XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg13-16-ext
Number of variables: 208
Number of constraints: 29
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 208
Number of constraints: 29

General features

Coarse blocks: 6,223
Value tables: 208

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

Arity 13 16 14.34 13.00 416 3.00e+33 77.08 1.49 0.10 0.69

Coarse blocks size 1 79 9.89 4.00 61,568 MAX VALUE 9,748.53 12.09 1.22 2.99

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -92,869.80 0.00 0.60 1.20

Tightness 1.00 1.00 1.00 1.00 29.00 1.00 -0.00 0.00 0.00 0.69

Tuples 17 279 161.55 279.00 4,685 MAX VALUE 126.93 130.30 0.81 0.69

Values 26 26 26.00 26.00 5,408 MAX VALUE 677.68 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 416 MAX VALUE 144.18 0.00 0.00 0.00

Value table partitions 15 24 20.70 21.00 4,306 MAX VALUE 629.24 2.02 0.10 2.02

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	13	16	14.34	13.00	416	3.00e+33	77.08	1.49	0.10	0.69
Coarse blocks size	1	79	9.89	4.00	61,568	MAX VALUE	9,748.53	12.09	1.22	2.99
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-92,869.80	0.00	0.60	1.20
Tightness	1.00	1.00	1.00	1.00	29.00	1.00	-0.00	0.00	0.00	0.69
Tuples	17	279	161.55	279.00	4,685	MAX VALUE	126.93	130.30	0.81	0.69
Values	26	26	26.00	26.00	5,408	MAX VALUE	677.68	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	416	MAX VALUE	144.18	0.00	0.00	0.00
Value table partitions	15	24	20.70	21.00	4,306	MAX VALUE	629.24	2.02	0.10	2.02

Tree decomposition

Number of clusters: 27
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-vg13-16-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-ext/Tree1.json

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

Cluster constraints 0 2 1.07 1.00 29 0 None 0.94 0.88 0.96

Variables per cluster 28 132 49.59 39.00 1,339 MAX VALUE 101.53 30.13 0.61 1.59

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

Separator variables 0 104 41.89 27.00 1,131 0 None 22.98 0.55 1.59

Clusters per var 1 8 6.44 7.00 1,339 MAX VALUE 366.95 2.03 0.32 1.58

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.07	1.00	29	0	None	0.94	0.88	0.96
Variables per cluster	28	132	49.59	39.00	1,339	MAX VALUE	101.53	30.13	0.61	1.59
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	104	41.89	27.00	1,131	0	None	22.98	0.55	1.59
Clusters per var	1	8	6.44	7.00	1,339	MAX VALUE	366.95	2.03	0.32	1.58

Dual tree decomposition

Number of clusters: 16
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-vg13-16-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-ext/DualTree1.json

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

Cluster constraints 13 13 13.00 13.00 208 6.65e+17 41.04 0.00 0.00 0.00

Variables per cluster 14 14 14.00 14.00 224 2.18e+18 42.22 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 12.19 13.00 195 0 None 3.15 0.26 0.23

Clusters per variable 1 16 7.72 1.00 224 4.50e+15 36.04 7.46 0.97 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	13	13	13.00	13.00	208	6.65e+17	41.04	0.00	0.00	0.00
Variables per cluster	14	14	14.00	14.00	224	2.18e+18	42.22	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	12.19	13.00	195	0	None	3.15	0.26	0.23
Clusters per variable	1	16	7.72	1.00	224	4.50e+15	36.04	7.46	0.97	0.69

Primal graph

Density: 13.04%
MCB compute time (ms): 1,748
MCB cycles: 2,601
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-ext/Primal1.json

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

Clustering coefficient 0.49 0.49 0.49 0.49 101.33 0.00 -149.58 0.00 0.00 0.00

Degree 27 27 27.00 27.00 5,616 MAX VALUE 685.53 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 7,983 MAX VALUE 2,909.27 0.25 0.08 0.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.49	0.49	0.49	101.33	0.00	-149.58	0.00	0.00	0.00
Degree	27	27	27.00	27.00	5,616	MAX VALUE	685.53	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	7,983	MAX VALUE	2,909.27	0.25	0.08	0.25

Triangulated primal graph

Density: 67.53%
MCB compute time (ms): 47,715
MCB cycles: 16,473
Triangles: None

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

Clustering coefficient 0.83 1.00 0.88 0.87 183.34 0.00 -26.60 0.05 0.06 2.87

Degree 27 177 139.78 159.50 29,074 MAX VALUE 1,006.55 46.94 0.34 2.84

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 49,419 MAX VALUE 18,097.40 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	183.34	0.00	-26.60	0.05	0.06	2.87
Degree	27	177	139.78	159.50	29,074	MAX VALUE	1,006.55	46.94	0.34	2.84
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	49,419	MAX VALUE	18,097.40	0.00	0.00	0.00

Dual graph

Density: 51.23%
MCB compute time (ms): 2
MCB cycles: 180
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-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 16 14.34 13.00 416 3.00e+33 77.08 1.49 0.10 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 720 MAX VALUE 249.53 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	16	14.34	13.00	416	3.00e+33	77.08	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	720	MAX VALUE	249.53	0.00	0.00	0.00

Minimal dual graph

Density: 51.23%
MCB compute time (ms): 2
MCB cycles: 180

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 16 14.34 13.00 416 3.00e+33 77.08 1.49 0.10 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 720 MAX VALUE 249.53 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	16	14.34	13.00	416	3.00e+33	77.08	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	720	MAX VALUE	249.53	0.00	0.00	0.00

Triangulated dual graph

Density: 70.44%
Triangles: 1,534

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

Clustering coefficient 0.68 1.00 0.86 1.00 24.87 0.01 -4.97 0.16 0.18 0.69

Degree 13 28 19.72 13.00 572 4.33e+36 84.36 7.46 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	0.68	1.00	0.86	1.00	24.87	0.01	-4.97	0.16	0.18	0.69
Degree	13	28	19.72	13.00	572	4.33e+36	84.36	7.46	0.38	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 70.44%

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

Clustering coefficient 0.68 1.00 0.86 1.00 24.87 0.01 -4.97 0.16 0.18 0.69

Degree 13 28 19.72 13.00 572 4.33e+36 84.36 7.46 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	0.68	1.00	0.86	1.00	24.87	0.01	-4.97	0.16	0.18	0.69
Degree	13	28	19.72	13.00	572	4.33e+36	84.36	7.46	0.38	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 77
MCB cycles: 180
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-16-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 16 3.51 2.00 832 MAX VALUE 221.26 4.08 1.16 0.46

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,440 MAX VALUE 374.30 0.00 0.00 0.00

XCSP 2.1 Benchmarks