XCSP 2.1 Benchmark Database

Instance: normalized-geo50-20-d4-75-59-ext
Number of variables: 50
Number of constraints: 386
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: 386

General features

Coarse blocks: 15,440
Value tables: 50

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

Arity 2 2 2.00 2.00 772 MAX VALUE 267.56 0.00 0.00 0.00

Coarse blocks size 8 20 14.99 15.00 231,418 MAX VALUE 41,664.30 1.94 0.13 2.07

Relational linkage 0.40 0.75 0.58 0.60 575.85 0.00 -558.17 0.06 0.11 1.65

Tightness 0.20 0.32 0.25 0.25 96.73 0.00 -535.75 0.02 0.09 3.54

Tuples 272 321 299.76 300.00 115,709 MAX VALUE 2,201.18 9.00 0.03 3.54

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

Value table constraints 5 24 15.44 16.00 772 MAX VALUE 134.45 4.40 0.28 2.60

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	772	MAX VALUE	267.56	0.00	0.00	0.00
Coarse blocks size	8	20	14.99	15.00	231,418	MAX VALUE	41,664.30	1.94	0.13	2.07
Relational linkage	0.40	0.75	0.58	0.60	575.85	0.00	-558.17	0.06	0.11	1.65
Tightness	0.20	0.32	0.25	0.25	96.73	0.00	-535.75	0.02	0.09	3.54
Tuples	272	321	299.76	300.00	115,709	MAX VALUE	2,201.18	9.00	0.03	3.54
Values	20	20	20.00	20.00	1,000	MAX VALUE	149.79	0.00	0.00	0.00
Value table constraints	5	24	15.44	16.00	772	MAX VALUE	134.45	4.40	0.28	2.60
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: 4
Tree depth: 8
CIR: 0.30
Independent Cluster Pairs: 98
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/Tree1.json

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

Cluster constraints 11 108 53.00 44.00 1,431 MAX VALUE 103.63 26.56 0.50 3.02

Variables per cluster 6 16 12.07 12.00 326 8.29e+28 66.59 2.49 0.21 1.87

Separator constraints 0 93 38.70 30.00 1,045 0 None 23.75 0.61 3.07

Separator variables 0 15 10.22 11.00 276 0 None 3.07 0.30 2.01

Clusters per var 1 15 6.52 6.00 326 1.27e+36 83.13 3.71 0.57 2.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	11	108	53.00	44.00	1,431	MAX VALUE	103.63	26.56	0.50	3.02
Variables per cluster	6	16	12.07	12.00	326	8.29e+28	66.59	2.49	0.21	1.87
Separator constraints	0	93	38.70	30.00	1,045	0	None	23.75	0.61	3.07
Separator variables	0	15	10.22	11.00	276	0	None	3.07	0.30	2.01
Clusters per var	1	15	6.52	6.00	326	1.27e+36	83.13	3.71	0.57	2.58

Dual tree decomposition

Number of clusters: 48
Number of leaves: 21
Tree depth: 7
CIR: 0.50
Independent Cluster Pairs: 545
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/DualTree1.json

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

Cluster constraints 42 1,162 380.19 323.00 18,249 MAX VALUE 274.25 241.49 0.64 3.78

Variables per cluster 12 111 46.19 36.50 2,217 MAX VALUE 177.74 23.60 0.51 3.43

Separator constraints 0 620 254.00 231.00 12,192 0 None 143.62 0.57 3.76

Separator variables 0 83 38.15 34.00 1,831 0 None 17.00 0.45 3.52

Clusters per variable 1 14 5.74 6.00 2,217 MAX VALUE 632.99 2.27 0.39 2.12

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	42	1,162	380.19	323.00	18,249	MAX VALUE	274.25	241.49	0.64	3.78
Variables per cluster	12	111	46.19	36.50	2,217	MAX VALUE	177.74	23.60	0.51	3.43
Separator constraints	0	620	254.00	231.00	12,192	0	None	143.62	0.57	3.76
Separator variables	0	83	38.15	34.00	1,831	0	None	17.00	0.45	3.52
Clusters per variable	1	14	5.74	6.00	2,217	MAX VALUE	632.99	2.27	0.39	2.12

Primal graph

Density: 31.51%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,398
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/Primal1.json

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

Clustering coefficient 0.47 0.97 0.72 0.74 36.06 0.00 -17.26 0.14 0.19 3.60

Degree 5 24 15.44 16.00 772 MAX VALUE 134.45 4.40 0.28 2.60

Eccentricity 2 4 3.38 3.00 169 1.51e+26 60.28 0.52 0.16 0.76

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	0.47	0.97	0.72	0.74	36.06	0.00	-17.26	0.14	0.19	3.60
Degree	5	24	15.44	16.00	772	MAX VALUE	134.45	4.40	0.28	2.60
Eccentricity	2	4	3.38	3.00	169	1.51e+26	60.28	0.52	0.16	0.76
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 39.92%
MCB compute time (ms): None
MCB cycles: None
Triangles: 2,458

