XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-41-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 12.51 13.00 112,552 MAX VALUE 22,537.30 2.53 0.20 2.35

Relational linkage 0.16 0.60 0.35 0.36 354.96 0.00 -1,054.82 0.07 0.19 1.92

Tightness 0.45 0.54 0.50 0.50 89.96 0.00 -124.98 0.02 0.04 3.66

Tuples 286 343 312.64 313.00 56,276 MAX VALUE 1,033.99 11.66 0.04 3.66

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 1.43e+37 85.55 2.86 0.32 2.35

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	12.51	13.00	112,552	MAX VALUE	22,537.30	2.53	0.20	2.35
Relational linkage	0.16	0.60	0.35	0.36	354.96	0.00	-1,054.82	0.07	0.19	1.92
Tightness	0.45	0.54	0.50	0.50	89.96	0.00	-124.98	0.02	0.04	3.66
Tuples	286	343	312.64	313.00	56,276	MAX VALUE	1,033.99	11.66	0.04	3.66
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	1.43e+37	85.55	2.86	0.32	2.35
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: 12
Tree depth: 3
CIR: 0.11
Independent Cluster Pairs: 21
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/Tree1.json

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

Cluster constraints 3 51 19.43 15.00 408 5.14e+24 56.90 14.05 0.72 2.71

Variables per cluster 4 20 10.24 9.00 215 2.01e+20 46.75 4.69 0.46 2.40

Separator constraints 0 43 10.86 7.00 228 0 None 11.84 1.09 2.56

Separator variables 0 18 8.33 7.00 175 0 None 4.55 0.55 2.40

Clusters per var 1 12 5.38 6.00 215 1.99e+22 51.35 3.90 0.73 2.07

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	51	19.43	15.00	408	5.14e+24	56.90	14.05	0.72	2.71
Variables per cluster	4	20	10.24	9.00	215	2.01e+20	46.75	4.69	0.46	2.40
Separator constraints	0	43	10.86	7.00	228	0	None	11.84	1.09	2.56
Separator variables	0	18	8.33	7.00	175	0	None	4.55	0.55	2.40
Clusters per var	1	12	5.38	6.00	215	1.99e+22	51.35	3.90	0.73	2.07

Dual tree decomposition

Number of clusters: 38
Number of leaves: 17
Tree depth: 5
CIR: 0.21
Independent Cluster Pairs: 138
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/DualTree1.json

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

Cluster constraints 28 406 127.50 107.00 4,845 MAX VALUE 175.60 87.60 0.69 3.56

Variables per cluster 10 87 28.74 21.50 1,092 MAX VALUE 121.17 18.49 0.64 3.27

Separator constraints 0 214 85.29 79.50 3,241 0 None 53.08 0.62 3.56

Separator variables 0 63 24.00 19.50 912 0 None 14.06 0.59 3.25

Clusters per variable 1 10 6.07 7.00 1,092 MAX VALUE 294.64 2.68 0.44 2.15

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	28	406	127.50	107.00	4,845	MAX VALUE	175.60	87.60	0.69	3.56
Variables per cluster	10	87	28.74	21.50	1,092	MAX VALUE	121.17	18.49	0.64	3.27
Separator constraints	0	214	85.29	79.50	3,241	0	None	53.08	0.62	3.56
Separator variables	0	63	24.00	19.50	912	0	None	14.06	0.59	3.25
Clusters per variable	1	10	6.07	7.00	1,092	MAX VALUE	294.64	2.68	0.44	2.15

Primal graph

Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 142
Triangles: 129
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/Primal1.json

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

Clustering coefficient 0.00 0.50 0.25 0.25 9.83 0.00 None 0.10 0.39 3.29

Degree 3 14 9.00 9.00 360 1.43e+37 85.55 2.86 0.32 2.35

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.18 3.00 452 MAX VALUE 163.48 0.39 0.12 0.48

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.50	0.25	0.25	9.83	0.00	None	0.10	0.39	3.29
Degree	3	14	9.00	9.00	360	1.43e+37	85.55	2.86	0.32	2.35
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.18	3.00	452	MAX VALUE	163.48	0.39	0.12	0.48

Triangulated primal graph

Density: 46.79%
MCB compute time (ms): 6
MCB cycles: 373
Triangles: 1,999

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

Clustering coefficient 0.63 1.00 0.84 0.81 33.41 0.00 -7.70 0.13 0.16 2.94

Degree 3 30 18.25 23.50 730 MAX VALUE 108.00 9.61 0.53 2.75

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,119 MAX VALUE 409.78 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	0.84	0.81	33.41	0.00	-7.70	0.13	0.16	2.94
Degree	3	30	18.25	23.50	730	MAX VALUE	108.00	9.61	0.53	2.75
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,119	MAX VALUE	409.78	0.00	0.00	0.00

Dual graph

Density: 9.96%
MCB compute time (ms): 479
MCB cycles: 1,646
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/Dual1.json

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

Clustering coefficient 0.45 0.74 0.51 0.50 92.67 0.00 -120.12 0.05 0.09 4.33

Degree 9 25 17.82 18.00 3,208 MAX VALUE 514.52 3.56 0.20 2.63

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.15 3.00 5,180 MAX VALUE 1,877.68 0.36 0.11 0.43

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.74	0.51	0.50	92.67	0.00	-120.12	0.05	0.09	4.33
Degree	9	25	17.82	18.00	3,208	MAX VALUE	514.52	3.56	0.20	2.63
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.15	3.00	5,180	MAX VALUE	1,877.68	0.36	0.11	0.43

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 6 3.56 4.00 640 MAX VALUE 224.44 0.73 0.21 1.10

Eccentricity None None None None None None None None None None

MCB cycle size 4 8 6.75 7.00 952 MAX VALUE 267.49 1.03 0.15 1.38

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	4.00	640	MAX VALUE	224.44	0.73	0.21	1.10
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	8	6.75	7.00	952	MAX VALUE	267.49	1.03	0.15	1.38

Triangulated dual graph

Density: 45.91%
Triangles: 192,962

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

Clustering coefficient 0.71 1.00 0.83 0.80 149.75 0.00 -34.08 0.09 0.11 4.58

Degree 9 127 82.18 94.50 14,792 MAX VALUE 757.31 40.62 0.49 3.89

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	0.71	1.00	0.83	0.80	149.75	0.00	-34.08	0.09	0.11	4.58
Degree	9	127	82.18	94.50	14,792	MAX VALUE	757.31	40.62	0.49	3.89
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 0.47 1.00 0.79 0.73 142.71 0.00 -45.43 0.16 0.20 3.35

Degree 2 63 20.44 7.00 3,680 MAX VALUE 420.98 22.27 1.09 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	0.47	1.00	0.79	0.73	142.71	0.00	-45.43	0.16	0.20	3.35
Degree	2	63	20.44	7.00	3,680	MAX VALUE	420.98	22.27	1.09	3.04
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-2-40-25-180-500-41-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-41-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 210.32 2.96 0.91 0.90

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.35 6.00 896 MAX VALUE 259.83 0.76 0.12 0.47

XCSP 2.1 Benchmarks