XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg12-14-ext
Number of variables: 168
Number of constraints: 26
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 168
Number of constraints: 26

General features

Coarse blocks: 6,650
Value tables: 168

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

Arity 12 14 12.92 12.00 336 7.28e+28 66.46 1.00 0.08 0.69

Coarse blocks size 1 170 17.91 9.00 119,112 MAX VALUE 14,502.70 22.15 1.24 3.67

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -115,338.00 0.00 0.84 2.76

Tightness 1.00 1.00 1.00 1.00 26.00 1.00 -0.00 0.00 0.00 0.69

Tuples 116 593 372.85 593.00 9,694 MAX VALUE 146.44 237.79 0.64 0.69

Values 26 26 26.00 26.00 4,368 MAX VALUE 547.36 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 336 MAX VALUE 116.45 0.00 0.00 0.00

Value table partitions 18 26 22.76 23.00 3,823 MAX VALUE 524.53 1.62 0.07 1.83

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	12	14	12.92	12.00	336	7.28e+28	66.46	1.00	0.08	0.69
Coarse blocks size	1	170	17.91	9.00	119,112	MAX VALUE	14,502.70	22.15	1.24	3.67
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-115,338.00	0.00	0.84	2.76
Tightness	1.00	1.00	1.00	1.00	26.00	1.00	-0.00	0.00	0.00	0.69
Tuples	116	593	372.85	593.00	9,694	MAX VALUE	146.44	237.79	0.64	0.69
Values	26	26	26.00	26.00	4,368	MAX VALUE	547.36	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	336	MAX VALUE	116.45	0.00	0.00	0.00
Value table partitions	18	26	22.76	23.00	3,823	MAX VALUE	524.53	1.62	0.07	1.83

Tree decomposition

Number of clusters: 24
Number of leaves: 12
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-ext/Tree1.json

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

Cluster constraints 0 2 1.08 1.50 26 0 None 0.95 0.88 0.92

Variables per cluster 25 108 43.00 30.00 1,032 6.65e+37 87.09 24.76 0.58 1.48

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

Separator variables 0 84 36.00 24.00 864 0 None 19.17 0.53 1.48

Clusters per var 1 8 6.14 7.00 1,032 MAX VALUE 287.50 2.02 0.33 1.72

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.08	1.50	26	0	None	0.95	0.88	0.92
Variables per cluster	25	108	43.00	30.00	1,032	6.65e+37	87.09	24.76	0.58	1.48
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	84	36.00	24.00	864	0	None	19.17	0.53	1.48
Clusters per var	1	8	6.14	7.00	1,032	MAX VALUE	287.50	2.02	0.33	1.72

Dual tree decomposition

Number of clusters: 14
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-vg12-14-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-ext/DualTree1.json

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

Cluster constraints 12 12 12.00 12.00 168 1.28e+15 34.79 0.00 0.00 0.00

Variables per cluster 13 13 13.00 13.00 182 3.94e+15 35.91 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 12 11.14 12.00 156 0 None 3.09 0.28 0.26

Clusters per variable 1 14 7.00 1.00 182 5.67e+13 31.67 6.48 0.93 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	12	12	12.00	12.00	168	1.28e+15	34.79	0.00	0.00	0.00
Variables per cluster	13	13	13.00	13.00	182	3.94e+15	35.91	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	12	11.14	12.00	156	0	None	3.09	0.28	0.26
Clusters per variable	1	14	7.00	1.00	182	5.67e+13	31.67	6.48	0.93	0.69

Primal graph

Density: 14.37%
MCB compute time (ms): 716
MCB cycles: 1,849
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-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 80.96 0.00 -122.65 0.00 0.00 0.00

Degree 24 24 24.00 24.00 4,032 MAX VALUE 533.91 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.08 3.00 5,690 MAX VALUE 2,072.47 0.27 0.09 0.27

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.48	0.48	0.48	80.96	0.00	-122.65	0.00	0.00	0.00
Degree	24	24	24.00	24.00	4,032	MAX VALUE	533.91	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.08	3.00	5,690	MAX VALUE	2,072.47	0.27	0.09	0.27

Triangulated primal graph

Density: 67.70%
MCB compute time (ms): 12,071
MCB cycles: 10,810
Triangles: None

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

Clustering coefficient 0.82 1.00 0.88 0.88 147.92 0.00 -21.69 0.05 0.06 2.47

Degree 24 145 113.06 127.50 18,994 MAX VALUE 777.96 37.63 0.33 2.47

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 32,430 MAX VALUE 11,876.00 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	0.88	147.92	0.00	-21.69	0.05	0.06	2.47
Degree	24	145	113.06	127.50	18,994	MAX VALUE	777.96	37.63	0.33	2.47
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	32,430	MAX VALUE	11,876.00	0.00	0.00	0.00

Dual graph

Density: 51.69%
MCB compute time (ms): 1
MCB cycles: 143
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-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 12 14 12.92 12.00 336 7.28e+28 66.46 1.00 0.08 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 572 MAX VALUE 198.24 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	12	14	12.92	12.00	336	7.28e+28	66.46	1.00	0.08	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	572	MAX VALUE	198.24	0.00	0.00	0.00

Minimal dual graph

Density: 51.69%
MCB compute time (ms): 1
MCB cycles: 143

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 12 14 12.92 12.00 336 7.28e+28 66.46 1.00 0.08 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 572 MAX VALUE 198.24 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	12	14	12.92	12.00	336	7.28e+28	66.46	1.00	0.08	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	572	MAX VALUE	198.24	0.00	0.00	0.00

Triangulated dual graph

Density: 72.00%
Triangles: 1,144

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

Clustering coefficient 0.70 1.00 0.86 1.00 22.36 0.01 -4.34 0.15 0.18 0.69

Degree 12 25 18.00 12.00 468 7.65e+31 73.42 6.48 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	22.36	0.01	-4.34	0.15	0.18	0.69
Degree	12	25	18.00	12.00	468	7.65e+31	73.42	6.48	0.36	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 72.00%

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

Clustering coefficient 0.70 1.00 0.86 1.00 22.36 0.01 -4.34 0.15 0.18 0.69

Degree 12 25 18.00 12.00 468 7.65e+31 73.42 6.48 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	22.36	0.01	-4.34	0.15	0.18	0.69
Degree	12	25	18.00	12.00	468	7.65e+31	73.42	6.48	0.36	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.79%
MCB compute time (ms): 40
MCB cycles: 143
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-14-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 14 3.46 2.00 672 MAX VALUE 182.91 3.74 1.08 0.49

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,144 MAX VALUE 297.36 0.00 0.00 0.00

XCSP 2.1 Benchmarks