XCSP 2.1 Benchmark Database

Instance: normalized-rand-3-20-20-60-632-fcd-17-ext
Number of variables: 20
Number of constraints: 58
Satisfiable: True
Timestamp: 2025-07-20 22:08:58
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 20
Number of constraints: 58

General features

Coarse blocks: 42,556
Value tables: 61

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

Arity 3 3 3.00 3.00 174 4.71e+27 63.72 0.00 0.00 0.00

Coarse blocks size 1 182 18.34 7.00 780,277 MAX VALUE 91,409.10 37.98 2.07 2.67

Relational linkage 0.05 0.65 0.28 0.30 4,667.54 0.00 -22,582.90 0.10 0.35 2.23

Tightness 0.63 0.87 0.64 0.63 37.12 0.00 -25.99 0.04 0.07 0.17

Tuples 1,058 2,944 2,879.84 2,944.00 167,031 MAX VALUE 461.28 339.51 0.12 0.17

Values 20 20 20.00 20.00 400 1.05e+26 59.91 0.00 0.00 0.00

Value table constraints 2 16 4.46 3.00 272 2.47e+33 76.89 3.41 0.77 1.83

Value table partitions 20 400 275.41 400.00 16,800 MAX VALUE 305.56 178.39 0.65 0.63

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	3	3	3.00	3.00	174	4.71e+27	63.72	0.00	0.00	0.00
Coarse blocks size	1	182	18.34	7.00	780,277	MAX VALUE	91,409.10	37.98	2.07	2.67
Relational linkage	0.05	0.65	0.28	0.30	4,667.54	0.00	-22,582.90	0.10	0.35	2.23
Tightness	0.63	0.87	0.64	0.63	37.12	0.00	-25.99	0.04	0.07	0.17
Tuples	1,058	2,944	2,879.84	2,944.00	167,031	MAX VALUE	461.28	339.51	0.12	0.17
Values	20	20	20.00	20.00	400	1.05e+26	59.91	0.00	0.00	0.00
Value table constraints	2	16	4.46	3.00	272	2.47e+33	76.89	3.41	0.77	1.83
Value table partitions	20	400	275.41	400.00	16,800	MAX VALUE	305.56	178.39	0.65	0.63

Tree decomposition

Number of clusters: 8
Number of leaves: 4
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/Tree1.json

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

Cluster constraints 9 18 13.50 13.50 108 872,467,000 20.59 3.20 0.24 2.08

Variables per cluster 9 13 11.12 11.00 89 213,548,000 19.18 1.69 0.15 1.32

Separator constraints 0 12 6.25 4.50 50 0 None 3.96 0.63 1.67

Separator variables 0 12 8.62 9.00 69 0 None 3.60 0.42 1.56

Clusters per var 1 8 4.45 5.00 89 1.34e+11 25.62 2.31 0.52 1.81

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	9	18	13.50	13.50	108	872,467,000	20.59	3.20	0.24	2.08
Variables per cluster	9	13	11.12	11.00	89	213,548,000	19.18	1.69	0.15	1.32
Separator constraints	0	12	6.25	4.50	50	0	None	3.96	0.63	1.67
Separator variables	0	12	8.62	9.00	69	0	None	3.60	0.42	1.56
Clusters per var	1	8	4.45	5.00	89	1.34e+11	25.62	2.31	0.52	1.81

Dual tree decomposition

Number of clusters: 15
Number of leaves: 3
Tree depth: 6
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/DualTree1.json

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

Cluster constraints 53 368 200.47 213.00 3,007 4.69e+33 77.53 92.37 0.46 2.71

Variables per cluster 14 41 28.47 30.00 427 3.39e+21 49.58 7.93 0.28 2.52

Separator constraints 0 328 155.53 180.00 2,333 0 None 86.00 0.55 2.71

Separator variables 0 39 24.60 27.00 369 0 None 9.58 0.39 2.62

Clusters per variable 1 14 7.36 7.00 427 MAX VALUE 105.88 3.59 0.49 2.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	53	368	200.47	213.00	3,007	4.69e+33	77.53	92.37	0.46	2.71
Variables per cluster	14	41	28.47	30.00	427	3.39e+21	49.58	7.93	0.28	2.52
Separator constraints	0	328	155.53	180.00	2,333	0	None	86.00	0.55	2.71
Separator variables	0	39	24.60	27.00	369	0	None	9.58	0.39	2.62
Clusters per variable	1	14	7.36	7.00	427	MAX VALUE	105.88	3.59	0.49	2.54

