XCSP 2.1 Benchmark Database

Instance: normalized-geo50-20-d4-75-94-ext
Number of variables: 50
Number of constraints: 496
Satisfiable: True
Timestamp: 2025-07-27 21:32:41
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0

Component #1

Number of variables: 50
Number of constraints: 496

General features

Coarse blocks: 19,840
Value tables: 50

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

Arity 2 2 2.00 2.00 992 MAX VALUE 343.80 0.00 0.00 0.00

Coarse blocks size 7 20 15.00 15.00 297,586 MAX VALUE 53,553.10 1.94 0.13 2.07

Relational linkage 0.35 0.75 0.56 0.55 564.35 0.00 -578.41 0.06 0.11 1.62

Tightness 0.18 0.31 0.25 0.25 124.02 0.00 -689.35 0.02 0.09 3.50

Tuples 275 327 299.99 300.00 148,793 MAX VALUE 2,828.85 8.53 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 7 30 19.84 20.50 992 MAX VALUE 146.42 6.24 0.31 2.81

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	992	MAX VALUE	343.80	0.00	0.00	0.00
Coarse blocks size	7	20	15.00	15.00	297,586	MAX VALUE	53,553.10	1.94	0.13	2.07
Relational linkage	0.35	0.75	0.56	0.55	564.35	0.00	-578.41	0.06	0.11	1.62
Tightness	0.18	0.31	0.25	0.25	124.02	0.00	-689.35	0.02	0.09	3.50
Tuples	275	327	299.99	300.00	148,793	MAX VALUE	2,828.85	8.53	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	7	30	19.84	20.50	992	MAX VALUE	146.42	6.24	0.31	2.81
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: 4
Tree depth: 12
CIR: 0.22
Independent Cluster Pairs: 67
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/Tree1.json

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

Cluster constraints 26 145 86.88 82.50 2,259 MAX VALUE 113.26 35.44 0.41 3.15

Variables per cluster 8 19 14.77 14.00 384 1.16e+30 69.23 3.32 0.22 1.80

Separator constraints 0 117 67.81 65.00 1,763 0 None 32.14 0.47 3.02

Separator variables 0 18 12.85 13.00 334 0 None 3.97 0.31 1.94

Clusters per var 1 20 7.68 6.50 384 MAX VALUE 91.54 4.31 0.56 2.59

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	26	145	86.88	82.50	2,259	MAX VALUE	113.26	35.44	0.41	3.15
Variables per cluster	8	19	14.77	14.00	384	1.16e+30	69.23	3.32	0.22	1.80
Separator constraints	0	117	67.81	65.00	1,763	0	None	32.14	0.47	3.02
Separator variables	0	18	12.85	13.00	334	0	None	3.97	0.31	1.94
Clusters per var	1	20	7.68	6.50	384	MAX VALUE	91.54	4.31	0.56	2.59

Dual tree decomposition

Number of clusters: 48
Number of leaves: 22
Tree depth: 8
CIR: 0.31
Independent Cluster Pairs: 333
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/DualTree1.json

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

Cluster constraints 63 2,526 737.38 569.50 35,394 MAX VALUE 302.32 571.07 0.77 3.87

Variables per cluster 15 185 66.54 52.00 3,194 MAX VALUE 192.72 42.53 0.64 3.53

Separator constraints 0 1,373 522.40 426.50 25,075 0 None 345.30 0.66 3.84

Separator variables 0 139 56.21 49.00 2,698 0 None 31.36 0.56 3.53

Clusters per variable 1 14 6.44 7.00 3,194 MAX VALUE 875.49 2.26 0.35 2.13

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	63	2,526	737.38	569.50	35,394	MAX VALUE	302.32	571.07	0.77	3.87
Variables per cluster	15	185	66.54	52.00	3,194	MAX VALUE	192.72	42.53	0.64	3.53
Separator constraints	0	1,373	522.40	426.50	25,075	0	None	345.30	0.66	3.84
Separator variables	0	139	56.21	49.00	2,698	0	None	31.36	0.56	3.53
Clusters per variable	1	14	6.44	7.00	3,194	MAX VALUE	875.49	2.26	0.35	2.13

Primal graph

Density: 40.49%
MCB compute time (ms): None
MCB cycles: None
Triangles: 2,375
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/Primal1.json

