XCSP 2.1 Benchmark Database

Instance: normalized-rand-3-20-20-60-632-fcd-15-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: 44,590
Value tables: 66

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 17.87 7.00 796,958 MAX VALUE 95,763.20 37.15 2.08 2.64

Relational linkage 0.05 0.65 0.29 0.30 5,426.29 0.00 -24,510.10 0.10 0.33 2.20

Tightness 0.63 0.86 0.64 0.63 37.12 0.00 -25.99 0.04 0.07 0.17

Tuples 1,084 2,944 2,880.10 2,944.00 167,046 MAX VALUE 461.29 338.11 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 15 4.20 2.00 277 6.92e+33 77.92 3.35 0.80 1.56

Value table partitions 20 400 284.85 400.00 18,800 MAX VALUE 335.52 174.64 0.61 0.61

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	17.87	7.00	796,958	MAX VALUE	95,763.20	37.15	2.08	2.64
Relational linkage	0.05	0.65	0.29	0.30	5,426.29	0.00	-24,510.10	0.10	0.33	2.20
Tightness	0.63	0.86	0.64	0.63	37.12	0.00	-25.99	0.04	0.07	0.17
Tuples	1,084	2,944	2,880.10	2,944.00	167,046	MAX VALUE	461.29	338.11	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	15	4.20	2.00	277	6.92e+33	77.92	3.35	0.80	1.56
Value table partitions	20	400	284.85	400.00	18,800	MAX VALUE	335.52	174.64	0.61	0.61

Tree decomposition

Number of clusters: 8
Number of leaves: 4
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: None
PDF-file path: None
JSON-file path: None

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

Cluster constraints 2 18 14.12 15.00 113 489,888,000 20.01 4.78 0.34 1.49

Variables per cluster 5 13 11.12 12.00 89 174,002,000 18.97 2.52 0.23 1.49

Separator constraints 0 11 6.88 9.00 55 0 None 4.04 0.59 1.21

Separator variables 0 12 8.62 10.50 69 0 None 4.06 0.47 1.73

Clusters per var 1 8 4.45 4.50 89 8.32e+10 25.14 2.52 0.57 1.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	2	18	14.12	15.00	113	489,888,000	20.01	4.78	0.34	1.49
Variables per cluster	5	13	11.12	12.00	89	174,002,000	18.97	2.52	0.23	1.49
Separator constraints	0	11	6.88	9.00	55	0	None	4.04	0.59	1.21
Separator variables	0	12	8.62	10.50	69	0	None	4.06	0.47	1.73
Clusters per var	1	8	4.45	4.50	89	8.32e+10	25.14	2.52	0.57	1.88

Dual tree decomposition

Number of clusters: 13
Number of leaves: 5
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: None
PDF-file path: None
JSON-file path: None

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

Cluster constraints 79 327 187.00 185.00 2,431 1.44e+29 67.14 65.54 0.35 2.46

Variables per cluster 17 39 27.31 26.00 355 3.21e+18 42.61 6.51 0.24 2.46

Separator constraints 0 218 135.46 152.00 1,761 0 None 58.75 0.43 2.46

Separator variables 0 33 22.85 25.00 297 0 None 8.27 0.36 2.46

Clusters per variable 1 11 6.12 7.00 355 MAX VALUE 95.37 2.87 0.47 2.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	79	327	187.00	185.00	2,431	1.44e+29	67.14	65.54	0.35	2.46
Variables per cluster	17	39	27.31	26.00	355	3.21e+18	42.61	6.51	0.24	2.46
Separator constraints	0	218	135.46	152.00	1,761	0	None	58.75	0.43	2.46
Separator variables	0	33	22.85	25.00	297	0	None	8.27	0.36	2.46
Clusters per variable	1	11	6.12	7.00	355	MAX VALUE	95.37	2.87	0.47	2.25

Primal graph

Density: 61.58%
MCB compute time (ms): 1
MCB cycles: 103
Triangles: None
Dot-file path: None
PDF-file path: None
JSON-file path: None

