XCSP 2.1 Benchmark Database

Instance: normalized-geo50-20-d4-75-26-ext
Number of variables: 50
Number of constraints: 399
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: 399

General features

Coarse blocks: 15,960
Value tables: 50

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

Arity 2 2 2.00 2.00 798 MAX VALUE 276.57 0.00 0.00 0.00

Coarse blocks size 5 20 15.00 15.00 239,432 MAX VALUE 43,080.80 1.95 0.13 2.08

Relational linkage 0.25 0.75 0.57 0.60 572.20 0.00 -565.44 0.07 0.12 1.67

Tightness 0.19 0.34 0.25 0.25 99.71 0.00 -554.98 0.02 0.09 3.56

Tuples 266 323 300.04 300.00 119,716 MAX VALUE 2,275.67 9.21 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 25 15.96 16.00 798 MAX VALUE 136.82 3.91 0.25 2.56

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	798	MAX VALUE	276.57	0.00	0.00	0.00
Coarse blocks size	5	20	15.00	15.00	239,432	MAX VALUE	43,080.80	1.95	0.13	2.08
Relational linkage	0.25	0.75	0.57	0.60	572.20	0.00	-565.44	0.07	0.12	1.67
Tightness	0.19	0.34	0.25	0.25	99.71	0.00	-554.98	0.02	0.09	3.56
Tuples	266	323	300.04	300.00	119,716	MAX VALUE	2,275.67	9.21	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	25	15.96	16.00	798	MAX VALUE	136.82	3.91	0.25	2.56
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: 0.28
Independent Cluster Pairs: 76
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/Tree1.json

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

Cluster constraints 25 92 60.96 60.00 1,524 MAX VALUE 101.44 18.60 0.31 3.00

Variables per cluster 8 17 13.08 13.00 327 5.68e+27 63.91 2.13 0.16 1.98

Separator constraints 0 74 45.00 41.00 1,125 0 None 18.86 0.42 3.00

Separator variables 0 15 11.08 11.00 277 0 None 2.95 0.27 2.04

Clusters per var 1 15 6.54 7.00 327 1.85e+36 83.51 3.48 0.53 2.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	25	92	60.96	60.00	1,524	MAX VALUE	101.44	18.60	0.31	3.00
Variables per cluster	8	17	13.08	13.00	327	5.68e+27	63.91	2.13	0.16	1.98
Separator constraints	0	74	45.00	41.00	1,125	0	None	18.86	0.42	3.00
Separator variables	0	15	11.08	11.00	277	0	None	2.95	0.27	2.04
Clusters per var	1	15	6.54	7.00	327	1.85e+36	83.51	3.48	0.53	2.28

Dual tree decomposition

Number of clusters: 48
Number of leaves: 23
Tree depth: 8
CIR: 0.45
Independent Cluster Pairs: 491
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/DualTree1.json

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

Cluster constraints 72 815 400.54 379.00 19,226 MAX VALUE 279.68 210.78 0.53 3.84

Variables per cluster 16 97 48.85 40.00 2,345 MAX VALUE 181.03 23.58 0.48 3.54

Separator constraints 0 504 268.21 269.00 12,874 0 None 115.75 0.43 3.81

Separator variables 0 68 40.54 36.50 1,946 0 None 16.60 0.41 3.42

Clusters per variable 1 15 5.88 6.00 2,345 MAX VALUE 661.99 2.42 0.41 2.16

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	72	815	400.54	379.00	19,226	MAX VALUE	279.68	210.78	0.53	3.84
Variables per cluster	16	97	48.85	40.00	2,345	MAX VALUE	181.03	23.58	0.48	3.54
Separator constraints	0	504	268.21	269.00	12,874	0	None	115.75	0.43	3.81
Separator variables	0	68	40.54	36.50	1,946	0	None	16.60	0.41	3.42
Clusters per variable	1	15	5.88	6.00	2,345	MAX VALUE	661.99	2.42	0.41	2.16

Primal graph

Density: 32.57%
MCB compute time (ms): None
MCB cycles: None
Triangles: 1,422
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/Primal1.json

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

Clustering coefficient 0.49 0.95 0.71 0.71 35.66 0.00 -17.73 0.13 0.18 3.83

Degree 7 25 15.96 16.00 798 MAX VALUE 136.82 3.91 0.25 2.56

Eccentricity 2 4 3.40 3.00 170 2.01e+26 60.57 0.53 0.16 0.77

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	0.49	0.95	0.71	0.71	35.66	0.00	-17.73	0.13	0.18	3.83
Degree	7	25	15.96	16.00	798	MAX VALUE	136.82	3.91	0.25	2.56
Eccentricity	2	4	3.40	3.00	170	2.01e+26	60.57	0.53	0.16	0.77
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Triangulated primal graph

