XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg8-9-ext
Number of variables: 72
Number of constraints: 17
Satisfiable: True
Timestamp: 2025-07-20 22:08:36
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 72
Number of constraints: 17

General features

Coarse blocks: 3,650
Value tables: 72

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

Arity 8 9 8.47 8.00 144 5.78e+15 36.29 0.50 0.06 0.69

Coarse blocks size 1 861 132.07 89.00 482,040 MAX VALUE 15,122.00 134.68 1.02 5.22

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -39,303.70 0.00 1.02 4.87

Tightness 1.00 1.00 1.00 1.00 17.00 1.00 -0.00 0.00 0.00 0.69

Tuples 3,088 3,607 3,362.76 3,607.00 57,167 MAX VALUE 138.00 259.05 0.08 0.69

Values 26 26 26.00 26.00 1,872 MAX VALUE 234.58 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 144 4.72e+21 49.91 0.00 0.00 0.00

Value table partitions 24 26 25.86 26.00 1,862 MAX VALUE 234.18 0.48 0.02 0.34

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	8	9	8.47	8.00	144	5.78e+15	36.29	0.50	0.06	0.69
Coarse blocks size	1	861	132.07	89.00	482,040	MAX VALUE	15,122.00	134.68	1.02	5.22
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-39,303.70	0.00	1.02	4.87
Tightness	1.00	1.00	1.00	1.00	17.00	1.00	-0.00	0.00	0.00	0.69
Tuples	3,088	3,607	3,362.76	3,607.00	57,167	MAX VALUE	138.00	259.05	0.08	0.69
Values	26	26	26.00	26.00	1,872	MAX VALUE	234.58	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	144	4.72e+21	49.91	0.00	0.00	0.00
Value table partitions	24	26	25.86	26.00	1,862	MAX VALUE	234.18	0.48	0.02	0.34

Tree decomposition

Number of clusters: 15
Number of leaves: 8
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/Tree1.json

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

Cluster constraints 0 2 1.13 2.00 17 0 None 0.96 0.84 0.88

Variables per cluster 16 46 23.80 16.00 357 1.39e+20 46.38 10.09 0.42 1.38

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

Separator variables 0 36 19.00 15.00 285 0 None 8.37 0.44 1.38

Clusters per var 1 7 4.96 6.00 357 MAX VALUE 106.59 1.79 0.36 1.55

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.13	2.00	17	0	None	0.96	0.84	0.88
Variables per cluster	16	46	23.80	16.00	357	1.39e+20	46.38	10.09	0.42	1.38
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	36	19.00	15.00	285	0	None	8.37	0.44	1.38
Clusters per var	1	7	4.96	6.00	357	MAX VALUE	106.59	1.79	0.36	1.55

Dual tree decomposition

Number of clusters: 9
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-vg8-9-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/DualTree1.json

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

Cluster constraints 8 8 8.00 8.00 72 134,218,000 18.71 0.00 0.00 0.00

Variables per cluster 9 9 9.00 9.00 81 387,420,000 19.77 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 8 7.11 8.00 64 0 None 2.51 0.35 0.35

Clusters per variable 1 9 4.76 1.00 81 43,046,700 17.58 3.99 0.84 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	8	8	8.00	8.00	72	134,218,000	18.71	0.00	0.00	0.00
Variables per cluster	9	9	9.00	9.00	81	387,420,000	19.77	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	8	7.11	8.00	64	0	None	2.51	0.35	0.35
Clusters per variable	1	9	4.76	1.00	81	43,046,700	17.58	3.99	0.84	0.69

Primal graph

Density: 21.13%
MCB compute time (ms): 29
MCB cycles: 469
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/Primal1.json

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

Clustering coefficient 0.47 0.47 0.47 0.47 33.60 0.00 -54.87 0.00 0.00 0.00

Degree 15 15 15.00 15.00 1,080 MAX VALUE 194.98 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.12 3.00 1,463 MAX VALUE 531.36 0.32 0.10 0.37

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.47	0.47	0.47	33.60	0.00	-54.87	0.00	0.00	0.00
Degree	15	15	15.00	15.00	1,080	MAX VALUE	194.98	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.12	3.00	1,463	MAX VALUE	531.36	0.32	0.10	0.37

Triangulated primal graph

Density: 68.23%
MCB compute time (ms): 91
MCB cycles: 2,224
Triangles: None

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

Clustering coefficient 0.81 1.00 0.87 0.85 62.86 0.00 -9.93 0.06 0.07 2.32

Degree 15 61 48.44 56.00 3,488 MAX VALUE 273.58 15.50 0.32 2.16

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 6,672 MAX VALUE 2,443.31 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.81	1.00	0.87	0.85	62.86	0.00	-9.93	0.06	0.07	2.32
Degree	15	61	48.44	56.00	3,488	MAX VALUE	273.58	15.50	0.32	2.16
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	6,672	MAX VALUE	2,443.31	0.00	0.00	0.00

Dual graph

Density: 52.94%
MCB compute time (ms): 0
MCB cycles: 56
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-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 8 9 8.47 8.00 144 5.78e+15 36.29 0.50 0.06 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 224 5.19e+33 77.63 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	8	9	8.47	8.00	144	5.78e+15	36.29	0.50	0.06	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	224	5.19e+33	77.63	0.00	0.00	0.00

Minimal dual graph

Density: 52.94%
MCB compute time (ms): 0
MCB cycles: 56

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 8 9 8.47 8.00 144 5.78e+15 36.29 0.50 0.06 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 224 5.19e+33 77.63 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	8	9	8.47	8.00	144	5.78e+15	36.29	0.50	0.06	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	224	5.19e+33	77.63	0.00	0.00	0.00

Triangulated dual graph

Density: 73.53%
Triangles: 308

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

Clustering coefficient 0.70 1.00 0.86 1.00 14.60 0.06 -2.85 0.15 0.17 0.69

Degree 8 16 11.76 8.00 200 5.76e+17 40.90 3.99 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	0.70	1.00	0.86	1.00	14.60	0.06	-2.85	0.15	0.17	0.69
Degree	8	16	11.76	8.00	200	5.76e+17	40.90	3.99	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 73.53%

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

Clustering coefficient 0.70 1.00 0.86 1.00 14.60 0.06 -2.85 0.15 0.17 0.69

Degree 8 16 11.76 8.00 200 5.76e+17 40.90 3.99 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	0.70	1.00	0.86	1.00	14.60	0.06	-2.85	0.15	0.17	0.69
Degree	8	16	11.76	8.00	200	5.76e+17	40.90	3.99	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 3.68%
MCB compute time (ms): 6
MCB cycles: 56
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-9-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 9 3.24 2.00 288 2.73e+37 86.20 2.55 0.79 0.62

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 448 MAX VALUE 116.45 0.00 0.00 0.00

XCSP 2.1 Benchmarks