XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg13-15-ext
Number of variables: 195
Number of constraints: 28
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 195
Number of constraints: 28

General features

Coarse blocks: 6,597
Value tables: 195

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

Arity 13 15 13.93 13.00 390 9.96e+31 73.68 1.00 0.07 0.69

Coarse blocks size 1 79 9.55 5.00 62,985 MAX VALUE 10,792.80 11.40 1.19 3.05

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -111,104.00 0.00 0.73 2.00

Tightness 1.00 1.00 1.00 1.00 28.00 1.00 -0.00 0.00 0.00 0.69

Tuples 44 279 169.89 279.00 4,757 MAX VALUE 133.66 117.20 0.69 0.69

Values 26 26 26.00 26.00 5,070 MAX VALUE 635.33 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 390 MAX VALUE 135.16 0.00 0.00 0.00

Value table partitions 17 25 21.07 21.00 4,109 MAX VALUE 593.61 1.80 0.09 1.96

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	13	15	13.93	13.00	390	9.96e+31	73.68	1.00	0.07	0.69
Coarse blocks size	1	79	9.55	5.00	62,985	MAX VALUE	10,792.80	11.40	1.19	3.05
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-111,104.00	0.00	0.73	2.00
Tightness	1.00	1.00	1.00	1.00	28.00	1.00	-0.00	0.00	0.00	0.69
Tuples	44	279	169.89	279.00	4,757	MAX VALUE	133.66	117.20	0.69	0.69
Values	26	26	26.00	26.00	5,070	MAX VALUE	635.33	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	390	MAX VALUE	135.16	0.00	0.00	0.00
Value table partitions	17	25	21.07	21.00	4,109	MAX VALUE	593.61	1.80	0.09	1.96

Tree decomposition

Number of clusters: 26
Number of leaves: 13
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/Tree1.json

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

Cluster constraints 0 2 1.08 1.50 28 0 None 0.96 0.89 0.91

Variables per cluster 27 125 47.46 32.50 1,234 MAX VALUE 96.69 28.38 0.60 1.56

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

Separator variables 0 97 39.96 26.00 1,039 0 None 21.76 0.54 1.56

Clusters per var 1 8 6.33 7.00 1,234 MAX VALUE 340.09 2.04 0.32 1.64

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.08	1.50	28	0	None	0.96	0.89	0.91
Variables per cluster	27	125	47.46	32.50	1,234	MAX VALUE	96.69	28.38	0.60	1.56
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	97	39.96	26.00	1,039	0	None	21.76	0.54	1.56
Clusters per var	1	8	6.33	7.00	1,234	MAX VALUE	340.09	2.04	0.32	1.64

Dual tree decomposition

Number of clusters: 15
Number of leaves: 2
Tree depth: 7
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/DualTree1.json

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

Cluster constraints 13 13 13.00 13.00 195 5.12e+16 38.47 0.00 0.00 0.00

Variables per cluster 14 14 14.00 14.00 210 1.56e+17 39.59 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 13 12.13 13.00 182 0 None 3.24 0.27 0.24

Clusters per variable 1 15 7.50 1.00 210 1.95e+15 35.20 6.98 0.93 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	13	13	13.00	13.00	195	5.12e+16	38.47	0.00	0.00	0.00
Variables per cluster	14	14	14.00	14.00	210	1.56e+17	39.59	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	13	12.13	13.00	182	0	None	3.24	0.27	0.24
Clusters per variable	1	15	7.50	1.00	210	1.95e+15	35.20	6.98	0.93	0.69

Primal graph

Density: 13.40%
MCB compute time (ms): 1,454
MCB cycles: 2,341
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/Primal1.json

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

Clustering coefficient 0.48 0.48 0.48 0.48 94.20 0.00 -141.88 0.00 0.00 0.00

Degree 26 26 26.00 26.00 5,070 MAX VALUE 635.33 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.07 3.00 7,191 MAX VALUE 2,620.18 0.26 0.08 0.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.48	0.48	0.48	94.20	0.00	-141.88	0.00	0.00	0.00
Degree	26	26	26.00	26.00	5,070	MAX VALUE	635.33	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.07	3.00	7,191	MAX VALUE	2,620.18	0.26	0.08	0.26

Triangulated primal graph

Density: 67.35%
MCB compute time (ms): 24,777
MCB cycles: 14,625
Triangles: None

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

Clustering coefficient 0.82 1.00 0.88 0.87 171.69 0.00 -25.17 0.05 0.06 2.97

Degree 26 166 130.67 144.00 25,480 MAX VALUE 930.59 43.95 0.34 2.84

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 43,875 MAX VALUE 16,067.20 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	171.69	0.00	-25.17	0.05	0.06	2.97
Degree	26	166	130.67	144.00	25,480	MAX VALUE	930.59	43.95	0.34	2.84
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	43,875	MAX VALUE	16,067.20	0.00	0.00	0.00

Dual graph

Density: 51.59%
MCB compute time (ms): 2
MCB cycles: 168
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-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 13 15 13.93 13.00 390 9.96e+31 73.68 1.00 0.07 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 672 MAX VALUE 232.90 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	13	15	13.93	13.00	390	9.96e+31	73.68	1.00	0.07	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	672	MAX VALUE	232.90	0.00	0.00	0.00

Minimal dual graph

Density: 51.59%
MCB compute time (ms): 1
MCB cycles: 168

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 13 15 13.93 13.00 390 9.96e+31 73.68 1.00 0.07 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 672 MAX VALUE 232.90 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	13	15	13.93	13.00	390	9.96e+31	73.68	1.00	0.07	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	672	MAX VALUE	232.90	0.00	0.00	0.00

Triangulated dual graph

Density: 72.22%
Triangles: 1,456

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

Clustering coefficient 0.70 1.00 0.86 1.00 24.11 0.01 -4.62 0.15 0.17 0.69

Degree 13 27 19.50 13.00 546 2.07e+35 81.32 6.98 0.36 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	0.70	1.00	0.86	1.00	24.11	0.01	-4.62	0.15	0.17	0.69
Degree	13	27	19.50	13.00	546	2.07e+35	81.32	6.98	0.36	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 72.22%

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

Clustering coefficient 0.70 1.00 0.86 1.00 24.11 0.01 -4.62 0.15 0.17 0.69

Degree 13 27 19.50 13.00 546 2.07e+35 81.32 6.98 0.36 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	0.70	1.00	0.86	1.00	24.11	0.01	-4.62	0.15	0.17	0.69
Degree	13	27	19.50	13.00	546	2.07e+35	81.32	6.98	0.36	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.58%
MCB compute time (ms): 65
MCB cycles: 168
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-15-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 15 3.50 2.00 780 MAX VALUE 208.84 3.97 1.13 0.46

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,344 MAX VALUE 349.35 0.00 0.00 0.00

XCSP 2.1 Benchmarks