Density: 43.02%
MCB compute time (ms): None
MCB cycles: None
Triangles: 2,854

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

Clustering coefficient 0.50 1.00 0.80 0.80 40.23 0.00 -11.61 0.13 0.17 3.48

Degree 7 39 21.08 21.00 1,054 MAX VALUE 149.15 7.06 0.34 2.81

Eccentricity 2 3 2.66 3.00 133 7.29e+20 48.04 0.47 0.18 0.64

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	0.50	1.00	0.80	0.80	40.23	0.00	-11.61	0.13	0.17	3.48
Degree	7	39	21.08	21.00	1,054	MAX VALUE	149.15	7.06	0.34	2.81
Eccentricity	2	3	2.66	3.00	133	7.29e+20	48.04	0.47	0.18	0.64
MCB cycle size	None	None	None	None	None	None	None	None	None	None

Dual graph

Density: 8.00%
MCB compute time (ms): 9,981
MCB cycles: 5,983
Triangles: 34,873
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/Dual1.json

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

Clustering coefficient 0.49 0.63 0.52 0.52 207.44 0.00 -261.26 0.02 0.04 5.17

Degree 15 46 31.84 32.00 12,704 MAX VALUE 1,374.01 5.62 0.18 3.10

Eccentricity 3 5 3.85 4.00 1,536 MAX VALUE 535.16 0.43 0.11 0.59

MCB cycle size 3 3 3.00 3.00 17,949 MAX VALUE 6,573.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.63	0.52	0.52	207.44	0.00	-261.26	0.02	0.04	5.17
Degree	15	46	31.84	32.00	12,704	MAX VALUE	1,374.01	5.62	0.18	3.10
Eccentricity	3	5	3.85	4.00	1,536	MAX VALUE	535.16	0.43	0.11	0.59
MCB cycle size	3	3	3.00	3.00	17,949	MAX VALUE	6,573.00	0.00	0.00	0.00

Minimal dual graph

Density: 0.94%
MCB compute time (ms): 1,296
MCB cycles: 350

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 9.20 0.10

Degree 2 6 3.75 4.00 1,496 MAX VALUE 517.14 0.86 0.23 1.19

Eccentricity 7 10 8.53 9.00 3,403 MAX VALUE 854.03 0.66 0.08 1.01

MCB cycle size 3 10 6.39 6.00 2,236 MAX VALUE 641.71 1.27 0.20 1.65

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	9.20	0.10
Degree	2	6	3.75	4.00	1,496	MAX VALUE	517.14	0.86	0.23	1.19
Eccentricity	7	10	8.53	9.00	3,403	MAX VALUE	854.03	0.66	0.08	1.01
MCB cycle size	3	10	6.39	6.00	2,236	MAX VALUE	641.71	1.27	0.20	1.65

Triangulated dual graph

Density: 30.69%
Triangles: 820,369

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

Clustering coefficient 0.42 1.00 0.80 0.82 319.91 0.00 -93.93 0.13 0.16 4.75

Degree 15 291 122.14 118.00 48,734 MAX VALUE 1,869.18 53.71 0.44 4.38

Eccentricity 2 4 3.11 3.00 1,240 MAX VALUE 447.89 0.47 0.15 0.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.42	1.00	0.80	0.82	319.91	0.00	-93.93	0.13	0.16	4.75
Degree	15	291	122.14	118.00	48,734	MAX VALUE	1,869.18	53.71	0.44	4.38
Eccentricity	2	4	3.11	3.00	1,240	MAX VALUE	447.89	0.47	0.15	0.67

Triangulated minimal dual graph

Density: 8.73%

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

Clustering coefficient 0.51 1.00 0.81 0.77 323.45 0.00 -90.88 0.15 0.19 3.76

Degree 2 134 34.76 8.00 13,870 MAX VALUE 1,033.54 43.59 1.25 3.53

Eccentricity 3 5 3.78 4.00 1,507 MAX VALUE 525.98 0.54 0.14 0.80

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.51	1.00	0.81	0.77	323.45	0.00	-90.88	0.15	0.19	3.76
Degree	2	134	34.76	8.00	13,870	MAX VALUE	1,033.54	43.59	1.25	3.53
Eccentricity	3	5	3.78	4.00	1,507	MAX VALUE	525.98	0.54	0.14	0.80

Incidence graph

Density: 0.79%
MCB compute time (ms): 365
MCB cycles: 350
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/geom/normalized-geo50-20-d4-75-26-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 25 3.55 2.00 1,596 MAX VALUE 413.39 4.58 1.29 0.63

Eccentricity 5 10 7.86 8.00 3,528 MAX VALUE 922.65 0.87 0.11 1.16

MCB cycle size 6 6 6.00 6.00 2,100 MAX VALUE 627.12 0.00 0.00 0.00

XCSP 2.1 Benchmarks