XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-89-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: 8,975
Value tables: 39

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 12.52 13.00 112,390 MAX VALUE 22,493.90 2.50 0.20 2.33

Relational linkage 0.16 0.52 0.35 0.36 344.92 0.00 -1,029.15 0.06 0.17 1.84

Tightness 0.43 0.56 0.50 0.50 89.84 0.00 -125.23 0.02 0.04 3.74

Tuples 273 358 313.04 314.00 56,347 MAX VALUE 1,034.19 12.63 0.04 3.74

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

Value table constraints 4 15 9.21 9.00 359 5.47e+36 84.59 2.78 0.30 2.23

Value table partitions 25 25 25.00 25.00 975 MAX VALUE 125.54 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	12.52	13.00	112,390	MAX VALUE	22,493.90	2.50	0.20	2.33
Relational linkage	0.16	0.52	0.35	0.36	344.92	0.00	-1,029.15	0.06	0.17	1.84
Tightness	0.43	0.56	0.50	0.50	89.84	0.00	-125.23	0.02	0.04	3.74
Tuples	273	358	313.04	314.00	56,347	MAX VALUE	1,034.19	12.63	0.04	3.74
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	15	9.21	9.00	359	5.47e+36	84.59	2.78	0.30	2.23
Value table partitions	25	25	25.00	25.00	975	MAX VALUE	125.54	0.00	0.00	0.00

Tree decomposition

Number of clusters: 22
Number of leaves: 10
Tree depth: 5
CIR: 0.16
Independent Cluster Pairs: 33
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Tree1.json

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

Cluster constraints 1 53 23.55 19.00 518 5.54e+26 61.58 17.23 0.73 2.75

Variables per cluster 2 19 11.23 10.00 247 6.38e+21 50.21 5.37 0.48 2.22

Separator constraints 0 44 15.36 9.00 338 0 None 15.58 1.01 2.71

Separator variables 0 18 9.41 8.00 207 0 None 5.49 0.58 2.33

Clusters per var 1 14 6.17 5.00 247 5.35e+24 56.94 4.54 0.74 2.31

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	1	53	23.55	19.00	518	5.54e+26	61.58	17.23	0.73	2.75
Variables per cluster	2	19	11.23	10.00	247	6.38e+21	50.21	5.37	0.48	2.22
Separator constraints	0	44	15.36	9.00	338	0	None	15.58	1.01	2.71
Separator variables	0	18	9.41	8.00	207	0	None	5.49	0.58	2.33
Clusters per var	1	14	6.17	5.00	247	5.35e+24	56.94	4.54	0.74	2.31

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-2-40-25-180-500-89-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/DualTree1.json

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

Cluster constraints 16 349 128.18 106.00 4,871 MAX VALUE 175.10 87.94 0.69 3.56

Variables per cluster 8 83 28.82 23.00 1,095 MAX VALUE 120.73 18.96 0.66 3.22

Separator constraints 0 214 85.47 75.00 3,248 0 None 54.33 0.64 3.53

Separator variables 0 63 24.08 20.00 915 0 None 14.57 0.61 3.26

Clusters per variable 1 11 6.08 7.00 1,095 MAX VALUE 295.39 2.70 0.44 2.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	349	128.18	106.00	4,871	MAX VALUE	175.10	87.94	0.69	3.56
Variables per cluster	8	83	28.82	23.00	1,095	MAX VALUE	120.73	18.96	0.66	3.22
Separator constraints	0	214	85.47	75.00	3,248	0	None	54.33	0.64	3.53
Separator variables	0	63	24.08	20.00	915	0	None	14.57	0.61	3.26
Clusters per variable	1	11	6.08	7.00	1,095	MAX VALUE	295.39	2.70	0.44	2.23

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 146
Triangles: 138
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Primal1.json

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

Clustering coefficient 0.00 0.42 None 0.25 None None None None None 3.40

Degree 1 15 9.00 9.00 360 5.47e+36 84.59 3.02 0.34 2.29

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.23 3.00 471 MAX VALUE 169.89 0.42 0.13 0.53

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.42	None	0.25	None	None	None	None	None	3.40
Degree	1	15	9.00	9.00	360	5.47e+36	84.59	3.02	0.34	2.29
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.23	3.00	471	MAX VALUE	169.89	0.42	0.13	0.53

Triangulated primal graph

Density: 48.46%
MCB compute time (ms): 15
MCB cycles: 339
Triangles: 2,171

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

Clustering coefficient 0.64 1.00 None 0.85 None None None None None 3.31

Degree 1 31 18.90 22.00 756 MAX VALUE 108.86 9.61 0.51 2.85

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,017 MAX VALUE 372.43 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	None	0.85	None	None	None	None	None	3.31
Degree	1	31	18.90	22.00	756	MAX VALUE	108.86	9.61	0.51	2.85
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,017	MAX VALUE	372.43	0.00	0.00	0.00

Dual graph

Density: 10.07%
MCB compute time (ms): 503
MCB cycles: 1,502
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Dual1.json

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

Clustering coefficient 0.43 1.00 0.51 0.50 92.37 0.00 -120.87 0.05 0.11 4.28

Degree 7 26 18.03 18.00 3,246 MAX VALUE 516.30 3.78 0.21 2.67

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.04 3.00 4,567 MAX VALUE 1,667.66 0.20 0.06 0.17

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	1.00	0.51	0.50	92.37	0.00	-120.87	0.05	0.11	4.28
Degree	7	26	18.03	18.00	3,246	MAX VALUE	516.30	3.78	0.21	2.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.04	3.00	4,567	MAX VALUE	1,667.66	0.20	0.06	0.17

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 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 5 3.56 3.00 640 MAX VALUE 224.10 0.76 0.21 1.13

Eccentricity None None None None None None None None None None

MCB cycle size 4 9 6.86 7.00 967 MAX VALUE 269.87 0.99 0.14 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	5	3.56	3.00	640	MAX VALUE	224.10	0.76	0.21	1.13
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	9	6.86	7.00	967	MAX VALUE	269.87	0.99	0.14	1.38

Triangulated dual graph

Density: 46.34%
Triangles: 195,764

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

Clustering coefficient 0.68 1.00 0.83 0.82 149.92 0.00 -33.90 0.09 0.11 4.67

Degree 7 133 82.96 100.00 14,932 MAX VALUE 758.93 40.53 0.49 4.10

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	149.92	0.00	-33.90	0.09	0.11	4.67
Degree	7	133	82.96	100.00	14,932	MAX VALUE	758.93	40.53	0.49	4.10
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.77%

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

Clustering coefficient 0.50 1.00 0.80 0.74 144.66 0.00 -42.79 0.16 0.20 3.23

Degree 2 64 21.07 7.00 3,792 MAX VALUE 419.24 23.30 1.11 3.03

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	0.50	1.00	0.80	0.74	144.66	0.00	-42.79	0.16	0.20	3.23
Degree	2	64	21.07	7.00	3,792	MAX VALUE	419.24	23.30	1.11	3.03
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 38
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-89-ext/Incidence1.json

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

Clustering coefficient 0.00 0.00 None 0.00 None None None None None 0.34

Degree 1 15 3.27 2.00 720 MAX VALUE 209.36 2.99 0.91 0.89

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.40 6.00 902 MAX VALUE 260.69 0.80 0.12 0.50

XCSP 2.1 Benchmarks