XCSP 2.1 Benchmark Database

Instance: normalized-geo50-20-d4-75-28-ext
Number of variables: 50
Number of constraints: 462
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: 462

General features

Coarse blocks: 18,480
Value tables: 50

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

Arity 2 2 2.00 2.00 924 MAX VALUE 320.23 0.00 0.00 0.00

Coarse blocks size 6 20 15.00 15.00 277,138 MAX VALUE 49,878.10 1.94 0.13 2.07

Relational linkage 0.30 0.80 0.57 0.55 568.40 0.00 -571.70 0.06 0.11 1.66

Tightness 0.18 0.32 0.25 0.25 115.58 0.00 -641.78 0.02 0.08 3.50

Tuples 271 326 299.93 300.00 138,569 MAX VALUE 2,634.86 8.38 0.03 3.50

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

Value table constraints 4 28 18.48 18.00 924 MAX VALUE 142.10 6.40 0.35 2.85

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	924	MAX VALUE	320.23	0.00	0.00	0.00
Coarse blocks size	6	20	15.00	15.00	277,138	MAX VALUE	49,878.10	1.94	0.13	2.07
Relational linkage	0.30	0.80	0.57	0.55	568.40	0.00	-571.70	0.06	0.11	1.66
Tightness	0.18	0.32	0.25	0.25	115.58	0.00	-641.78	0.02	0.08	3.50
Tuples	271	326	299.93	300.00	138,569	MAX VALUE	2,634.86	8.38	0.03	3.50
Values	20	20	20.00	20.00	1,000	MAX VALUE	149.79	0.00	0.00	0.00
Value table constraints	4	28	18.48	18.00	924	MAX VALUE	142.10	6.40	0.35	2.85
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: 27
Number of leaves: 5
Tree depth: 9
CIR: 0.27
Independent Cluster Pairs: 88
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/Tree1.json

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

Cluster constraints 10 147 76.96 85.00 2,078 MAX VALUE 114.00 31.76 0.41 3.09

Variables per cluster 5 19 14.11 15.00 381 3.89e+30 70.44 3.44 0.24 2.21

Separator constraints 0 130 59.85 68.00 1,616 0 None 28.53 0.48 3.14

Separator variables 0 18 12.26 13.00 331 0 None 3.95 0.32 2.24

Clusters per var 1 16 7.62 7.00 381 2.87e+38 88.55 4.39 0.58 2.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	10	147	76.96	85.00	2,078	MAX VALUE	114.00	31.76	0.41	3.09
Variables per cluster	5	19	14.11	15.00	381	3.89e+30	70.44	3.44	0.24	2.21
Separator constraints	0	130	59.85	68.00	1,616	0	None	28.53	0.48	3.14
Separator variables	0	18	12.26	13.00	331	0	None	3.95	0.32	2.24
Clusters per var	1	16	7.62	7.00	381	2.87e+38	88.55	4.39	0.58	2.54

Dual tree decomposition

Number of clusters: 48
Number of leaves: 21
Tree depth: 7
CIR: 0.41
Independent Cluster Pairs: 442
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/DualTree1.json

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

Cluster constraints 77 2,047 628.69 496.50 30,177 MAX VALUE 294.06 487.89 0.78 3.84

Variables per cluster 17 160 60.60 49.50 2,909 MAX VALUE 188.27 37.93 0.63 3.52

Separator constraints 0 1,253 439.10 353.50 21,077 0 None 300.25 0.68 3.84

Separator variables 0 114 50.98 46.00 2,447 0 None 27.94 0.55 3.60

Clusters per variable 1 12 6.30 6.00 2,909 MAX VALUE 803.22 2.29 0.36 2.18

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	77	2,047	628.69	496.50	30,177	MAX VALUE	294.06	487.89	0.78	3.84
Variables per cluster	17	160	60.60	49.50	2,909	MAX VALUE	188.27	37.93	0.63	3.52
Separator constraints	0	1,253	439.10	353.50	21,077	0	None	300.25	0.68	3.84
Separator variables	0	114	50.98	46.00	2,447	0	None	27.94	0.55	3.60
Clusters per variable	1	12	6.30	6.00	2,909	MAX VALUE	803.22	2.29	0.36	2.18

Primal graph

Density: 37.71%
MCB compute time (ms): None
MCB cycles: None
Triangles: 2,032
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/Primal1.json

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

Clustering coefficient 0.53 1.00 0.72 0.72 36.14 0.00 -16.80 0.11 0.15 3.80

Degree 4 28 18.48 18.00 924 MAX VALUE 142.10 6.40 0.35 2.85

Eccentricity 2 4 3.04 3.00 152 5.60e+23 54.68 0.56 0.19 0.85

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	0.53	1.00	0.72	0.72	36.14	0.00	-16.80	0.11	0.15	3.80
Degree	4	28	18.48	18.00	924	MAX VALUE	142.10	6.40	0.35	2.85
Eccentricity	2	4	3.04	3.00	152	5.60e+23	54.68	0.56	0.19	0.85
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 47.59%
MCB compute time (ms): None
MCB cycles: None
Triangles: 3,662

