XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg16-17-ext
Number of variables: 272
Number of constraints: 33
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 272
Number of constraints: 33

General features

Coarse blocks: 4,011
Value tables: 272

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

Arity 16 17 16.48 16.00 544 MAX VALUE 92.47 0.50 0.03 0.69

Coarse blocks size 1 6 1.63 1.00 6,528 MAX VALUE 1,436.48 0.95 0.58 1.07

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -43,306.20 0.00 0.45 0.82

Tightness 1.00 1.00 1.00 1.00 33.00 1.00 0.00 0.00 0.00 0.00

Tuples 7 17 12.15 17.00 401 2.75e+34 79.30 5.00 0.41 0.69

Values 26 26 26.00 26.00 7,072 MAX VALUE 886.20 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 544 MAX VALUE 188.54 0.00 0.00 0.00

Value table partitions 8 16 11.68 11.50 3,176 MAX VALUE 665.62 1.68 0.14 1.91

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	16	17	16.48	16.00	544	MAX VALUE	92.47	0.50	0.03	0.69
Coarse blocks size	1	6	1.63	1.00	6,528	MAX VALUE	1,436.48	0.95	0.58	1.07
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-43,306.20	0.00	0.45	0.82
Tightness	1.00	1.00	1.00	1.00	33.00	1.00	0.00	0.00	0.00	0.00
Tuples	7	17	12.15	17.00	401	2.75e+34	79.30	5.00	0.41	0.69
Values	26	26	26.00	26.00	7,072	MAX VALUE	886.20	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	544	MAX VALUE	188.54	0.00	0.00	0.00
Value table partitions	8	16	11.68	11.50	3,176	MAX VALUE	665.62	1.68	0.14	1.91

Tree decomposition

Number of clusters: 31
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-vg16-17-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/Tree1.json

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

Cluster constraints 0 2 1.06 2.00 33 0 None 0.98 0.92 0.81

Variables per cluster 32 172 59.13 32.00 1,833 MAX VALUE 121.32 39.09 0.66 1.46

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

Separator variables 0 136 50.35 31.00 1,561 0 None 29.73 0.59 1.46

Clusters per var 1 9 6.74 8.00 1,833 MAX VALUE 493.47 2.06 0.31 1.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.06	2.00	33	0	None	0.98	0.92	0.81
Variables per cluster	32	172	59.13	32.00	1,833	MAX VALUE	121.32	39.09	0.66	1.46
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	136	50.35	31.00	1,561	0	None	29.73	0.59	1.46
Clusters per var	1	9	6.74	8.00	1,833	MAX VALUE	493.47	2.06	0.31	1.54

Dual tree decomposition

Number of clusters: 17
Number of leaves: 2
Tree depth: 8
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/DualTree1.json

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

Cluster constraints 16 16 16.00 16.00 272 2.95e+20 47.13 0.00 0.00 0.00

Variables per cluster 17 17 17.00 17.00 289 8.27e+20 48.16 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 15.06 16.00 256 0 None 3.76 0.25 0.22

Clusters per variable 1 17 8.76 1.00 289 4.87e+19 45.33 8.00 0.91 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	16	16.00	16.00	272	2.95e+20	47.13	0.00	0.00	0.00
Variables per cluster	17	17	17.00	17.00	289	8.27e+20	48.16	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	15.06	16.00	256	0	None	3.76	0.25	0.22
Clusters per variable	1	17	8.76	1.00	289	4.87e+19	45.33	8.00	0.91	0.69

Primal graph

Density: 11.44%
MCB compute time (ms): 4,878
MCB cycles: 3,945
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/Primal1.json

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

Clustering coefficient 0.48 0.48 0.48 0.48 131.61 0.00 -197.46 0.00 0.00 0.00

Degree 31 31 31.00 31.00 8,432 MAX VALUE 934.04 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 12,075 MAX VALUE 4,403.07 0.24 0.08 0.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.48	0.48	0.48	131.61	0.00	-197.46	0.00	0.00	0.00
Degree	31	31	31.00	31.00	8,432	MAX VALUE	934.04	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	12,075	MAX VALUE	4,403.07	0.24	0.08	0.23

Triangulated primal graph

Density: 67.12%
MCB compute time (ms): 167,042
MCB cycles: 38,017
Triangles: None

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

Clustering coefficient 0.83 1.00 0.88 0.86 239.99 0.00 -34.50 0.05 0.06 2.49

Degree 31 229 181.88 211.00 49,472 MAX VALUE 1,386.14 62.07 0.34 2.39

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 114,051 MAX VALUE 41,765.90 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	239.99	0.00	-34.50	0.05	0.06	2.49
Degree	31	229	181.88	211.00	49,472	MAX VALUE	1,386.14	62.07	0.34	2.39
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	114,051	MAX VALUE	41,765.90	0.00	0.00	0.00

Dual graph

Density: 51.52%
MCB compute time (ms): 4
MCB cycles: 240
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-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 17 16.48 16.00 544 MAX VALUE 92.47 0.50 0.03 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 960 MAX VALUE 332.71 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	17	16.48	16.00	544	MAX VALUE	92.47	0.50	0.03	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	960	MAX VALUE	332.71	0.00	0.00	0.00

Minimal dual graph

Density: 51.52%
MCB compute time (ms): 3
MCB cycles: 240

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 17 16.48 16.00 544 MAX VALUE 92.47 0.50 0.03 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 960 MAX VALUE 332.71 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	17	16.48	16.00	544	MAX VALUE	92.47	0.50	0.03	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	960	MAX VALUE	332.71	0.00	0.00	0.00

Triangulated dual graph

Density: 74.24%
Triangles: 2,600

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

Clustering coefficient 0.73 1.00 0.87 1.00 28.61 0.01 -5.13 0.14 0.16 0.69

Degree 16 32 23.76 16.00 784 MAX VALUE 102.59 8.00 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	0.73	1.00	0.87	1.00	28.61	0.01	-5.13	0.14	0.16	0.69
Degree	16	32	23.76	16.00	784	MAX VALUE	102.59	8.00	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 74.24%

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

Clustering coefficient 0.73 1.00 0.87 1.00 28.61 0.01 -5.13 0.14 0.16 0.69

Degree 16 32 23.76 16.00 784 MAX VALUE 102.59 8.00 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	0.73	1.00	0.87	1.00	28.61	0.01	-5.13	0.14	0.16	0.69
Degree	16	32	23.76	16.00	784	MAX VALUE	102.59	8.00	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.17%
MCB compute time (ms): 118
MCB cycles: 240
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-17-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 17 3.57 2.00 1,088 MAX VALUE 281.00 4.50 1.26 0.42

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,920 MAX VALUE 499.07 0.00 0.00 0.00

XCSP 2.1 Benchmarks