XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg7-11-ext
Number of variables: 77
Number of constraints: 18
Satisfiable: True
Timestamp: 2025-07-20 22:08:36
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 77
Number of constraints: 18

General features

Coarse blocks: 3,731
Value tables: 77

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

Arity 7 11 8.56 7.00 154 3.85e+16 38.19 1.95 0.23 0.67

Coarse blocks size 1 875 106.53 61.00 397,474 MAX VALUE 14,346.20 130.55 1.23 5.00

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -51,727.70 0.00 1.02 4.38

Tightness 1.00 1.00 1.00 1.00 18.00 1.00 -0.00 0.00 0.00 0.67

Tuples 1,120 4,042 2,905.67 4,042.00 52,302 MAX VALUE 140.50 1,424.47 0.49 0.67

Values 26 26 26.00 26.00 2,002 MAX VALUE 250.87 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 154 1.51e+23 53.37 0.00 0.00 0.00

Value table partitions 23 26 25.57 26.00 1,969 MAX VALUE 249.56 0.71 0.03 0.86

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	7	11	8.56	7.00	154	3.85e+16	38.19	1.95	0.23	0.67
Coarse blocks size	1	875	106.53	61.00	397,474	MAX VALUE	14,346.20	130.55	1.23	5.00
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-51,727.70	0.00	1.02	4.38
Tightness	1.00	1.00	1.00	1.00	18.00	1.00	-0.00	0.00	0.00	0.67
Tuples	1,120	4,042	2,905.67	4,042.00	52,302	MAX VALUE	140.50	1,424.47	0.49	0.67
Values	26	26	26.00	26.00	2,002	MAX VALUE	250.87	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	154	1.51e+23	53.37	0.00	0.00	0.00
Value table partitions	23	26	25.57	26.00	1,969	MAX VALUE	249.56	0.71	0.03	0.86

Tree decomposition

Number of clusters: 16
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-vg7-11-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-ext/Tree1.json

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

Cluster constraints 0 2 1.12 1.00 18 0 None 0.86 0.76 1.07

Variables per cluster 17 51 25.19 22.00 403 8.17e+21 50.45 10.48 0.42 1.57

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

Separator variables 0 37 20.38 18.50 326 0 None 8.60 0.42 1.57

Clusters per var 1 7 5.23 6.00 403 MAX VALUE 118.27 1.89 0.36 1.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.12	1.00	18	0	None	0.86	0.76	1.07
Variables per cluster	17	51	25.19	22.00	403	8.17e+21	50.45	10.48	0.42	1.57
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	37	20.38	18.50	326	0	None	8.60	0.42	1.57
Clusters per var	1	7	5.23	6.00	403	MAX VALUE	118.27	1.89	0.36	1.67

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-vg7-11-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-ext/DualTree1.json

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

Cluster constraints 7 7 7.00 7.00 77 1.98e+09 21.41 0.00 0.00 0.00

Variables per cluster 8 8 8.00 8.00 88 8.59e+09 22.87 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 6.36 7.00 70 0 None 2.01 0.32 0.30

Clusters per variable 1 11 4.89 1.00 88 19,487,200 16.79 4.87 1.00 0.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	7	7	7.00	7.00	77	1.98e+09	21.41	0.00	0.00	0.00
Variables per cluster	8	8	8.00	8.00	88	8.59e+09	22.87	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	6.36	7.00	70	0	None	2.01	0.32	0.30
Clusters per variable	1	11	4.89	1.00	88	19,487,200	16.79	4.87	1.00	0.67

Primal graph

Density: 21.05%
MCB compute time (ms): 27
MCB cycles: 540
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-ext/Primal1.json

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

Clustering coefficient 0.50 0.50 0.50 0.50 38.50 0.00 -53.37 0.00 0.00 0.00

Degree 16 16 16.00 16.00 1,232 MAX VALUE 213.49 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.11 3.00 1,680 MAX VALUE 610.51 0.31 0.10 0.35

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	0.50	0.50	0.50	38.50	0.00	-53.37	0.00	0.00	0.00
Degree	16	16	16.00	16.00	1,232	MAX VALUE	213.49	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.11	3.00	1,680	MAX VALUE	610.51	0.31	0.10	0.35

Triangulated primal graph

Density: 68.46%
MCB compute time (ms): 315
MCB cycles: 2,032
Triangles: None

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

Clustering coefficient 0.82 1.00 0.87 0.85 67.28 0.00 -10.56 0.06 0.07 3.05

Degree 16 65 52.03 61.00 4,006 MAX VALUE 298.22 16.52 0.32 2.53

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 6,096 MAX VALUE 2,232.38 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.82	1.00	0.87	0.85	67.28	0.00	-10.56	0.06	0.07	3.05
Degree	16	65	52.03	61.00	4,006	MAX VALUE	298.22	16.52	0.32	2.53
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	6,096	MAX VALUE	2,232.38	0.00	0.00	0.00

Dual graph

Density: 50.33%
MCB compute time (ms): 0
MCB cycles: 60
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-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 7 11 8.56 7.00 154 3.85e+16 38.19 1.95 0.23 0.67

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 240 1.33e+36 83.18 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	11	8.56	7.00	154	3.85e+16	38.19	1.95	0.23	0.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	240	1.33e+36	83.18	0.00	0.00	0.00

Minimal dual graph

Density: 50.33%
MCB compute time (ms): 0
MCB cycles: 60

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 11 8.56 7.00 154 3.85e+16 38.19 1.95 0.23 0.67

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 240 1.33e+36 83.18 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	11	8.56	7.00	154	3.85e+16	38.19	1.95	0.23	0.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	240	1.33e+36	83.18	0.00	0.00	0.00

Triangulated dual graph

Density: 64.05%
Triangles: 266

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

Clustering coefficient 0.60 1.00 0.84 1.00 15.17 0.03 -3.63 0.20 0.23 0.67

Degree 7 17 10.89 7.00 196 8.11e+17 41.24 4.87 0.45 0.67

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	0.60	1.00	0.84	1.00	15.17	0.03	-3.63	0.20	0.23	0.67
Degree	7	17	10.89	7.00	196	8.11e+17	41.24	4.87	0.45	0.67
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 64.05%

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

Clustering coefficient 0.60 1.00 0.84 1.00 15.17 0.03 -3.63 0.20 0.23 0.67

Degree 7 17 10.89 7.00 196 8.11e+17 41.24 4.87 0.45 0.67

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	0.60	1.00	0.84	1.00	15.17	0.03	-3.63	0.20	0.23	0.67
Degree	7	17	10.89	7.00	196	8.11e+17	41.24	4.87	0.45	0.67
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 3.45%
MCB compute time (ms): 7
MCB cycles: 60
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg7-11-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 3.24 2.00 308 MAX VALUE 91.56 2.71 0.83 0.61

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 480 MAX VALUE 124.77 0.00 0.00 0.00

XCSP 2.1 Benchmarks