XCSP 2.1 Benchmark Database

Instance: normalized-geo50-20-d4-75-24-ext
Number of variables: 50
Number of constraints: 393
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: 393

General features

Coarse blocks: 15,720
Value tables: 50

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

Arity 2 2 2.00 2.00 786 MAX VALUE 272.41 0.00 0.00 0.00

Coarse blocks size 6 20 14.98 15.00 235,408 MAX VALUE 42,410.10 1.91 0.13 2.06

Relational linkage 0.30 0.80 0.58 0.60 575.60 0.00 -558.18 0.06 0.11 1.61

Tightness 0.20 0.31 0.25 0.25 98.74 0.00 -544.23 0.02 0.08 3.47

Tuples 276 321 299.50 299.00 117,704 MAX VALUE 2,240.78 8.33 0.03 3.47

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

Value table constraints 7 22 15.72 16.00 786 MAX VALUE 135.94 3.82 0.24 2.47

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	786	MAX VALUE	272.41	0.00	0.00	0.00
Coarse blocks size	6	20	14.98	15.00	235,408	MAX VALUE	42,410.10	1.91	0.13	2.06
Relational linkage	0.30	0.80	0.58	0.60	575.60	0.00	-558.18	0.06	0.11	1.61
Tightness	0.20	0.31	0.25	0.25	98.74	0.00	-544.23	0.02	0.08	3.47
Tuples	276	321	299.50	299.00	117,704	MAX VALUE	2,240.78	8.33	0.03	3.47
Values	20	20	20.00	20.00	1,000	MAX VALUE	149.79	0.00	0.00	0.00
Value table constraints	7	22	15.72	16.00	786	MAX VALUE	135.94	3.82	0.24	2.47
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: 26
Number of leaves: 3
Tree depth: 10
CIR: 0.33
Independent Cluster Pairs: 99
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/Tree1.json

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

Cluster constraints 25 97 54.62 47.50 1,420 MAX VALUE 101.94 21.78 0.40 3.10

Variables per cluster 8 15 12.35 12.00 321 1.66e+28 64.98 1.96 0.16 1.87

Separator constraints 0 74 39.50 36.50 1,027 0 None 18.55 0.47 3.15

Separator variables 0 13 10.42 11.00 271 0 None 2.68 0.26 1.85

Clusters per var 1 17 6.42 6.00 321 1.71e+36 83.43 3.68 0.57 2.47

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	97	54.62	47.50	1,420	MAX VALUE	101.94	21.78	0.40	3.10
Variables per cluster	8	15	12.35	12.00	321	1.66e+28	64.98	1.96	0.16	1.87
Separator constraints	0	74	39.50	36.50	1,027	0	None	18.55	0.47	3.15
Separator variables	0	13	10.42	11.00	271	0	None	2.68	0.26	1.85
Clusters per var	1	17	6.42	6.00	321	1.71e+36	83.43	3.68	0.57	2.47

Dual tree decomposition

Number of clusters: 48
Number of leaves: 22
Tree depth: 8
CIR: 0.47
Independent Cluster Pairs: 504
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/DualTree1.json

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

Cluster constraints 55 1,013 397.65 344.00 19,087 MAX VALUE 277.76 235.77 0.59 3.77

Variables per cluster 14 106 48.00 37.50 2,304 MAX VALUE 179.93 23.91 0.50 3.46

Separator constraints 0 538 269.52 278.50 12,937 0 None 135.68 0.50 3.77

Separator variables 0 76 39.81 35.00 1,911 0 None 17.05 0.43 3.32

Clusters per variable 1 13 5.86 6.00 2,304 MAX VALUE 652.29 2.30 0.39 2.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	55	1,013	397.65	344.00	19,087	MAX VALUE	277.76	235.77	0.59	3.77
Variables per cluster	14	106	48.00	37.50	2,304	MAX VALUE	179.93	23.91	0.50	3.46
Separator constraints	0	538	269.52	278.50	12,937	0	None	135.68	0.50	3.77
Separator variables	0	76	39.81	35.00	1,911	0	None	17.05	0.43	3.32
Clusters per variable	1	13	5.86	6.00	2,304	MAX VALUE	652.29	2.30	0.39	2.09

Primal graph

Density: 32.08%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,443
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/Primal1.json

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

Clustering coefficient 0.46 1.00 0.73 0.73 36.47 0.00 -16.66 0.13 0.18 3.65

Degree 7 22 15.72 16.00 786 MAX VALUE 135.94 3.82 0.24 2.47

Eccentricity 2 4 3.34 3.00 167 7.55e+25 59.59 0.55 0.17 0.81

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	0.46	1.00	0.73	0.73	36.47	0.00	-16.66	0.13	0.18	3.65
Degree	7	22	15.72	16.00	786	MAX VALUE	135.94	3.82	0.24	2.47
Eccentricity	2	4	3.34	3.00	167	7.55e+25	59.59	0.55	0.17	0.81
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 40.90%
MCB compute time (ms): None
MCB cycles: None
Triangles: 2,551

