XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg7-7-ext
Number of variables: 49
Number of constraints: 14
Satisfiable: True
Timestamp: 2025-07-20 22:08:36
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 49
Number of constraints: 14

General features

Coarse blocks: 2,450
Value tables: 49

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

Arity 7 7 7.00 7.00 98 6.78e+11 27.24 0.00 0.00 0.00

Coarse blocks size 1 875 161.68 115.00 396,116 MAX VALUE 10,959.00 156.26 0.97 4.85

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -18,297.80 0.00 0.98 4.63

Tightness 1.00 1.00 1.00 1.00 14.00 1.00 -0.00 0.00 0.00 0.00

Tuples 4,042 4,042 4,042.00 4,042.00 56,588 MAX VALUE 116.26 0.00 0.00 0.00

Values 26 26 26.00 26.00 1,274 MAX VALUE 159.65 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 98 5.63e+14 33.96 0.00 0.00 0.00

Value table partitions 23 26 25.73 26.00 1,261 MAX VALUE 159.13 0.66 0.03 0.60

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	7	7	7.00	7.00	98	6.78e+11	27.24	0.00	0.00	0.00
Coarse blocks size	1	875	161.68	115.00	396,116	MAX VALUE	10,959.00	156.26	0.97	4.85
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-18,297.80	0.00	0.98	4.63
Tightness	1.00	1.00	1.00	1.00	14.00	1.00	-0.00	0.00	0.00	0.00
Tuples	4,042	4,042	4,042.00	4,042.00	56,588	MAX VALUE	116.26	0.00	0.00	0.00
Values	26	26	26.00	26.00	1,274	MAX VALUE	159.65	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	98	5.63e+14	33.96	0.00	0.00	0.00
Value table partitions	23	26	25.73	26.00	1,261	MAX VALUE	159.13	0.66	0.03	0.60

Tree decomposition

Number of clusters: 12
Number of leaves: 7
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/Tree1.json

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

Cluster constraints 0 2 1.17 2.00 14 0 None 0.99 0.85 0.68

Variables per cluster 13 32 18.08 13.00 217 5.99e+14 34.03 6.58 0.36 1.08

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

Separator variables 0 24 14.00 12.00 168 0 None 6.00 0.43 1.08

Clusters per var 1 6 4.43 5.00 217 8.03e+28 66.56 1.69 0.38 1.47

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.17	2.00	14	0	None	0.99	0.85	0.68
Variables per cluster	13	32	18.08	13.00	217	5.99e+14	34.03	6.58	0.36	1.08
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	24	14.00	12.00	168	0	None	6.00	0.43	1.08
Clusters per var	1	6	4.43	5.00	217	8.03e+28	66.56	1.69	0.38	1.47

Dual tree decomposition

Number of clusters: 7
Number of leaves: 2
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/DualTree1.json

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

Cluster constraints 7 7 7.00 7.00 49 823,543 13.62 0.00 0.00 0.00

Variables per cluster 8 8 8.00 8.00 56 2,097,150 14.56 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 7 6.00 7.00 42 0 None 2.45 0.41 0.41

Clusters per variable 1 7 4.00 4.00 56 823,543 13.62 3.00 0.75 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	7	7.00	7.00	49	823,543	13.62	0.00	0.00	0.00
Variables per cluster	8	8	8.00	8.00	56	2,097,150	14.56	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	7	6.00	7.00	42	0	None	2.45	0.41	0.41
Clusters per variable	1	7	4.00	4.00	56	823,543	13.62	3.00	0.75	0.69

Primal graph

Density: 25.00%
MCB compute time (ms): 8
MCB cycles: 261
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/Primal1.json

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

Clustering coefficient 0.45 0.45 0.45 0.45 22.27 0.00 -38.63 0.00 0.00 0.00

Degree 12 12 12.00 12.00 588 MAX VALUE 121.76 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.20 3.00 834 MAX VALUE 301.41 0.40 0.12 0.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.45	0.45	0.45	0.45	22.27	0.00	-38.63	0.00	0.00	0.00
Degree	12	12	12.00	12.00	588	MAX VALUE	121.76	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.20	3.00	834	MAX VALUE	301.41	0.40	0.12	0.49

Triangulated primal graph

Density: 68.45%
MCB compute time (ms): 34
MCB cycles: 958
Triangles: None

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

Clustering coefficient 0.81 1.00 0.87 0.85 42.51 0.00 -7.09 0.06 0.07 1.70

Degree 12 41 32.86 37.00 1,610 MAX VALUE 167.56 10.24 0.31 1.70

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 2,874 MAX VALUE 1,052.47 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.81	1.00	0.87	0.85	42.51	0.00	-7.09	0.06	0.07	1.70
Degree	12	41	32.86	37.00	1,610	MAX VALUE	167.56	10.24	0.31	1.70
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	2,874	MAX VALUE	1,052.47	0.00	0.00	0.00

Dual graph

Density: 53.85%
MCB compute time (ms): 0
MCB cycles: 36
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-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 7 7 7.00 7.00 98 6.78e+11 27.24 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 144 4.72e+21 49.91 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	7	7	7.00	7.00	98	6.78e+11	27.24	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	144	4.72e+21	49.91	0.00	0.00	0.00

Minimal dual graph

Density: 53.85%
MCB compute time (ms): 0
MCB cycles: 36

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 7 7 7.00 7.00 98 6.78e+11 27.24 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 144 4.72e+21 49.91 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	7	7	7.00	7.00	98	6.78e+11	27.24	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	144	4.72e+21	49.91	0.00	0.00	0.00

Triangulated dual graph

Density: 76.92%
Triangles: 182

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

Clustering coefficient 0.73 1.00 0.87 0.87 12.12 0.11 -2.20 0.13 0.16 0.69

Degree 7 13 10.00 10.00 140 5.17e+13 31.58 3.00 0.30 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	0.87	12.12	0.11	-2.20	0.13	0.16	0.69
Degree	7	13	10.00	10.00	140	5.17e+13	31.58	3.00	0.30	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 76.92%

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

Clustering coefficient 0.73 1.00 0.87 0.87 12.12 0.11 -2.20 0.13 0.16 0.69

Degree 7 13 10.00 10.00 140 5.17e+13 31.58 3.00 0.30 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	0.87	12.12	0.11	-2.20	0.13	0.16	0.69
Degree	7	13	10.00	10.00	140	5.17e+13	31.58	3.00	0.30	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 5.02%
MCB compute time (ms): 1
MCB cycles: 36
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-7-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 7 3.11 2.00 196 3.82e+26 61.21 2.08 0.67 0.53

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 288 3.25e+32 74.86 0.00 0.00 0.00

XCSP 2.1 Benchmarks