAX VALUE 224.39 0.75 0.21 1.08

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.63 7.00 935 MAX VALUE 264.08 1.21 0.18 1.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.04	7.99	0.10
Degree	2	5	3.56	3.00	640	MAX VALUE	224.39	0.75	0.21	1.08
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.63	7.00	935	MAX VALUE	264.08	1.21	0.18	1.54

Triangulated dual graph

Density: 45.43%
Triangles: 186,922

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

Clustering coefficient 0.69 1.00 0.83 0.80 149.30 0.00 -34.74 0.09 0.11 4.62

Degree 10 130 81.32 101.50 14,638 MAX VALUE 756.40 40.01 0.49 3.79

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	0.69	1.00	0.83	0.80	149.30	0.00	-34.74	0.09	0.11	4.62
Degree	10	130	81.32	101.50	14,638	MAX VALUE	756.40	40.01	0.49	3.79
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.42%

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

Clustering coefficient 0.51 1.00 0.79 0.74 143.03 0.00 -44.99 0.16 0.20 3.27

Degree 2 65 20.43 7.00 3,678 MAX VALUE 419.24 22.39 1.10 3.04

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	0.74	143.03	0.00	-44.99	0.16	0.20	3.27
Degree	2	65	20.43	7.00	3,678	MAX VALUE	419.24	22.39	1.10	3.04
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 42
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-46-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 211.19 2.89 0.88 0.86

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.61 6.00 932 MAX VALUE 265.01 0.92 0.14 0.62

XCSP 2.1 Benchmarks