XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg15-18-ext
Number of variables: 270
Number of constraints: 33
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 270
Number of constraints: 33

General features

Coarse blocks: 4,677
Value tables: 270

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

Arity 15 18 16.36 15.00 540 MAX VALUE 92.10 1.49 0.09 0.69

Coarse blocks size 1 17 2.77 2.00 12,960 MAX VALUE 3,431.61 2.33 0.84 1.78

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -44,816.90 0.00 0.26 0.29

Tightness 1.00 1.00 1.00 1.00 33.00 1.00 0.00 0.00 0.00 0.00

Tuples 4 44 25.82 44.00 852 MAX VALUE 88.91 19.92 0.77 0.69

Values 26 26 26.00 26.00 7,020 MAX VALUE 879.69 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 540 MAX VALUE 187.15 0.00 0.00 0.00

Value table partitions 11 18 14.32 14.00 3,867 MAX VALUE 716.86 1.68 0.12 1.82

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	15	18	16.36	15.00	540	MAX VALUE	92.10	1.49	0.09	0.69
Coarse blocks size	1	17	2.77	2.00	12,960	MAX VALUE	3,431.61	2.33	0.84	1.78
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-44,816.90	0.00	0.26	0.29
Tightness	1.00	1.00	1.00	1.00	33.00	1.00	0.00	0.00	0.00	0.00
Tuples	4	44	25.82	44.00	852	MAX VALUE	88.91	19.92	0.77	0.69
Values	26	26	26.00	26.00	7,020	MAX VALUE	879.69	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	540	MAX VALUE	187.15	0.00	0.00	0.00
Value table partitions	11	18	14.32	14.00	3,867	MAX VALUE	716.86	1.68	0.12	1.82

Tree decomposition

Number of clusters: 31
Number of leaves: 15
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/Tree1.json

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

Cluster constraints 0 2 1.06 1.00 33 0 None 0.95 0.89 0.94

Variables per cluster 32 174 59.13 45.00 1,833 MAX VALUE 121.41 38.79 0.66 1.63

Separator constraints 0 0 0.00 0.00 0 0 None 0.00 None 0.00

Separator variables 0 134 50.42 31.00 1,563 0 None 29.54 0.59 1.63

Clusters per var 1 9 6.79 8.00 1,833 MAX VALUE 491.97 2.09 0.31 1.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.06	1.00	33	0	None	0.95	0.89	0.94
Variables per cluster	32	174	59.13	45.00	1,833	MAX VALUE	121.41	38.79	0.66	1.63
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	134	50.42	31.00	1,563	0	None	29.54	0.59	1.63
Clusters per var	1	9	6.79	8.00	1,833	MAX VALUE	491.97	2.09	0.31	1.69

Dual tree decomposition

Number of clusters: 18
Number of leaves: 2
Tree depth: 9
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/DualTree1.json

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

Cluster constraints 15 15 15.00 15.00 270 1.48e+21 48.74 0.00 0.00 0.00

Variables per cluster 16 16 16.00 16.00 288 4.72e+21 49.91 0.00 0.00 0.00

Separator constraints 0 0 0.00 0.00 0 0 None 0.00 None 0.00

Separator variables 0 15 14.17 15.00 255 0 None 3.44 0.24 0.21

Clusters per variable 1 18 8.73 1.00 288 6.75e+18 43.36 8.46 0.97 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	15	15	15.00	15.00	270	1.48e+21	48.74	0.00	0.00	0.00
Variables per cluster	16	16	16.00	16.00	288	4.72e+21	49.91	0.00	0.00	0.00
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	15	14.17	15.00	255	0	None	3.44	0.24	0.21
Clusters per variable	1	18	8.73	1.00	288	6.75e+18	43.36	8.46	0.97	0.69

Primal graph

Density: 11.52%
MCB compute time (ms): 4,177
MCB cycles: 3,916
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/Primal1.json

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

Clustering coefficient 0.49 0.49 0.49 0.49 131.81 0.00 -193.61 0.00 0.00 0.00

Degree 31 31 31.00 31.00 8,370 MAX VALUE 927.18 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.06 3.00 11,986 MAX VALUE 4,370.63 0.24 0.08 0.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.49	0.49	0.49	131.81	0.00	-193.61	0.00	0.00	0.00
Degree	31	31	31.00	31.00	8,370	MAX VALUE	927.18	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.06	3.00	11,986	MAX VALUE	4,370.63	0.24	0.08	0.23

Triangulated primal graph

Density: 67.33%
MCB compute time (ms): 317,686
MCB cycles: 35,719
Triangles: None

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

Clustering coefficient 0.83 1.00 0.88 0.87 238.26 0.00 -34.21 0.05 0.06 3.15

Degree 31 230 181.12 202.00 48,902 MAX VALUE 1,375.30 61.38 0.34 3.04

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 107,157 MAX VALUE 39,241.30 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.83	1.00	0.88	0.87	238.26	0.00	-34.21	0.05	0.06	3.15
Degree	31	230	181.12	202.00	48,902	MAX VALUE	1,375.30	61.38	0.34	3.04
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	107,157	MAX VALUE	39,241.30	0.00	0.00	0.00

Dual graph

Density: 51.14%
MCB compute time (ms): 3
MCB cycles: 238
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/Dual1.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 15 18 16.36 15.00 540 MAX VALUE 92.10 1.49 0.09 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 952 MAX VALUE 329.94 0.00 0.00 0.00

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	15	18	16.36	15.00	540	MAX VALUE	92.10	1.49	0.09	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	952	MAX VALUE	329.94	0.00	0.00	0.00

Minimal dual graph

Density: 51.14%
MCB compute time (ms): 3
MCB cycles: 238

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 15 18 16.36 15.00 540 MAX VALUE 92.10 1.49 0.09 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 952 MAX VALUE 329.94 0.00 0.00 0.00

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	15	18	16.36	15.00	540	MAX VALUE	92.10	1.49	0.09	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	952	MAX VALUE	329.94	0.00	0.00	0.00

Triangulated dual graph

Density: 71.02%
Triangles: 2,345

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

Clustering coefficient 0.69 1.00 0.86 1.00 28.37 0.00 -5.53 0.15 0.18 0.69

Degree 15 32 22.73 15.00 750 MAX VALUE 100.73 8.46 0.37 0.69

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	0.69	1.00	0.86	1.00	28.37	0.00	-5.53	0.15	0.18	0.69
Degree	15	32	22.73	15.00	750	MAX VALUE	100.73	8.46	0.37	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 71.02%

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

Clustering coefficient 0.69 1.00 0.86 1.00 28.37 0.00 -5.53 0.15 0.18 0.69

Degree 15 32 22.73 15.00 750 MAX VALUE 100.73 8.46 0.37 0.69

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	0.69	1.00	0.86	1.00	28.37	0.00	-5.53	0.15	0.18	0.69
Degree	15	32	22.73	15.00	750	MAX VALUE	100.73	8.46	0.37	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.18%
MCB compute time (ms): 118
MCB cycles: 238
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-18-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 18 3.56 2.00 1,080 MAX VALUE 279.25 4.50 1.26 0.42

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,904 MAX VALUE 494.91 0.00 0.00 0.00

XCSP 2.1 Benchmarks