XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-words-vg16-16-ext
Number of variables: 256
Number of constraints: 32
Satisfiable: True
Timestamp: 2025-07-20 22:09:46
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 256
Number of constraints: 32

General features

Coarse blocks: 8,192
Value tables: 256

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

Arity 16 16 16.00 16.00 512 MAX VALUE 88.72 0.00 0.00 0.00

Coarse blocks size 1 33 6.44 4.00 52,736 MAX VALUE 11,483.50 6.18 0.96 2.68

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -152,378.00 0.00 0.88 2.40

Tightness 1.00 1.00 1.00 1.00 32.00 1.00 0.00 0.00 0.00 0.00

Tuples 103 103 103.00 103.00 3,296 MAX VALUE 148.31 0.00 0.00 0.00

Values 26 26 26.00 26.00 6,656 MAX VALUE 834.07 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 512 MAX VALUE 177.45 0.00 0.00 0.00

Value table partitions 8 23 19.52 20.00 4,996 MAX VALUE 758.45 2.36 0.12 2.11

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	16	16	16.00	16.00	512	MAX VALUE	88.72	0.00	0.00	0.00
Coarse blocks size	1	33	6.44	4.00	52,736	MAX VALUE	11,483.50	6.18	0.96	2.68
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-152,378.00	0.00	0.88	2.40
Tightness	1.00	1.00	1.00	1.00	32.00	1.00	0.00	0.00	0.00	0.00
Tuples	103	103	103.00	103.00	3,296	MAX VALUE	148.31	0.00	0.00	0.00
Values	26	26	26.00	26.00	6,656	MAX VALUE	834.07	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	512	MAX VALUE	177.45	0.00	0.00	0.00
Value table partitions	8	23	19.52	20.00	4,996	MAX VALUE	758.45	2.36	0.12	2.11

Tree decomposition

Number of clusters: 30
Number of leaves: 16
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/Tree1.json

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

Cluster constraints 0 2 1.07 2.00 32 0 None 1.00 0.94 0.69

Variables per cluster 31 160 56.53 31.00 1,696 MAX VALUE 116.16 36.91 0.65 1.14

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

Separator variables 0 128 48.00 30.00 1,440 0 None 28.06 0.58 1.18

Clusters per var 1 8 6.62 7.50 1,696 MAX VALUE 459.79 2.03 0.31 1.30

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.07	2.00	32	0	None	1.00	0.94	0.69
Variables per cluster	31	160	56.53	31.00	1,696	MAX VALUE	116.16	36.91	0.65	1.14
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	128	48.00	30.00	1,440	0	None	28.06	0.58	1.18
Clusters per var	1	8	6.62	7.50	1,696	MAX VALUE	459.79	2.03	0.31	1.30

Dual tree decomposition

Number of clusters: 16
Number of leaves: 2
Tree depth: 8
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/DualTree1.json

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

Cluster constraints 16 16 16.00 16.00 256 1.84e+19 44.36 0.00 0.00 0.00

Variables per cluster 17 17 17.00 17.00 272 4.87e+19 45.33 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 16 15.00 16.00 240 0 None 3.87 0.26 0.23

Clusters per variable 1 16 8.50 8.50 272 1.84e+19 44.36 7.50 0.88 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	16	16.00	16.00	256	1.84e+19	44.36	0.00	0.00	0.00
Variables per cluster	17	17	17.00	17.00	272	4.87e+19	45.33	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	16	15.00	16.00	240	0	None	3.87	0.26	0.23
Clusters per variable	1	16	8.50	8.50	272	1.84e+19	44.36	7.50	0.88	0.69

Primal graph

Density: 11.76%
MCB compute time (ms): 4,447
MCB cycles: 3,690
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/Primal1.json

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

Clustering coefficient 0.48 0.48 0.48 0.48 123.59 0.00 -186.43 0.00 0.00 0.00

Degree 30 30 30.00 30.00 7,680 MAX VALUE 870.71 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.09 3.00 11,400 MAX VALUE 4,148.81 0.29 0.09 0.30

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.48	0.48	0.48	123.59	0.00	-186.43	0.00	0.00	0.00
Degree	30	30	30.00	30.00	7,680	MAX VALUE	870.71	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.09	3.00	11,400	MAX VALUE	4,148.81	0.29	0.09	0.30

Triangulated primal graph

Density: 67.03%
MCB compute time (ms): 10,314
MCB cycles: 34,456
Triangles: None

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

Clustering coefficient 0.84 1.00 0.88 0.86 225.77 0.00 -32.58 0.05 0.06 1.30

Degree 30 213 170.94 197.00 43,760 MAX VALUE 1,288.73 58.43 0.34 1.30

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 103,368 MAX VALUE 37,853.80 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.84	1.00	0.88	0.86	225.77	0.00	-32.58	0.05	0.06	1.30
Degree	30	213	170.94	197.00	43,760	MAX VALUE	1,288.73	58.43	0.34	1.30
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	103,368	MAX VALUE	37,853.80	0.00	0.00	0.00

Dual graph

Density: 51.61%
MCB compute time (ms): 3
MCB cycles: 225
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-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 16 16.00 16.00 512 MAX VALUE 88.72 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 900 MAX VALUE 311.92 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	16	16.00	16.00	512	MAX VALUE	88.72	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	900	MAX VALUE	311.92	0.00	0.00	0.00

Minimal dual graph

Density: 51.61%
MCB compute time (ms): 3
MCB cycles: 225

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 16 16.00 16.00 512 MAX VALUE 88.72 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 900 MAX VALUE 311.92 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	16	16.00	16.00	512	MAX VALUE	88.72	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	900	MAX VALUE	311.92	0.00	0.00	0.00

Triangulated dual graph

Density: 75.81%
Triangles: 2,480

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

Clustering coefficient 0.74 1.00 0.87 0.87 27.87 0.01 -4.78 0.13 0.15 0.69

Degree 16 31 23.50 23.50 752 MAX VALUE 99.31 7.50 0.32 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	0.74	1.00	0.87	0.87	27.87	0.01	-4.78	0.13	0.15	0.69
Degree	16	31	23.50	23.50	752	MAX VALUE	99.31	7.50	0.32	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 75.81%

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

Clustering coefficient 0.74 1.00 0.87 0.87 27.87 0.01 -4.78 0.13 0.15 0.69

Degree 16 31 23.50 23.50 752 MAX VALUE 99.31 7.50 0.32 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	0.74	1.00	0.87	0.87	27.87	0.01	-4.78	0.13	0.15	0.69
Degree	16	31	23.50	23.50	752	MAX VALUE	99.31	7.50	0.32	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.24%
MCB compute time (ms): 110
MCB cycles: 225
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg16-16-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 16 3.56 2.00 1,024 MAX VALUE 266.17 4.40 1.24 0.35

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,800 MAX VALUE 467.87 0.00 0.00 0.00

XCSP 2.1 Benchmarks