XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg14-17-ext
Number of variables: 238
Number of constraints: 31
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 238
Number of constraints: 31

General features

Coarse blocks: 5,369
Value tables: 238

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

Arity 14 17 15.35 14.00 476 5.13e+36 84.53 1.49 0.10 0.69

Coarse blocks size 1 40 5.45 3.00 29,274 MAX VALUE 6,635.11 5.46 1.00 2.52

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -58,102.10 0.00 0.44 0.80

Tightness 1.00 1.00 1.00 1.00 31.00 1.00 0.00 0.00 0.00 0.00

Tuples 7 116 66.77 116.00 2,070 MAX VALUE 108.05 54.24 0.81 0.69

Values 26 26 26.00 26.00 6,188 MAX VALUE 775.43 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 476 MAX VALUE 164.97 0.00 0.00 0.00

Value table partitions 14 21 17.85 18.00 4,249 MAX VALUE 685.00 1.58 0.09 1.82

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	14	17	15.35	14.00	476	5.13e+36	84.53	1.49	0.10	0.69
Coarse blocks size	1	40	5.45	3.00	29,274	MAX VALUE	6,635.11	5.46	1.00	2.52
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-58,102.10	0.00	0.44	0.80
Tightness	1.00	1.00	1.00	1.00	31.00	1.00	0.00	0.00	0.00	0.00
Tuples	7	116	66.77	116.00	2,070	MAX VALUE	108.05	54.24	0.81	0.69
Values	26	26	26.00	26.00	6,188	MAX VALUE	775.43	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	476	MAX VALUE	164.97	0.00	0.00	0.00
Value table partitions	14	21	17.85	18.00	4,249	MAX VALUE	685.00	1.58	0.09	1.82

Tree decomposition

Number of clusters: 29
Number of leaves: 14
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/Tree1.json

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

Cluster constraints 0 2 1.07 1.00 31 0 None 0.94 0.88 0.95

Variables per cluster 30 154 54.31 42.00 1,575 MAX VALUE 111.40 34.32 0.63 1.65

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

Separator variables 0 118 46.10 29.00 1,337 0 None 26.12 0.57 1.65

Clusters per var 1 9 6.62 7.00 1,575 MAX VALUE 427.01 2.06 0.31 1.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.07	1.00	31	0	None	0.94	0.88	0.95
Variables per cluster	30	154	54.31	42.00	1,575	MAX VALUE	111.40	34.32	0.63	1.65
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	118	46.10	29.00	1,337	0	None	26.12	0.57	1.65
Clusters per var	1	9	6.62	7.00	1,575	MAX VALUE	427.01	2.06	0.31	1.67

Dual tree decomposition

Number of clusters: 17
Number of leaves: 2
Tree depth: 8
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/DualTree1.json

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

Cluster constraints 14 14 14.00 14.00 238 3.05e+19 44.86 0.00 0.00 0.00

Variables per cluster 15 15 15.00 15.00 255 9.85e+19 46.04 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 14 13.18 14.00 224 0 None 3.29 0.25 0.22

Clusters per variable 1 17 8.23 1.00 255 1.68e+17 39.66 7.96 0.97 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	14	14	14.00	14.00	238	3.05e+19	44.86	0.00	0.00	0.00
Variables per cluster	15	15	15.00	15.00	255	9.85e+19	46.04	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	14	13.18	14.00	224	0	None	3.29	0.25	0.22
Clusters per variable	1	17	8.23	1.00	255	1.68e+17	39.66	7.96	0.97	0.69

Primal graph

Density: 12.24%
MCB compute time (ms): 2,496
MCB cycles: 3,214
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/Primal1.json

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

Clustering coefficient 0.49 0.49 0.49 0.49 116.07 0.00 -170.90 0.00 0.00 0.00

Degree 29 29 29.00 29.00 6,902 MAX VALUE 801.42 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 9,850 MAX VALUE 3,590.78 0.25 0.08 0.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.49	0.49	0.49	116.07	0.00	-170.90	0.00	0.00	0.00
Degree	29	29	29.00	29.00	6,902	MAX VALUE	801.42	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	9,850	MAX VALUE	3,590.78	0.25	0.08	0.24

Triangulated primal graph

Density: 67.41%
MCB compute time (ms): 7,270
MCB cycles: 30,482
Triangles: None

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

Clustering coefficient 0.82 1.00 0.88 0.87 209.92 0.00 -30.27 0.05 0.06 3.10

Degree 29 203 159.77 179.00 38,026 MAX VALUE 1,182.96 53.94 0.34 2.98

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 91,446 MAX VALUE 33,487.90 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.82	1.00	0.88	0.87	209.92	0.00	-30.27	0.05	0.06	3.10
Degree	29	203	159.77	179.00	38,026	MAX VALUE	1,182.96	53.94	0.34	2.98
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	91,446	MAX VALUE	33,487.90	0.00	0.00	0.00

Dual graph

Density: 51.18%
MCB compute time (ms): 2
MCB cycles: 208
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-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 14 17 15.35 14.00 476 5.13e+36 84.53 1.49 0.10 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 832 MAX VALUE 288.35 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	14	17	15.35	14.00	476	5.13e+36	84.53	1.49	0.10	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	832	MAX VALUE	288.35	0.00	0.00	0.00

Minimal dual graph

Density: 51.18%
MCB compute time (ms): 2
MCB cycles: 208

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 14 17 15.35 14.00 476 5.13e+36 84.53 1.49 0.10 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 832 MAX VALUE 288.35 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	14	17	15.35	14.00	476	5.13e+36	84.53	1.49	0.10	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	832	MAX VALUE	288.35	0.00	0.00	0.00

Triangulated dual graph

Density: 70.75%
Triangles: 1,911

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

Clustering coefficient 0.69 1.00 0.86 1.00 26.62 0.01 -5.25 0.16 0.18 0.69

Degree 14 30 21.23 14.00 658 MAX VALUE 92.48 7.96 0.38 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	26.62	0.01	-5.25	0.16	0.18	0.69
Degree	14	30	21.23	14.00	658	MAX VALUE	92.48	7.96	0.38	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 70.75%

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

Clustering coefficient 0.69 1.00 0.86 1.00 26.62 0.01 -5.25 0.16 0.18 0.69

Degree 14 30 21.23 14.00 658 MAX VALUE 92.48 7.96 0.38 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	26.62	0.01	-5.25	0.16	0.18	0.69
Degree	14	30	21.23	14.00	658	MAX VALUE	92.48	7.96	0.38	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.32%
MCB compute time (ms): 87
MCB cycles: 208
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-17-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 17 3.54 2.00 952 MAX VALUE 249.50 4.29 1.21 0.44

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,664 MAX VALUE 432.52 0.00 0.00 0.00

XCSP 2.1 Benchmarks