XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg10-11-ext
Number of variables: 110
Number of constraints: 21
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 110
Number of constraints: 21

General features

Coarse blocks: 5,308
Value tables: 110

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

Arity 10 11 10.48 10.00 220 2.59e+21 49.31 0.50 0.05 0.69

Coarse blocks size 1 538 64.06 41.00 340,010 MAX VALUE 18,093.00 70.02 1.09 4.79

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -73,501.50 0.00 1.02 4.39

Tightness 1.00 1.00 1.00 1.00 21.00 1.00 -0.00 0.00 0.00 0.69

Tuples 1,120 1,971 1,565.76 1,971.00 32,881 MAX VALUE 153.66 425.02 0.27 0.69

Values 26 26 26.00 26.00 2,860 MAX VALUE 358.39 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 220 1.30e+33 76.25 0.00 0.00 0.00

Value table partitions 22 26 25.49 26.00 2,804 MAX VALUE 356.15 0.87 0.03 0.94

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	10	11	10.48	10.00	220	2.59e+21	49.31	0.50	0.05	0.69
Coarse blocks size	1	538	64.06	41.00	340,010	MAX VALUE	18,093.00	70.02	1.09	4.79
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-73,501.50	0.00	1.02	4.39
Tightness	1.00	1.00	1.00	1.00	21.00	1.00	-0.00	0.00	0.00	0.69
Tuples	1,120	1,971	1,565.76	1,971.00	32,881	MAX VALUE	153.66	425.02	0.27	0.69
Values	26	26	26.00	26.00	2,860	MAX VALUE	358.39	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	220	1.30e+33	76.25	0.00	0.00	0.00
Value table partitions	22	26	25.49	26.00	2,804	MAX VALUE	356.15	0.87	0.03	0.94

Tree decomposition

Number of clusters: 19
Number of leaves: 10
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/Tree1.json

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

Cluster constraints 0 2 1.11 2.00 21 0 None 0.97 0.88 0.86

Variables per cluster 20 72 31.95 20.00 607 5.37e+27 63.85 15.91 0.50 1.37

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

Separator variables 0 52 26.16 19.00 497 0 None 12.50 0.48 1.37

Clusters per var 1 7 5.52 6.00 607 MAX VALUE 175.51 1.89 0.34 1.51

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.11	2.00	21	0	None	0.97	0.88	0.86
Variables per cluster	20	72	31.95	20.00	607	5.37e+27	63.85	15.91	0.50	1.37
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	52	26.16	19.00	497	0	None	12.50	0.48	1.37
Clusters per var	1	7	5.52	6.00	607	MAX VALUE	175.51	1.89	0.34	1.51

Dual tree decomposition

Number of clusters: 11
Number of leaves: 2
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/DualTree1.json

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

Cluster constraints 10 10 10.00 10.00 110 1.00e+11 25.33 0.00 0.00 0.00

Variables per cluster 11 11 11.00 11.00 121 2.85e+11 26.38 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 10 9.09 10.00 100 0 None 2.87 0.32 0.30

Clusters per variable 1 11 5.76 1.00 121 2.59e+10 23.98 4.99 0.87 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	10	10	10.00	10.00	110	1.00e+11	25.33	0.00	0.00	0.00
Variables per cluster	11	11	11.00	11.00	121	2.85e+11	26.38	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	10	9.09	10.00	100	0	None	2.87	0.32	0.30
Clusters per variable	1	11	5.76	1.00	121	2.59e+10	23.98	4.99	0.87	0.69

Primal graph

Density: 17.43%
MCB compute time (ms): 171
MCB cycles: 936
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-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 52.11 0.00 -82.19 0.00 0.00 0.00

Degree 19 19 19.00 19.00 2,090 MAX VALUE 323.89 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.10 3.00 2,898 MAX VALUE 1,054.19 0.29 0.10 0.32

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.47	0.47	0.47	52.11	0.00	-82.19	0.00	0.00	0.00
Degree	19	19	19.00	19.00	2,090	MAX VALUE	323.89	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.10	3.00	2,898	MAX VALUE	1,054.19	0.29	0.10	0.32

Triangulated primal graph

Density: 67.72%
MCB compute time (ms): 1,652
MCB cycles: 5,053
Triangles: None

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

Clustering coefficient 0.82 1.00 0.88 0.86 96.45 0.00 -14.67 0.06 0.06 1.96

Degree 19 93 73.82 86.00 8,120 MAX VALUE 463.25 24.29 0.33 1.82

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 15,159 MAX VALUE 5,551.29 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	0.86	96.45	0.00	-14.67	0.06	0.06	1.96
Degree	19	93	73.82	86.00	8,120	MAX VALUE	463.25	24.29	0.33	1.82
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	15,159	MAX VALUE	5,551.29	0.00	0.00	0.00

Dual graph

Density: 52.38%
MCB compute time (ms): 0
MCB cycles: 90
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-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 10 11 10.48 10.00 220 2.59e+21 49.31 0.50 0.05 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 360 MAX VALUE 124.77 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	10	11	10.48	10.00	220	2.59e+21	49.31	0.50	0.05	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	360	MAX VALUE	124.77	0.00	0.00	0.00

Minimal dual graph

Density: 52.38%
MCB compute time (ms): 0
MCB cycles: 90

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 10 11 10.48 10.00 220 2.59e+21 49.31 0.50 0.05 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 360 MAX VALUE 124.77 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	10	11	10.48	10.00	220	2.59e+21	49.31	0.50	0.05	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	360	MAX VALUE	124.77	0.00	0.00	0.00

Triangulated dual graph

Density: 73.81%
Triangles: 615

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

Clustering coefficient 0.71 1.00 0.86 1.00 18.11 0.03 -3.42 0.14 0.17 0.69

Degree 10 20 14.76 10.00 310 1.02e+24 55.29 4.99 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	0.71	1.00	0.86	1.00	18.11	0.03	-3.42	0.14	0.17	0.69
Degree	10	20	14.76	10.00	310	1.02e+24	55.29	4.99	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 73.81%

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

Clustering coefficient 0.71 1.00 0.86 1.00 18.11 0.03 -3.42 0.14 0.17 0.69

Degree 10 20 14.76 10.00 310 1.02e+24 55.29 4.99 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	0.71	1.00	0.86	1.00	18.11	0.03	-3.42	0.14	0.17	0.69
Degree	10	20	14.76	10.00	310	1.02e+24	55.29	4.99	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.58%
MCB compute time (ms): 19
MCB cycles: 90
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-11-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 11 3.36 2.00 440 MAX VALUE 125.55 3.12 0.93 0.55

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 720 MAX VALUE 187.15 0.00 0.00 0.00

XCSP 2.1 Benchmarks