XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg16-18-ext
Number of variables: 288
Number of constraints: 34
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 288
Number of constraints: 34

General features

Coarse blocks: 3,862
Value tables: 288

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

Arity 16 18 16.94 16.00 576 MAX VALUE 96.15 1.00 0.06 0.69

Coarse blocks size 1 6 1.57 1.00 6,048 MAX VALUE 1,218.16 0.96 0.61 1.01

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -36,791.20 0.00 0.26 0.30

Tightness 1.00 1.00 1.00 1.00 34.00 1.00 0.00 0.00 0.00 0.00

Tuples 4 17 10.88 17.00 370 6.04e+31 73.18 6.49 0.60 0.69

Values 26 26 26.00 26.00 7,488 MAX VALUE 938.33 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 576 MAX VALUE 199.63 0.00 0.00 0.00

Value table partitions 8 16 11.10 11.00 3,197 MAX VALUE 689.72 1.72 0.16 1.94

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	16	18	16.94	16.00	576	MAX VALUE	96.15	1.00	0.06	0.69
Coarse blocks size	1	6	1.57	1.00	6,048	MAX VALUE	1,218.16	0.96	0.61	1.01
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-36,791.20	0.00	0.26	0.30
Tightness	1.00	1.00	1.00	1.00	34.00	1.00	0.00	0.00	0.00	0.00
Tuples	4	17	10.88	17.00	370	6.04e+31	73.18	6.49	0.60	0.69
Values	26	26	26.00	26.00	7,488	MAX VALUE	938.33	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	576	MAX VALUE	199.63	0.00	0.00	0.00
Value table partitions	8	16	11.10	11.00	3,197	MAX VALUE	689.72	1.72	0.16	1.94

Tree decomposition

Number of clusters: 32
Number of leaves: 16
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/Tree1.json

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

Cluster constraints 0 2 1.06 1.50 34 0 None 0.97 0.91 0.88

Variables per cluster 33 184 61.62 40.00 1,972 MAX VALUE 126.44 41.40 0.67 1.51

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

Separator variables 0 144 52.62 32.00 1,684 0 None 31.54 0.60 1.51

Clusters per var 1 9 6.85 8.00 1,972 MAX VALUE 527.61 2.08 0.30 1.63

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.06	1.50	34	0	None	0.97	0.91	0.88
Variables per cluster	33	184	61.62	40.00	1,972	MAX VALUE	126.44	41.40	0.67	1.51
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	144	52.62	32.00	1,684	0	None	31.54	0.60	1.51
Clusters per var	1	9	6.85	8.00	1,972	MAX VALUE	527.61	2.08	0.30	1.63

Dual tree decomposition

Number of clusters: 18
Number of leaves: 2
Tree depth: 9
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/DualTree1.json

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

Cluster constraints 16 16 16.00 16.00 288 4.72e+21 49.91 0.00 0.00 0.00

Variables per cluster 17 17 17.00 17.00 306 1.41e+22 51.00 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 16 15.11 16.00 272 0 None 3.66 0.24 0.21

Clusters per variable 1 18 9.00 1.00 306 1.21e+20 46.25 8.49 0.94 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	16	16.00	16.00	288	4.72e+21	49.91	0.00	0.00	0.00
Variables per cluster	17	17	17.00	17.00	306	1.41e+22	51.00	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	16	15.11	16.00	272	0	None	3.66	0.24	0.21
Clusters per variable	1	18	9.00	1.00	306	1.21e+20	46.25	8.49	0.94	0.69

Primal graph

Density: 11.15%
MCB compute time (ms): 5,938
MCB cycles: 4,321
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/Primal1.json

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

Clustering coefficient 0.49 0.49 0.49 0.49 139.94 0.00 -207.87 0.00 0.00 0.00

Degree 32 32 32.00 32.00 9,216 MAX VALUE 998.13 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.06 3.00 13,218 MAX VALUE 4,820.46 0.24 0.08 0.22

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.49	0.49	0.49	139.94	0.00	-207.87	0.00	0.00	0.00
Degree	32	32	32.00	32.00	9,216	MAX VALUE	998.13	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.06	3.00	13,218	MAX VALUE	4,820.46	0.24	0.08	0.22

Triangulated primal graph

Density: 67.31%
MCB compute time (ms): 261,648
MCB cycles: 31,393
Triangles: None

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

Clustering coefficient 0.83 1.00 0.88 0.86 254.32 0.00 -36.28 0.05 0.06 2.43

Degree 32 244 193.19 224.50 55,638 MAX VALUE 1,485.07 65.69 0.34 2.43

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 94,179 MAX VALUE 34,488.70 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	0.86	254.32	0.00	-36.28	0.05	0.06	2.43
Degree	32	244	193.19	224.50	55,638	MAX VALUE	1,485.07	65.69	0.34	2.43
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	94,179	MAX VALUE	34,488.70	0.00	0.00	0.00

Dual graph

Density: 51.34%
MCB compute time (ms): 4
MCB cycles: 255
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-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 16 18 16.94 16.00 576 MAX VALUE 96.15 1.00 0.06 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 1,020 MAX VALUE 353.50 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	16	18	16.94	16.00	576	MAX VALUE	96.15	1.00	0.06	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	1,020	MAX VALUE	353.50	0.00	0.00	0.00

Minimal dual graph

Density: 51.34%
MCB compute time (ms): 4
MCB cycles: 255

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 16 18 16.94 16.00 576 MAX VALUE 96.15 1.00 0.06 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 1,020 MAX VALUE 353.50 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	16	18	16.94	16.00	576	MAX VALUE	96.15	1.00	0.06	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	1,020	MAX VALUE	353.50	0.00	0.00	0.00

Triangulated dual graph

Density: 72.73%
Triangles: 2,720

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

Clustering coefficient 0.71 1.00 0.86 1.00 29.36 0.00 -5.47 0.14 0.17 0.69

Degree 16 33 24.00 16.00 816 MAX VALUE 105.85 8.49 0.35 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	29.36	0.00	-5.47	0.14	0.17	0.69
Degree	16	33	24.00	16.00	816	MAX VALUE	105.85	8.49	0.35	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 72.73%

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

Clustering coefficient 0.71 1.00 0.86 1.00 29.36 0.00 -5.47 0.14 0.17 0.69

Degree 16 33 24.00 16.00 816 MAX VALUE 105.85 8.49 0.35 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	29.36	0.00	-5.47	0.14	0.17	0.69
Degree	16	33	24.00	16.00	816	MAX VALUE	105.85	8.49	0.35	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.11%
MCB compute time (ms): 154
MCB cycles: 255
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-18-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 18 3.58 2.00 1,152 MAX VALUE 295.78 4.60 1.29 0.41

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 2,040 MAX VALUE 530.26 0.00 0.00 0.00

XCSP 2.1 Benchmarks