XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-87-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 12.47 12.00 112,222 MAX VALUE 22,515.00 2.50 0.20 2.34

Relational linkage 0.12 0.56 0.36 0.36 355.36 0.00 -1,052.26 0.06 0.18 1.88

Tightness 0.45 0.55 0.50 0.50 90.22 0.00 -124.47 0.02 0.04 3.77

Tuples 281 346 311.73 313.00 56,111 MAX VALUE 1,033.44 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 4 15 9.00 9.50 360 1.36e+37 85.50 2.94 0.33 2.31

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	12.47	12.00	112,222	MAX VALUE	22,515.00	2.50	0.20	2.34
Relational linkage	0.12	0.56	0.36	0.36	355.36	0.00	-1,052.26	0.06	0.18	1.88
Tightness	0.45	0.55	0.50	0.50	90.22	0.00	-124.47	0.02	0.04	3.77
Tuples	281	346	311.73	313.00	56,111	MAX VALUE	1,033.44	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	4	15	9.00	9.50	360	1.36e+37	85.50	2.94	0.33	2.31
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: 4
CIR: 0.13
Independent Cluster Pairs: 23
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/Tree1.json

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

Cluster constraints 5 67 22.15 13.50 443 1.46e+24 55.64 17.86 0.81 2.58

Variables per cluster 5 21 10.60 9.00 212 3.99e+19 45.13 4.94 0.47 2.36

Separator constraints 0 50 13.15 6.00 263 0 None 14.31 1.09 2.69

Separator variables 0 19 8.60 7.50 172 0 None 4.76 0.55 2.36

Clusters per var 1 12 5.30 6.00 212 1.53e+23 53.38 3.52 0.66 2.19

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	5	67	22.15	13.50	443	1.46e+24	55.64	17.86	0.81	2.58
Variables per cluster	5	21	10.60	9.00	212	3.99e+19	45.13	4.94	0.47	2.36
Separator constraints	0	50	13.15	6.00	263	0	None	14.31	1.09	2.69
Separator variables	0	19	8.60	7.50	172	0	None	4.76	0.55	2.36
Clusters per var	1	12	5.30	6.00	212	1.53e+23	53.38	3.52	0.66	2.19

Dual tree decomposition

Number of clusters: 38
Number of leaves: 15
Tree depth: 5
CIR: 0.22
Independent Cluster Pairs: 144
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/DualTree1.json

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

Cluster constraints 21 438 129.47 109.00 4,920 MAX VALUE 173.59 100.12 0.77 3.60

Variables per cluster 9 92 29.05 22.00 1,104 MAX VALUE 120.72 19.83 0.68 3.19

Separator constraints 0 247 87.03 82.00 3,307 0 None 61.60 0.71 3.44

Separator variables 0 67 24.32 20.50 924 0 None 15.21 0.63 3.25

Clusters per variable 1 11 6.13 7.00 1,104 MAX VALUE 298.02 2.64 0.43 2.14

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	21	438	129.47	109.00	4,920	MAX VALUE	173.59	100.12	0.77	3.60
Variables per cluster	9	92	29.05	22.00	1,104	MAX VALUE	120.72	19.83	0.68	3.19
Separator constraints	0	247	87.03	82.00	3,307	0	None	61.60	0.71	3.44
Separator variables	0	67	24.32	20.50	924	0	None	15.21	0.63	3.25
Clusters per variable	1	11	6.13	7.00	1,104	MAX VALUE	298.02	2.64	0.43	2.14

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 150
Triangles: 132
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/Primal1.json

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

Clustering coefficient 0.00 0.50 0.24 0.24 9.63 0.00 None 0.10 0.42 3.27

Degree 4 15 9.00 9.50 360 1.36e+37 85.50 2.94 0.33 2.31

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.26 3.00 489 MAX VALUE 176.01 0.44 0.13 0.57

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.50	0.24	0.24	9.63	0.00	None	0.10	0.42	3.27
Degree	4	15	9.00	9.50	360	1.36e+37	85.50	2.94	0.33	2.31
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.26	3.00	489	MAX VALUE	176.01	0.44	0.13	0.57

Triangulated primal graph

Density: 48.97%
MCB compute time (ms): 6
MCB cycles: 419
Triangles: 2,210

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

Clustering coefficient 0.64 1.00 0.84 0.81 33.49 0.00 -7.48 0.11 0.14 3.08

Degree 4 31 19.10 25.00 764 MAX VALUE 110.32 9.57 0.50 2.73

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,257 MAX VALUE 460.32 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.64	1.00	0.84	0.81	33.49	0.00	-7.48	0.11	0.14	3.08
Degree	4	31	19.10	25.00	764	MAX VALUE	110.32	9.57	0.50	2.73
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,257	MAX VALUE	460.32	0.00	0.00	0.00

Dual graph

Density: 10.01%
MCB compute time (ms): 354
MCB cycles: 1,586
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/Dual1.json

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

Clustering coefficient 0.44 0.68 0.51 0.50 92.38 0.00 -120.57 0.04 0.08 4.35

Degree 8 27 17.92 18.00 3,226 MAX VALUE 514.63 3.95 0.22 2.75

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.09 3.00 4,900 MAX VALUE 1,782.99 0.29 0.10 0.31

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.68	0.51	0.50	92.38	0.00	-120.57	0.04	0.08	4.35
Degree	8	27	17.92	18.00	3,226	MAX VALUE	514.63	3.95	0.22	2.75
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.09	3.00	4,900	MAX VALUE	1,782.99	0.29	0.10	0.31

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 73
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 223.87 0.79 0.22 1.16

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.82 7.00 962 MAX VALUE 268.59 1.12 0.16 1.44

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	223.87	0.79	0.22	1.16
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.82	7.00	962	MAX VALUE	268.59	1.12	0.16	1.44

Triangulated dual graph

Density: 48.36%
Triangles: 217,785

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

Clustering coefficient 0.73 1.00 0.84 0.81 151.44 0.00 -31.85 0.08 0.09 4.64

Degree 8 130 86.57 113.50 15,582 MAX VALUE 765.65 42.10 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	0.73	1.00	0.84	0.81	151.44	0.00	-31.85	0.08	0.09	4.64
Degree	8	130	86.57	113.50	15,582	MAX VALUE	765.65	42.10	0.49	3.79
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.71%

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

Clustering coefficient 0.54 1.00 0.80 0.76 144.23 0.00 -43.06 0.15 0.19 3.24

Degree 2 68 20.97 7.00 3,774 MAX VALUE 419.12 23.29 1.11 3.00

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	0.54	1.00	0.80	0.76	144.23	0.00	-43.06	0.15	0.19	3.24
Degree	2	68	20.97	7.00	3,774	MAX VALUE	419.12	23.29	1.11	3.00
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-2-40-25-180-500-87-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-87-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 210.27 2.98 0.91 0.89

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