XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg9-11-ext
Number of variables: 99
Number of constraints: 20
Satisfiable: True
Timestamp: 2025-07-20 22:08:36
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 99
Number of constraints: 20

General features

Coarse blocks: 4,841
Value tables: 99

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

Arity 9 11 9.90 9.00 198 7.40e+19 45.75 0.99 0.10 0.69

Coarse blocks size 1 852 86.05 55.00 416,592 MAX VALUE 17,520.50 104.38 1.21 4.94

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -67,519.00 0.00 1.03 4.38

Tightness 1.00 1.00 1.00 1.00 20.00 1.00 -0.00 0.00 0.00 0.69

Tuples 1,120 3,088 2,202.40 3,088.00 44,048 MAX VALUE 151.58 979.07 0.44 0.69

Values 26 26 26.00 26.00 2,574 MAX VALUE 322.55 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 198 6.34e+29 68.62 0.00 0.00 0.00

Value table partitions 24 26 25.69 26.00 2,543 MAX VALUE 321.32 0.61 0.02 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	9	11	9.90	9.00	198	7.40e+19	45.75	0.99	0.10	0.69
Coarse blocks size	1	852	86.05	55.00	416,592	MAX VALUE	17,520.50	104.38	1.21	4.94
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-67,519.00	0.00	1.03	4.38
Tightness	1.00	1.00	1.00	1.00	20.00	1.00	-0.00	0.00	0.00	0.69
Tuples	1,120	3,088	2,202.40	3,088.00	44,048	MAX VALUE	151.58	979.07	0.44	0.69
Values	26	26	26.00	26.00	2,574	MAX VALUE	322.55	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	198	6.34e+29	68.62	0.00	0.00	0.00
Value table partitions	24	26	25.69	26.00	2,543	MAX VALUE	321.32	0.61	0.02	0.69

Tree decomposition

Number of clusters: 18
Number of leaves: 9
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-ext/Tree1.json

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

Cluster constraints 0 2 1.11 1.50 20 0 None 0.94 0.84 0.96

Variables per cluster 19 63 29.89 22.50 538 6.50e+25 59.44 14.22 0.48 1.53

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

Separator variables 0 49 24.39 18.00 439 0 None 11.37 0.47 1.53

Clusters per var 1 8 5.43 6.00 538 MAX VALUE 156.13 1.92 0.35 1.76

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.11	1.50	20	0	None	0.94	0.84	0.96
Variables per cluster	19	63	29.89	22.50	538	6.50e+25	59.44	14.22	0.48	1.53
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	49	24.39	18.00	439	0	None	11.37	0.47	1.53
Clusters per var	1	8	5.43	6.00	538	MAX VALUE	156.13	1.92	0.35	1.76

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-vg9-11-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-ext/DualTree1.json

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

Cluster constraints 9 9 9.00 9.00 99 3.14e+10 24.17 0.00 0.00 0.00

Variables per cluster 10 10 10.00 10.00 110 1.00e+11 25.33 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 9 8.18 9.00 90 0 None 2.59 0.32 0.30

Clusters per variable 1 11 5.50 1.00 110 2.36e+09 21.58 4.97 0.90 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	9	9	9.00	9.00	99	3.14e+10	24.17	0.00	0.00	0.00
Variables per cluster	10	10	10.00	10.00	110	1.00e+11	25.33	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	9	8.18	9.00	90	0	None	2.59	0.32	0.30
Clusters per variable	1	11	5.50	1.00	110	2.36e+09	21.58	4.97	0.90	0.69

Primal graph

Density: 18.37%
MCB compute time (ms): 88
MCB cycles: 793
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-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 47.24 0.00 -73.26 0.00 0.00 0.00

Degree 18 18 18.00 18.00 1,782 MAX VALUE 286.15 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 2,459 MAX VALUE 894.21 0.30 0.10 0.33

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.48	0.48	0.48	47.24	0.00	-73.26	0.00	0.00	0.00
Degree	18	18	18.00	18.00	1,782	MAX VALUE	286.15	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	2,459	MAX VALUE	894.21	0.30	0.10	0.33

Triangulated primal graph

Density: 67.90%
MCB compute time (ms): 1,023
MCB cycles: 3,574
Triangles: None

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

Clustering coefficient 0.80 1.00 0.88 0.86 86.68 0.00 -13.37 0.06 0.07 3.12

Degree 18 86 66.55 74.00 6,588 MAX VALUE 407.05 21.62 0.32 2.83

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 10,722 MAX VALUE 3,926.44 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.80	1.00	0.88	0.86	86.68	0.00	-13.37	0.06	0.07	3.12
Degree	18	86	66.55	74.00	6,588	MAX VALUE	407.05	21.62	0.32	2.83
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	10,722	MAX VALUE	3,926.44	0.00	0.00	0.00

Dual graph

Density: 52.11%
MCB compute time (ms): 0
MCB cycles: 80
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-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 9 11 9.90 9.00 198 7.40e+19 45.75 0.99 0.10 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 320 MAX VALUE 110.90 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	9	11	9.90	9.00	198	7.40e+19	45.75	0.99	0.10	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	320	MAX VALUE	110.90	0.00	0.00	0.00

Minimal dual graph

Density: 52.11%
MCB compute time (ms): 0
MCB cycles: 80

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 9 11 9.90 9.00 198 7.40e+19 45.75 0.99 0.10 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 320 MAX VALUE 110.90 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	9	11	9.90	9.00	198	7.40e+19	45.75	0.99	0.10	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	320	MAX VALUE	110.90	0.00	0.00	0.00

Triangulated dual graph

Density: 71.05%
Triangles: 480

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

Clustering coefficient 0.68 1.00 0.86 1.00 17.11 0.03 -3.49 0.16 0.19 0.69

Degree 9 19 13.50 9.00 270 1.01e+22 50.67 4.97 0.37 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	17.11	0.03	-3.49	0.16	0.19	0.69
Degree	9	19	13.50	9.00	270	1.01e+22	50.67	4.97	0.37	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 71.05%

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

Clustering coefficient 0.68 1.00 0.86 1.00 17.11 0.03 -3.49 0.16 0.19 0.69

Degree 9 19 13.50 9.00 270 1.01e+22 50.67 4.97 0.37 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	17.11	0.03	-3.49	0.16	0.19	0.69
Degree	9	19	13.50	9.00	270	1.01e+22	50.67	4.97	0.37	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.82%
MCB compute time (ms): 11
MCB cycles: 80
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg9-11-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 3.33 2.00 396 MAX VALUE 114.37 2.98 0.90 0.57

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 640 MAX VALUE 166.35 0.00 0.00 0.00

XCSP 2.1 Benchmarks