XCSP 2.1 Benchmark Database

Instance: normalized-geo50-20-d4-75-73-ext
Number of variables: 50
Number of constraints: 470
Satisfiable: True
Timestamp: 2025-07-27 21:32:40
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 50
Number of constraints: 470

General features

Coarse blocks: 18,800
Value tables: 50

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

Arity 2 2 2.00 2.00 940 MAX VALUE 325.78 0.00 0.00 0.00

Coarse blocks size 6 20 14.99 15.00 281,760 MAX VALUE 50,727.40 1.95 0.13 2.08

Relational linkage 0.30 0.75 0.56 0.55 564.15 0.00 -579.63 0.07 0.12 1.67

Tightness 0.20 0.31 0.25 0.25 117.80 0.00 -652.24 0.02 0.09 3.56

Tuples 277 321 299.75 299.50 140,880 MAX VALUE 2,680.17 8.90 0.03 3.56

Values 20 20 20.00 20.00 1,000 MAX VALUE 149.79 0.00 0.00 0.00

Value table constraints 7 31 18.80 19.00 940 MAX VALUE 143.83 5.99 0.32 2.94

Value table partitions 20 20 20.00 20.00 1,000 MAX VALUE 149.79 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	940	MAX VALUE	325.78	0.00	0.00	0.00
Coarse blocks size	6	20	14.99	15.00	281,760	MAX VALUE	50,727.40	1.95	0.13	2.08
Relational linkage	0.30	0.75	0.56	0.55	564.15	0.00	-579.63	0.07	0.12	1.67
Tightness	0.20	0.31	0.25	0.25	117.80	0.00	-652.24	0.02	0.09	3.56
Tuples	277	321	299.75	299.50	140,880	MAX VALUE	2,680.17	8.90	0.03	3.56
Values	20	20	20.00	20.00	1,000	MAX VALUE	149.79	0.00	0.00	0.00
Value table constraints	7	31	18.80	19.00	940	MAX VALUE	143.83	5.99	0.32	2.94
Value table partitions	20	20	20.00	20.00	1,000	MAX VALUE	149.79	0.00	0.00	0.00

Tree decomposition

Number of clusters: 25
Number of leaves: 4
Tree depth: 9
CIR: 0.18
Independent Cluster Pairs: 51
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/Tree1.json

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

Cluster constraints 24 128 87.60 101.00 2,190 MAX VALUE 108.69 35.18 0.40 3.16

Variables per cluster 8 21 15.12 17.00 378 1.14e+29 66.91 3.85 0.25 2.19

Separator constraints 0 111 68.80 85.00 1,720 0 None 33.36 0.48 3.11

Separator variables 0 18 13.12 15.00 328 0 None 4.41 0.34 2.16

Clusters per var 1 14 7.56 7.50 378 MAX VALUE 89.31 4.19 0.55 2.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	24	128	87.60	101.00	2,190	MAX VALUE	108.69	35.18	0.40	3.16
Variables per cluster	8	21	15.12	17.00	378	1.14e+29	66.91	3.85	0.25	2.19
Separator constraints	0	111	68.80	85.00	1,720	0	None	33.36	0.48	3.11
Separator variables	0	18	13.12	15.00	328	0	None	4.41	0.34	2.16
Clusters per var	1	14	7.56	7.50	378	MAX VALUE	89.31	4.19	0.55	2.55

Dual tree decomposition

Number of clusters: 48
Number of leaves: 22
Tree depth: 7
CIR: 0.36
Independent Cluster Pairs: 388
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/DualTree1.json

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

Cluster constraints 55 1,667 639.02 496.50 30,673 MAX VALUE 295.58 468.30 0.73 3.84

Variables per cluster 14 162 62.10 49.50 2,981 MAX VALUE 189.47 39.00 0.63 3.66

Separator constraints 0 1,025 446.04 398.00 21,410 0 None 278.25 0.62 3.84

Separator variables 0 121 52.31 45.00 2,511 0 None 28.86 0.55 3.64

Clusters per variable 1 13 6.34 6.00 2,981 MAX VALUE 818.36 2.42 0.38 2.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	55	1,667	639.02	496.50	30,673	MAX VALUE	295.58	468.30	0.73	3.84
Variables per cluster	14	162	62.10	49.50	2,981	MAX VALUE	189.47	39.00	0.63	3.66
Separator constraints	0	1,025	446.04	398.00	21,410	0	None	278.25	0.62	3.84
Separator variables	0	121	52.31	45.00	2,511	0	None	28.86	0.55	3.64
Clusters per variable	1	13	6.34	6.00	2,981	MAX VALUE	818.36	2.42	0.38	2.26

Primal graph

Density: 38.37%
MCB compute time (ms): None
MCB cycles: None
Triangles: 2,062
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/Primal1.json