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

Clustering coefficient 0.63 1.00 0.81 0.81 40.27 0.00 -11.31 0.11 0.14 3.51

Degree 4 35 23.32 24.00 1,166 MAX VALUE 152.63 8.73 0.37 2.92

Eccentricity 2 3 2.62 3.00 131 3.24e+20 47.23 0.49 0.19 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	0.63	1.00	0.81	0.81	40.27	0.00	-11.31	0.11	0.14	3.51
Degree	4	35	23.32	24.00	1,166	MAX VALUE	152.63	8.73	0.37	2.92
Eccentricity	2	3	2.62	3.00	131	3.24e+20	47.23	0.49	0.19	0.66
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 8.55%
MCB compute time (ms): 18,201
MCB cycles: 8,674
Triangles: 63,950
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/Dual1.json

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

Clustering coefficient 0.50 0.79 0.53 0.52 243.64 0.00 -296.48 0.03 0.06 5.55

Degree 16 54 39.39 40.00 18,200 MAX VALUE 1,682.94 9.10 0.23 3.48

Eccentricity 3 4 3.44 3.00 1,587 MAX VALUE 565.38 0.50 0.14 0.68

MCB cycle size 3 4 3.00 3.00 26,025 MAX VALUE 9,530.23 0.02 0.01 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	0.79	0.53	0.52	243.64	0.00	-296.48	0.03	0.06	5.55
Degree	16	54	39.39	40.00	18,200	MAX VALUE	1,682.94	9.10	0.23	3.48
Eccentricity	3	4	3.44	3.00	1,587	MAX VALUE	565.38	0.50	0.14	0.68
MCB cycle size	3	4	3.00	3.00	26,025	MAX VALUE	9,530.23	0.02	0.01	0.00

Minimal dual graph

Density: 0.82%
MCB compute time (ms): 2,308
MCB cycles: 413

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 10.40 0.09

Degree 2 6 3.78 4.00 1,748 MAX VALUE 602.86 0.88 0.23 1.21

Eccentricity 7 10 8.62 9.00 3,984 MAX VALUE 993.77 0.72 0.08 1.08

MCB cycle size 3 10 6.38 6.00 2,635 MAX VALUE 757.37 1.21 0.19 1.60

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	10.40	0.09
Degree	2	6	3.78	4.00	1,748	MAX VALUE	602.86	0.88	0.23	1.21
Eccentricity	7	10	8.62	9.00	3,984	MAX VALUE	993.77	0.72	0.08	1.08
MCB cycle size	3	10	6.38	6.00	2,635	MAX VALUE	757.37	1.21	0.19	1.60

Triangulated dual graph

Density: 38.82%
Triangles: 2,192,990

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

Clustering coefficient 0.57 1.00 0.81 0.82 374.66 0.00 -100.81 0.11 0.13 5.09

Degree 16 341 178.94 192.00 82,672 MAX VALUE 2,325.40 80.33 0.45 4.52

Eccentricity 2 4 2.98 3.00 1,379 MAX VALUE 499.19 0.47 0.16 0.68

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.57	1.00	0.81	0.82	374.66	0.00	-100.81	0.11	0.13	5.09
Degree	16	341	178.94	192.00	82,672	MAX VALUE	2,325.40	80.33	0.45	4.52
Eccentricity	2	4	2.98	3.00	1,379	MAX VALUE	499.19	0.47	0.16	0.68

Triangulated minimal dual graph

Density: 7.57%

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

Clustering coefficient 0.50 1.00 0.80 0.76 370.96 0.00 -110.03 0.16 0.19 3.81

Degree 2 144 34.92 8.50 16,132 MAX VALUE 1,198.70 44.42 1.27 3.61

Eccentricity 3 5 3.85 4.00 1,780 MAX VALUE 618.07 0.56 0.15 0.84

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	1.00	0.80	0.76	370.96	0.00	-110.03	0.16	0.19	3.81
Degree	2	144	34.92	8.50	16,132	MAX VALUE	1,198.70	44.42	1.27	3.61
Eccentricity	3	5	3.85	4.00	1,780	MAX VALUE	618.07	0.56	0.15	0.84

Incidence graph

Density: 0.71%
MCB compute time (ms): 502
MCB cycles: 413
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-28-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 28 3.61 2.00 1,848 MAX VALUE 462.33 5.29 1.46 0.60

Eccentricity 5 9 7.06 7.00 3,613 MAX VALUE 995.60 0.96 0.14 1.24

MCB cycle size 6 6 6.00 6.00 2,478 MAX VALUE 740.00 0.00 0.00 0.00

XCSP 2.1 Benchmarks