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

Clustering coefficient 0.53 1.00 0.81 0.86 40.32 0.00 -11.70 0.15 0.19 3.51

Degree 5 36 19.56 18.00 978 MAX VALUE 145.01 7.00 0.36 2.87

Eccentricity 2 4 2.92 3.00 146 7.87e+22 52.72 0.52 0.18 0.78

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	0.81	0.86	40.32	0.00	-11.70	0.15	0.19	3.51
Degree	5	36	19.56	18.00	978	MAX VALUE	145.01	7.00	0.36	2.87
Eccentricity	2	4	2.92	3.00	146	7.87e+22	52.72	0.52	0.18	0.78
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 8.15%
MCB compute time (ms): 3,539
MCB cycles: 5,686
Triangles: 33,285
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/Dual1.json

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

Clustering coefficient 0.49 0.60 0.52 0.52 200.91 0.00 -252.26 0.02 0.03 4.98

Degree 11 46 31.38 32.00 12,114 MAX VALUE 1,320.02 6.73 0.21 3.22

Eccentricity 3 5 3.84 4.00 1,482 MAX VALUE 516.63 0.43 0.11 0.60

MCB cycle size 3 3 3.00 3.00 17,058 MAX VALUE 6,246.71 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.60	0.52	0.52	200.91	0.00	-252.26	0.02	0.03	4.98
Degree	11	46	31.38	32.00	12,114	MAX VALUE	1,320.02	6.73	0.21	3.22
Eccentricity	3	5	3.84	4.00	1,482	MAX VALUE	516.63	0.43	0.11	0.60
MCB cycle size	3	3	3.00	3.00	17,058	MAX VALUE	6,246.71	0.00	0.00	0.00

Minimal dual graph

Density: 0.97%
MCB compute time (ms): 1,500
MCB cycles: 337

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

Clustering coefficient 0.00 0.33 0.00 0.00 1.17 0.00 None 0.03 9.05 0.10

Degree 2 6 3.74 4.00 1,444 MAX VALUE 499.74 0.85 0.23 1.18

Eccentricity 7 10 8.44 8.00 3,257 MAX VALUE 821.81 0.72 0.09 1.08

MCB cycle size 3 9 6.44 6.00 2,171 MAX VALUE 620.35 1.30 0.20 1.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	1.17	0.00	None	0.03	9.05	0.10
Degree	2	6	3.74	4.00	1,444	MAX VALUE	499.74	0.85	0.23	1.18
Eccentricity	7	10	8.44	8.00	3,257	MAX VALUE	821.81	0.72	0.09	1.08
MCB cycle size	3	9	6.44	6.00	2,171	MAX VALUE	620.35	1.30	0.20	1.66

Triangulated dual graph

Density: 30.30%
Triangles: 747,936

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

Clustering coefficient 0.47 1.00 0.81 0.83 311.00 0.00 -88.60 0.13 0.16 4.72

Degree 11 274 116.65 126.50 45,026 MAX VALUE 1,786.45 51.30 0.44 4.29

Eccentricity 2 4 3.02 3.00 1,166 MAX VALUE 424.01 0.35 0.12 0.46

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.81	0.83	311.00	0.00	-88.60	0.13	0.16	4.72
Degree	11	274	116.65	126.50	45,026	MAX VALUE	1,786.45	51.30	0.44	4.29
Eccentricity	2	4	3.02	3.00	1,166	MAX VALUE	424.01	0.35	0.12	0.46

Triangulated minimal dual graph

Density: 8.07%

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

Clustering coefficient 0.49 1.00 0.80 0.75 308.32 0.00 -94.28 0.16 0.20 3.73

Degree 2 124 31.06 8.00 11,988 MAX VALUE 987.37 37.73 1.21 3.52

Eccentricity 3 5 3.95 4.00 1,523 MAX VALUE 525.58 0.58 0.15 0.86

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	1.00	0.80	0.75	308.32	0.00	-94.28	0.16	0.20	3.73
Degree	2	124	31.06	8.00	11,988	MAX VALUE	987.37	37.73	1.21	3.52
Eccentricity	3	5	3.95	4.00	1,523	MAX VALUE	525.58	0.58	0.15	0.86

Incidence graph

Density: 0.81%
MCB compute time (ms): 382
MCB cycles: 337
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-59-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 24 3.54 2.00 1,544 MAX VALUE 402.00 4.53 1.28 0.65

Eccentricity 5 10 7.83 8.00 3,412 MAX VALUE 894.25 0.86 0.11 1.15

MCB cycle size 6 6 6.00 6.00 2,022 MAX VALUE 603.82 0.00 0.00 0.00

XCSP 2.1 Benchmarks