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

Clustering coefficient 0.54 0.90 0.72 0.72 36.03 0.00 -16.98 0.11 0.15 3.83

Degree 7 31 18.80 19.00 940 MAX VALUE 143.83 5.99 0.32 2.94

Eccentricity 2 4 2.90 3.00 145 6.64e+22 52.55 0.46 0.16 0.66

MCB cycle size 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	0.90	0.72	0.72	36.03	0.00	-16.98	0.11	0.15	3.83
Degree	7	31	18.80	19.00	940	MAX VALUE	143.83	5.99	0.32	2.94
Eccentricity	2	4	2.90	3.00	145	6.64e+22	52.55	0.46	0.16	0.66
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 50.86%
MCB compute time (ms): None
MCB cycles: None
Triangles: 4,242

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

Clustering coefficient 0.65 1.00 0.82 0.83 41.00 0.00 -10.46 0.12 0.15 3.48

Degree 7 37 24.92 24.00 1,246 MAX VALUE 156.56 9.00 0.36 2.89

Eccentricity 2 3 2.38 2.00 119 2.50e+18 42.36 0.49 0.20 0.66

MCB cycle size 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	0.65	1.00	0.82	0.83	41.00	0.00	-10.46	0.12	0.15	3.48
Degree	7	37	24.92	24.00	1,246	MAX VALUE	156.56	9.00	0.36	2.89
Eccentricity	2	3	2.38	2.00	119	2.50e+18	42.36	0.49	0.20	0.66
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 8.40%
MCB compute time (ms): 18,966
MCB cycles: 9,164
Triangles: 64,966
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/Dual1.json

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

Clustering coefficient 0.50 0.65 0.52 0.52 246.59 0.00 -303.66 0.03 0.05 5.62

Degree 13 58 39.42 40.00 18,526 MAX VALUE 1,713.28 8.85 0.22 3.52

Eccentricity 3 4 3.43 3.00 1,613 MAX VALUE 574.75 0.50 0.14 0.68

MCB cycle size 3 4 3.01 3.00 27,538 MAX VALUE 10,080.90 0.07 0.02 0.03

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	0.65	0.52	0.52	246.59	0.00	-303.66	0.03	0.05	5.62
Degree	13	58	39.42	40.00	18,526	MAX VALUE	1,713.28	8.85	0.22	3.52
Eccentricity	3	4	3.43	3.00	1,613	MAX VALUE	574.75	0.50	0.14	0.68
MCB cycle size	3	4	3.01	3.00	27,538	MAX VALUE	10,080.90	0.07	0.02	0.03

Minimal dual graph

Density: 0.81%
MCB compute time (ms): 2,006
MCB cycles: 421

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

Clustering coefficient 0.00 0.33 0.00 0.00 1.07 0.00 None 0.02 10.49 0.09

Degree 2 6 3.79 4.00 1,780 MAX VALUE 613.19 0.90 0.24 1.21

Eccentricity 7 10 8.39 8.00 3,942 MAX VALUE 998.27 0.62 0.07 0.94

MCB cycle size 3 10 6.55 7.00 2,757 MAX VALUE 783.22 1.23 0.19 1.62

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	1.07	0.00	None	0.02	10.49	0.09
Degree	2	6	3.79	4.00	1,780	MAX VALUE	613.19	0.90	0.24	1.21
Eccentricity	7	10	8.39	8.00	3,942	MAX VALUE	998.27	0.62	0.07	0.94
MCB cycle size	3	10	6.55	7.00	2,757	MAX VALUE	783.22	1.23	0.19	1.62

Triangulated dual graph

Density: None%
Triangles: None

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

Clustering coefficient None None None None None None None None None None

Degree None None None None None None None None None None

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	None	None	None	None	None	None	None	None	None	None
Degree	None	None	None	None	None	None	None	None	None	None
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 8.67%

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

Clustering coefficient 0.45 1.00 0.82 0.77 384.03 0.00 -102.40 0.14 0.18 3.84

Degree 2 161 40.64 9.00 19,102 MAX VALUE 1,251.13 52.36 1.29 3.61

Eccentricity 3 5 3.82 4.00 1,794 MAX VALUE 624.43 0.55 0.15 0.83

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	1.00	0.82	0.77	384.03	0.00	-102.40	0.14	0.18	3.84
Degree	2	161	40.64	9.00	19,102	MAX VALUE	1,251.13	52.36	1.29	3.61
Eccentricity	3	5	3.82	4.00	1,794	MAX VALUE	624.43	0.55	0.15	0.83

Incidence graph

Density: 0.70%
MCB compute time (ms): 515
MCB cycles: 421
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-73-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 31 3.62 2.00 1,880 MAX VALUE 469.61 5.29 1.46 0.60

Eccentricity 5 9 6.93 7.00 3,604 MAX VALUE 1,001.78 0.95 0.14 1.10

MCB cycle size 6 6 6.00 6.00 2,526 MAX VALUE 754.33 0.00 0.00 0.00

XCSP 2.1 Benchmarks