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

Clustering coefficient 0.53 0.76 0.66 0.66 13.26 0.00 -8.31 0.06 0.09 2.86

Degree 4 16 11.70 11.00 234 1.12e+21 48.47 2.74 0.23 2.06

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 309 MAX VALUE 113.16 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.53	0.76	0.66	0.66	13.26	0.00	-8.31	0.06	0.09	2.86
Degree	4	16	11.70	11.00	234	1.12e+21	48.47	2.74	0.23	2.06
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	309	MAX VALUE	113.16	0.00	0.00	0.00

Triangulated primal graph

Density: 77.37%
MCB compute time (ms): 2
MCB cycles: 128
Triangles: None

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

Clustering coefficient 0.75 1.00 0.89 0.89 17.79 0.09 -2.44 0.09 0.10 2.42

Degree 4 19 14.70 15.50 294 8.05e+22 52.74 3.85 0.26 2.25

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 384 MAX VALUE 140.62 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	0.89	0.89	17.79	0.09	-2.44	0.09	0.10	2.42
Degree	4	19	14.70	15.50	294	8.05e+22	52.74	3.85	0.26	2.25
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	384	MAX VALUE	140.62	0.00	0.00	0.00

Dual graph

Density: 40.53%
MCB compute time (ms): 18
MCB cycles: 615
Triangles: None
Dot-file path: None
PDF-file path: None
JSON-file path: None

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

Clustering coefficient 0.47 0.67 0.54 0.53 31.08 0.00 -36.38 0.04 0.08 3.96

Degree 16 32 23.10 23.00 1,340 MAX VALUE 181.63 3.03 0.13 2.39

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,845 MAX VALUE 675.65 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.67	0.54	0.53	31.08	0.00	-36.38	0.04	0.08	3.96
Degree	16	32	23.10	23.00	1,340	MAX VALUE	181.63	3.03	0.13	2.39
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,845	MAX VALUE	675.65	0.00	0.00	0.00

Minimal dual graph

Density: 6.23%
MCB compute time (ms): 4
MCB cycles: 46

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

Clustering coefficient 0.00 0.33 0.01 0.00 0.67 0.00 None 0.05 4.56 0.24

Degree 3 4 3.55 4.00 206 4.69e+31 72.93 0.50 0.14 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 3 7 5.91 6.00 272 1.49e+35 80.99 1.00 0.17 1.31

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	0.67	0.00	None	0.05	4.56	0.24
Degree	3	4	3.55	4.00	206	4.69e+31	72.93	0.50	0.14	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	7	5.91	6.00	272	1.49e+35	80.99	1.00	0.17	1.31

Triangulated dual graph

Density: 75.98%
Triangles: 16,161

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

Clustering coefficient 0.78 1.00 0.88 0.87 51.32 0.00 -7.25 0.06 0.07 3.46

Degree 16 55 43.31 47.50 2,512 MAX VALUE 216.25 10.59 0.24 2.97

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	0.78	1.00	0.88	0.87	51.32	0.00	-7.25	0.06	0.07	3.46
Degree	16	55	43.31	47.50	2,512	MAX VALUE	216.25	10.59	0.24	2.97
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 21.23%

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

Clustering coefficient 0.52 1.00 0.77 0.71 44.90 0.00 -16.40 0.18 0.23 2.77

Degree 3 28 12.10 8.50 702 MAX VALUE 124.42 9.28 0.77 2.63

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	0.52	1.00	0.77	0.71	44.90	0.00	-16.40	0.18	0.23	2.77
Degree	3	28	12.10	8.50	702	MAX VALUE	124.42	9.28	0.77	2.63
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 5.79%
MCB compute time (ms): 6
MCB cycles: 97
Dot-file path: None
PDF-file path: None
JSON-file path: None

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 4.46 3.00 348 MAX VALUE 105.71 2.84 0.64 1.09

Eccentricity None None None None None None None None None None

MCB cycle size 4 6 4.82 4.00 468 MAX VALUE 150.69 0.98 0.20 0.68

XCSP 2.1 Benchmarks