Primal graph

Density: 61.58%
MCB compute time (ms): 1
MCB cycles: 104
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/Primal1.json

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

Clustering coefficient 0.56 0.86 0.67 0.67 13.32 0.00 -8.23 0.07 0.11 2.83

Degree 8 17 11.70 11.50 234 1.38e+21 48.67 2.69 0.23 2.14

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 312 MAX VALUE 114.26 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.56	0.86	0.67	0.67	13.32	0.00	-8.23	0.07	0.11	2.83
Degree	8	17	11.70	11.50	234	1.38e+21	48.67	2.69	0.23	2.14
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	312	MAX VALUE	114.26	0.00	0.00	0.00

Triangulated primal graph

Density: 77.37%
MCB compute time (ms): 1
MCB cycles: 130
Triangles: None

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

Clustering coefficient 0.75 1.00 0.88 0.86 17.53 0.07 -2.72 0.08 0.09 2.44

Degree 8 19 14.70 16.00 294 1.10e+23 53.05 3.52 0.24 2.02

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 390 MAX VALUE 142.82 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.75	1.00	0.88	0.86	17.53	0.07	-2.72	0.08	0.09	2.44
Degree	8	19	14.70	16.00	294	1.10e+23	53.05	3.52	0.24	2.02
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	390	MAX VALUE	142.82	0.00	0.00	0.00

Dual graph

Density: 40.77%
MCB compute time (ms): 16
MCB cycles: 665
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/Dual1.json

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

Clustering coefficient 0.42 0.66 0.54 0.54 31.53 0.00 -35.56 0.05 0.08 4.04

Degree 13 34 23.24 23.00 1,348 MAX VALUE 181.38 4.42 0.19 2.77

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.01 3.00 2,000 MAX VALUE 732.02 0.09 0.03 0.04

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.42	0.66	0.54	0.54	31.53	0.00	-35.56	0.05	0.08	4.04
Degree	13	34	23.24	23.00	1,348	MAX VALUE	181.38	4.42	0.19	2.77
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.01	3.00	2,000	MAX VALUE	732.02	0.09	0.03	0.04

Minimal dual graph

Density: 6.11%
MCB compute time (ms): 4
MCB cycles: 44

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

Clustering coefficient 0.00 0.33 0.02 0.00 1.10 0.00 None 0.06 3.18 0.42

Degree 3 5 3.48 3.00 202 1.22e+31 71.58 0.59 0.17 0.84

Eccentricity None None None None None None None None None None

MCB cycle size 3 8 5.93 6.00 261 4.34e+33 77.45 1.10 0.18 1.44

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.02	0.00	1.10	0.00	None	0.06	3.18	0.42
Degree	3	5	3.48	3.00	202	1.22e+31	71.58	0.59	0.17	0.84
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	8	5.93	6.00	261	4.34e+33	77.45	1.10	0.18	1.44

Triangulated dual graph

Density: 78.22%
Triangles: 17,484

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

Clustering coefficient 0.79 1.00 0.90 0.90 52.07 0.00 -6.36 0.05 0.06 3.66

Degree 13 56 44.59 48.00 2,586 MAX VALUE 217.84 10.68 0.24 2.96

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	0.79	1.00	0.90	0.90	52.07	0.00	-6.36	0.05	0.06	3.66
Degree	13	56	44.59	48.00	2,586	MAX VALUE	217.84	10.68	0.24	2.96
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 20.45%

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

Clustering coefficient 0.49 1.00 0.78 0.78 45.24 0.00 -16.02 0.18 0.23 2.65

Degree 3 28 11.66 7.00 676 MAX VALUE 121.18 9.31 0.80 2.49

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	0.49	1.00	0.78	0.78	45.24	0.00	-16.02	0.18	0.23	2.65
Degree	3	28	11.66	7.00	676	MAX VALUE	121.18	9.31	0.80	2.49
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 5.79%
MCB compute time (ms): 7
MCB cycles: 103
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/rand-3-20-20-fcd/normalized-rand-3-20-20-60-632-fcd-17-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 3 16 4.46 3.00 348 MAX VALUE 106.06 2.87 0.64 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 4 6 4.89 4.00 504 MAX VALUE 161.44 0.99 0.20 0.69

XCSP 2.1 Benchmarks