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

Clustering coefficient 0.51 1.00 0.81 0.83 40.27 0.00 -11.57 0.13 0.17 3.52

Degree 7 35 20.04 20.00 1,002 MAX VALUE 147.24 6.25 0.31 2.92

Eccentricity 2 3 2.68 3.00 134 1.09e+21 48.44 0.47 0.17 0.63

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	0.51	1.00	0.81	0.83	40.27	0.00	-11.57	0.13	0.17	3.52
Degree	7	35	20.04	20.00	1,002	MAX VALUE	147.24	6.25	0.31	2.92
Eccentricity	2	3	2.68	3.00	134	1.09e+21	48.44	0.47	0.17	0.63
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 7.98%
MCB compute time (ms): 2,884
MCB cycles: 5,821
Triangles: 32,979
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/Dual1.json

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

Clustering coefficient 0.49 0.64 0.52 0.51 204.12 0.00 -257.72 0.02 0.04 4.90

Degree 13 42 31.30 32.00 12,300 MAX VALUE 1,346.82 5.25 0.17 2.96

Eccentricity 3 5 4.03 4.00 1,582 MAX VALUE 542.91 0.59 0.15 0.89

MCB cycle size 3 4 3.00 3.00 17,481 MAX VALUE 6,400.20 0.06 0.02 0.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.64	0.52	0.51	204.12	0.00	-257.72	0.02	0.04	4.90
Degree	13	42	31.30	32.00	12,300	MAX VALUE	1,346.82	5.25	0.17	2.96
Eccentricity	3	5	4.03	4.00	1,582	MAX VALUE	542.91	0.59	0.15	0.89
MCB cycle size	3	4	3.00	3.00	17,481	MAX VALUE	6,400.20	0.06	0.02	0.02

Minimal dual graph

Density: 0.96%
MCB compute time (ms): 1,119
MCB cycles: 346

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 6 3.75 4.00 1,472 MAX VALUE 508.92 0.86 0.23 1.20

Eccentricity 7 11 8.76 9.00 3,444 MAX VALUE 851.41 0.80 0.09 1.18

MCB cycle size 4 11 6.41 6.00 2,217 MAX VALUE 636.29 1.20 0.19 1.57

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	6	3.75	4.00	1,472	MAX VALUE	508.92	0.86	0.23	1.20
Eccentricity	7	11	8.76	9.00	3,444	MAX VALUE	851.41	0.80	0.09	1.18
MCB cycle size	4	11	6.41	6.00	2,217	MAX VALUE	636.29	1.20	0.19	1.57

Triangulated dual graph

Density: 30.90%
Triangles: 810,925

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

Clustering coefficient 0.49 1.00 0.81 0.83 317.47 0.00 -88.91 0.12 0.15 4.74

Degree 13 250 121.12 125.00 47,602 MAX VALUE 1,838.42 50.02 0.41 4.26

Eccentricity 2 4 3.11 3.00 1,222 MAX VALUE 442.83 0.39 0.13 0.52

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	1.00	0.81	0.83	317.47	0.00	-88.91	0.12	0.15	4.74
Degree	13	250	121.12	125.00	47,602	MAX VALUE	1,838.42	50.02	0.41	4.26
Eccentricity	2	4	3.11	3.00	1,222	MAX VALUE	442.83	0.39	0.13	0.52

Triangulated minimal dual graph

Density: 7.70%

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

Clustering coefficient 0.45 1.00 0.79 0.74 311.64 0.00 -98.94 0.16 0.20 3.72

Degree 2 124 30.17 8.00 11,856 MAX VALUE 1,000.48 36.29 1.20 3.53

Eccentricity 3 6 4.28 4.00 1,682 MAX VALUE 567.37 0.60 0.14 0.91

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	1.00	0.79	0.74	311.64	0.00	-98.94	0.16	0.20	3.72
Degree	2	124	30.17	8.00	11,856	MAX VALUE	1,000.48	36.29	1.20	3.53
Eccentricity	3	6	4.28	4.00	1,682	MAX VALUE	567.37	0.60	0.14	0.91

Incidence graph

Density: 0.80%
MCB compute time (ms): 302
MCB cycles: 344
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-24-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 22 3.55 2.00 1,572 MAX VALUE 408.35 4.53 1.28 0.63

Eccentricity 5 10 8.04 8.00 3,560 MAX VALUE 918.64 1.14 0.14 1.24

MCB cycle size 6 6 6.00 6.00 2,064 MAX VALUE 616.37 0.00 0.00 0.00

XCSP 2.1 Benchmarks