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

Clustering coefficient 0.53 1.00 0.74 0.74 36.84 0.00 -15.78 0.11 0.14 3.77

Degree 7 30 19.84 20.50 992 MAX VALUE 146.42 6.24 0.31 2.81

Eccentricity 2 4 3.12 3.00 156 2.83e+24 56.30 0.47 0.15 0.69

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	0.74	0.74	36.84	0.00	-15.78	0.11	0.14	3.77
Degree	7	30	19.84	20.50	992	MAX VALUE	146.42	6.24	0.31	2.81
Eccentricity	2	4	3.12	3.00	156	2.83e+24	56.30	0.47	0.15	0.69
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 49.31%
MCB compute time (ms): None
MCB cycles: None
Triangles: 3,928

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

Clustering coefficient 0.56 1.00 0.82 0.82 40.75 0.00 -10.70 0.11 0.13 3.57

Degree 7 43 24.16 24.50 1,208 MAX VALUE 155.58 8.22 0.34 3.12

Eccentricity 2 4 2.92 3.00 146 8.85e+22 52.84 0.48 0.17 0.70

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	0.56	1.00	0.82	0.82	40.75	0.00	-10.70	0.11	0.13	3.57
Degree	7	43	24.16	24.50	1,208	MAX VALUE	155.58	8.22	0.34	3.12
Eccentricity	2	4	2.92	3.00	146	8.85e+22	52.84	0.48	0.17	0.70
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 8.41%
MCB compute time (ms): 6,376
MCB cycles: 10,186
Triangles: 75,948
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/Dual1.json

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

Clustering coefficient 0.50 0.67 0.52 0.51 260.00 0.00 -321.01 0.03 0.05 5.63

Degree 14 58 41.61 43.00 20,638 MAX VALUE 1,836.11 8.96 0.22 3.50

Eccentricity 3 4 3.50 4.00 1,738 MAX VALUE 616.83 0.50 0.14 0.69

MCB cycle size 3 4 3.00 3.00 30,583 MAX VALUE 11,197.70 0.05 0.02 0.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	0.67	0.52	0.51	260.00	0.00	-321.01	0.03	0.05	5.63
Degree	14	58	41.61	43.00	20,638	MAX VALUE	1,836.11	8.96	0.22	3.50
Eccentricity	3	4	3.50	4.00	1,738	MAX VALUE	616.83	0.50	0.14	0.69
MCB cycle size	3	4	3.00	3.00	30,583	MAX VALUE	11,197.70	0.05	0.02	0.02

Minimal dual graph

Density: 0.77%
MCB compute time (ms): 2,716
MCB cycles: 447

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

Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.02 13.33 0.04

Degree 2 6 3.80 4.00 1,884 MAX VALUE 649.24 0.88 0.23 1.18

Eccentricity 7 11 8.72 9.00 4,325 MAX VALUE 1,072.50 0.70 0.08 1.07

MCB cycle size 3 10 6.53 7.00 2,920 MAX VALUE 830.66 1.20 0.18 1.57

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.00	0.00	0.83	0.00	None	0.02	13.33	0.04
Degree	2	6	3.80	4.00	1,884	MAX VALUE	649.24	0.88	0.23	1.18
Eccentricity	7	11	8.72	9.00	4,325	MAX VALUE	1,072.50	0.70	0.08	1.07
MCB cycle size	3	10	6.53	7.00	2,920	MAX VALUE	830.66	1.20	0.18	1.57

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: 8.29%

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

Clustering coefficient 0.47 1.00 0.82 0.76 404.56 0.00 -109.14 0.15 0.18 3.84

Degree 2 154 41.02 9.00 20,346 MAX VALUE 1,324.54 53.06 1.29 3.56

Eccentricity 3 5 3.88 4.00 1,922 MAX VALUE 666.54 0.56 0.14 0.83

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	1.00	0.82	0.76	404.56	0.00	-109.14	0.15	0.18	3.84
Degree	2	154	41.02	9.00	20,346	MAX VALUE	1,324.54	53.06	1.29	3.56
Eccentricity	3	5	3.88	4.00	1,922	MAX VALUE	666.54	0.56	0.14	0.83

Incidence graph

Density: 0.67%
MCB compute time (ms): 540
MCB cycles: 447
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-94-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 30 3.63 2.00 1,984 MAX VALUE 490.22 5.48 1.51 0.56

Eccentricity 5 9 7.21 7.00 3,935 MAX VALUE 1,073.88 0.91 0.13 1.19

MCB cycle size 6 6 6.00 6.00 2,682 MAX VALUE 800.92 0.00 0.00 0.00

XCSP 2.1 Benchmarks