XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg7-8-ext
Number of variables: 56
Number of constraints: 15
Satisfiable: True
Timestamp: 2025-07-20 22:08:36
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 56
Number of constraints: 15

General features

Coarse blocks: 2,814
Value tables: 56

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

Arity 7 8 7.47 7.00 112 1.21e+13 30.12 0.50 0.07 0.69

Coarse blocks size 1 875 152.22 111.00 428,344 MAX VALUE 12,284.60 149.31 0.98 5.27

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -25,316.90 0.00 0.96 4.88

Tightness 1.00 1.00 1.00 1.00 15.00 1.00 -0.00 0.00 0.00 0.69

Tuples 3,607 4,042 3,839.00 4,042.00 57,585 MAX VALUE 123.77 217.02 0.06 0.69

Values 26 26 26.00 26.00 1,456 MAX VALUE 182.45 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 112 7.21e+16 38.82 0.00 0.00 0.00

Value table partitions 24 26 25.79 26.00 1,444 MAX VALUE 181.98 0.56 0.02 0.51

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	7	8	7.47	7.00	112	1.21e+13	30.12	0.50	0.07	0.69
Coarse blocks size	1	875	152.22	111.00	428,344	MAX VALUE	12,284.60	149.31	0.98	5.27
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-25,316.90	0.00	0.96	4.88
Tightness	1.00	1.00	1.00	1.00	15.00	1.00	-0.00	0.00	0.00	0.69
Tuples	3,607	4,042	3,839.00	4,042.00	57,585	MAX VALUE	123.77	217.02	0.06	0.69
Values	26	26	26.00	26.00	1,456	MAX VALUE	182.45	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	112	7.21e+16	38.82	0.00	0.00	0.00
Value table partitions	24	26	25.79	26.00	1,444	MAX VALUE	181.98	0.56	0.02	0.51

Tree decomposition

Number of clusters: 13
Number of leaves: 7
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/Tree1.json

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

Cluster constraints 0 2 1.15 2.00 15 0 None 0.95 0.82 0.90

Variables per cluster 14 36 19.92 14.00 259 3.39e+16 38.06 7.61 0.38 1.26

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

Separator variables 0 28 15.62 13.00 203 0 None 6.64 0.43 1.26

Clusters per var 1 6 4.62 5.00 259 1.69e+34 78.81 1.71 0.37 1.41

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.15	2.00	15	0	None	0.95	0.82	0.90
Variables per cluster	14	36	19.92	14.00	259	3.39e+16	38.06	7.61	0.38	1.26
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	28	15.62	13.00	203	0	None	6.64	0.43	1.26
Clusters per var	1	6	4.62	5.00	259	1.69e+34	78.81	1.71	0.37	1.41

Dual tree decomposition

Number of clusters: 8
Number of leaves: 2
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/DualTree1.json

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

Cluster constraints 7 7 7.00 7.00 56 5,764,800 15.57 0.00 0.00 0.00

Variables per cluster 8 8 8.00 8.00 64 16,777,200 16.64 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 7 6.12 7.00 49 0 None 2.32 0.38 0.38

Clusters per variable 1 8 4.27 1.00 64 2,097,150 14.56 3.49 0.82 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	7	7.00	7.00	56	5,764,800	15.57	0.00	0.00	0.00
Variables per cluster	8	8	8.00	8.00	64	16,777,200	16.64	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	7	6.12	7.00	49	0	None	2.32	0.38	0.38
Clusters per variable	1	8	4.27	1.00	64	2,097,150	14.56	3.49	0.82	0.69

Primal graph

Density: 23.64%
MCB compute time (ms): 11
MCB cycles: 309
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/Primal1.json

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

Clustering coefficient 0.46 0.46 0.46 0.46 25.85 0.00 -43.30 0.00 0.00 0.00

Degree 13 13 13.00 13.00 728 MAX VALUE 143.64 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.14 3.00 969 MAX VALUE 351.55 0.34 0.11 0.40

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.46	0.46	0.46	0.46	25.85	0.00	-43.30	0.00	0.00	0.00
Degree	13	13	13.00	13.00	728	MAX VALUE	143.64	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.14	3.00	969	MAX VALUE	351.55	0.34	0.11	0.40

Triangulated primal graph

Density: 68.64%
MCB compute time (ms): 64
MCB cycles: 1,069
Triangles: None

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

Clustering coefficient 0.82 1.00 0.87 0.86 48.75 0.00 -7.90 0.06 0.07 1.98

Degree 13 47 37.75 43.00 2,114 MAX VALUE 199.15 11.82 0.31 1.98

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 3,207 MAX VALUE 1,174.42 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	0.87	0.86	48.75	0.00	-7.90	0.06	0.07	1.98
Degree	13	47	37.75	43.00	2,114	MAX VALUE	199.15	11.82	0.31	1.98
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	3,207	MAX VALUE	1,174.42	0.00	0.00	0.00

Dual graph

Density: 53.33%
MCB compute time (ms): 0
MCB cycles: 42
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-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 7 8 7.47 7.00 112 1.21e+13 30.12 0.50 0.07 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 168 1.93e+25 58.22 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	7	8	7.47	7.00	112	1.21e+13	30.12	0.50	0.07	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	168	1.93e+25	58.22	0.00	0.00	0.00

Minimal dual graph

Density: 53.33%
MCB compute time (ms): 0
MCB cycles: 42

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 7 8 7.47 7.00 112 1.21e+13 30.12 0.50 0.07 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 168 1.93e+25 58.22 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	7	8	7.47	7.00	112	1.21e+13	30.12	0.50	0.07	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	168	1.93e+25	58.22	0.00	0.00	0.00

Triangulated dual graph

Density: 73.33%
Triangles: 203

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

Clustering coefficient 0.69 1.00 0.86 1.00 12.85 0.08 -2.57 0.15 0.18 0.69

Degree 7 14 10.27 7.00 154 6.08e+14 34.04 3.49 0.34 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	12.85	0.08	-2.57	0.15	0.18	0.69
Degree	7	14	10.27	7.00	154	6.08e+14	34.04	3.49	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 73.33%

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

Clustering coefficient 0.69 1.00 0.86 1.00 12.85 0.08 -2.57 0.15 0.18 0.69

Degree 7 14 10.27 7.00 154 6.08e+14 34.04 3.49 0.34 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	12.85	0.08	-2.57	0.15	0.18	0.69
Degree	7	14	10.27	7.00	154	6.08e+14	34.04	3.49	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 4.51%
MCB compute time (ms): 3
MCB cycles: 42
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-8-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 8 3.15 2.00 224 8.71e+29 68.94 2.24 0.71 0.66

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 336 8.51e+37 87.34 0.00 0.00 0.00

XCSP 2.1 Benchmarks