XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg8-12-ext
Number of variables: 96
Number of constraints: 20
Satisfiable: True
Timestamp: 2025-07-20 22:08:36
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 96
Number of constraints: 20

General features

Coarse blocks: 4,544
Value tables: 96

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

Arity 8 12 9.60 8.00 192 2.95e+19 44.83 1.96 0.20 0.67

Coarse blocks size 1 861 88.73 37.50 403,200 MAX VALUE 16,054.30 119.74 1.35 4.81

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -69,337.20 0.00 0.96 4.05

Tightness 1.00 1.00 1.00 1.00 20.00 1.00 -0.00 0.00 0.00 0.67

Tuples 593 3,607 2,401.40 3,607.00 48,028 MAX VALUE 149.37 1,476.55 0.61 0.67

Values 26 26 26.00 26.00 2,496 MAX VALUE 312.78 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 192 7.92e+28 66.54 0.00 0.00 0.00

Value table partitions 23 26 25.52 26.00 2,450 MAX VALUE 310.94 0.85 0.03 0.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	8	12	9.60	8.00	192	2.95e+19	44.83	1.96	0.20	0.67
Coarse blocks size	1	861	88.73	37.50	403,200	MAX VALUE	16,054.30	119.74	1.35	4.81
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-69,337.20	0.00	0.96	4.05
Tightness	1.00	1.00	1.00	1.00	20.00	1.00	-0.00	0.00	0.00	0.67
Tuples	593	3,607	2,401.40	3,607.00	48,028	MAX VALUE	149.37	1,476.55	0.61	0.67
Values	26	26	26.00	26.00	2,496	MAX VALUE	312.78	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	192	7.92e+28	66.54	0.00	0.00	0.00
Value table partitions	23	26	25.52	26.00	2,450	MAX VALUE	310.94	0.85	0.03	0.88

Tree decomposition

Number of clusters: 18
Number of leaves: 8
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/Tree1.json

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

Cluster constraints 0 2 1.11 1.00 20 0 None 0.87 0.79 1.06

Variables per cluster 19 60 29.33 25.00 528 5.35e+25 59.24 13.51 0.46 1.43

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

Separator variables 0 48 24.00 21.00 432 0 None 10.75 0.45 1.50

Clusters per var 1 8 5.50 6.00 528 MAX VALUE 152.70 1.94 0.35 1.78

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.11	1.00	20	0	None	0.87	0.79	1.06
Variables per cluster	19	60	29.33	25.00	528	5.35e+25	59.24	13.51	0.46	1.43
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	48	24.00	21.00	432	0	None	10.75	0.45	1.50
Clusters per var	1	8	5.50	6.00	528	MAX VALUE	152.70	1.94	0.35	1.78

Dual tree decomposition

Number of clusters: 12
Number of leaves: 2
Tree depth: 6
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/DualTree1.json

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

Cluster constraints 8 8 8.00 8.00 96 6.87e+10 24.95 0.00 0.00 0.00

Variables per cluster 9 9 9.00 9.00 108 2.82e+11 26.37 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 8 7.33 8.00 88 0 None 2.21 0.30 0.29

Clusters per variable 1 12 5.40 1.00 108 429,982,000 19.88 5.39 1.00 0.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	8	8	8.00	8.00	96	6.87e+10	24.95	0.00	0.00	0.00
Variables per cluster	9	9	9.00	9.00	108	2.82e+11	26.37	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	8	7.33	8.00	88	0	None	2.21	0.30	0.29
Clusters per variable	1	12	5.40	1.00	108	429,982,000	19.88	5.39	1.00	0.67

Primal graph

Density: 18.95%
MCB compute time (ms): 65
MCB cycles: 769
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-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 47.69 0.00 -67.17 0.00 0.00 0.00

Degree 18 18 18.00 18.00 1,728 MAX VALUE 277.48 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.10 3.00 2,384 MAX VALUE 866.98 0.30 0.10 0.33

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	0.50	0.50	0.50	47.69	0.00	-67.17	0.00	0.00	0.00
Degree	18	18	18.00	18.00	1,728	MAX VALUE	277.48	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.10	3.00	2,384	MAX VALUE	866.98	0.30	0.10	0.33

Triangulated primal graph

Density: 68.29%
MCB compute time (ms): 531
MCB cycles: 3,690
Triangles: None

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

Clustering coefficient 0.81 1.00 0.88 0.86 84.11 0.00 -12.88 0.06 0.06 2.37

Degree 18 83 64.88 72.50 6,228 MAX VALUE 392.51 20.87 0.32 2.37

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 11,070 MAX VALUE 4,053.88 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	0.88	0.86	84.11	0.00	-12.88	0.06	0.06	2.37
Degree	18	83	64.88	72.50	6,228	MAX VALUE	392.51	20.87	0.32	2.37
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	11,070	MAX VALUE	4,053.88	0.00	0.00	0.00

Dual graph

Density: 50.53%
MCB compute time (ms): 0
MCB cycles: 77
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-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 8 12 9.60 8.00 192 2.95e+19 44.83 1.96 0.20 0.67

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 308 MAX VALUE 106.75 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	8	12	9.60	8.00	192	2.95e+19	44.83	1.96	0.20	0.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	308	MAX VALUE	106.75	0.00	0.00	0.00

Minimal dual graph

Density: 50.53%
MCB compute time (ms): 0
MCB cycles: 77

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 8 12 9.60 8.00 192 2.95e+19 44.83 1.96 0.20 0.67

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 308 MAX VALUE 106.75 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	8	12	9.60	8.00	192	2.95e+19	44.83	1.96	0.20	0.67
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	308	MAX VALUE	106.75	0.00	0.00	0.00

Triangulated dual graph

Density: 65.26%
Triangles: 392

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

Clustering coefficient 0.61 1.00 0.85 1.00 16.91 0.02 -3.90 0.19 0.22 0.67

Degree 8 19 12.40 8.00 248 1.17e+21 48.51 5.39 0.43 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	0.61	1.00	0.85	1.00	16.91	0.02	-3.90	0.19	0.22	0.67
Degree	8	19	12.40	8.00	248	1.17e+21	48.51	5.39	0.43	0.67
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 65.26%

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

Clustering coefficient 0.61 1.00 0.85 1.00 16.91 0.02 -3.90 0.19 0.22 0.67

Degree 8 19 12.40 8.00 248 1.17e+21 48.51 5.39 0.43 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	0.61	1.00	0.85	1.00	16.91	0.02	-3.90	0.19	0.22	0.67
Degree	8	19	12.40	8.00	248	1.17e+21	48.51	5.39	0.43	0.67
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.88%
MCB compute time (ms): 10
MCB cycles: 77
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-12-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 12 3.31 2.00 384 MAX VALUE 111.38 2.98 0.90 0.58

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 616 MAX VALUE 160.12 0.00 0.00 0.00

XCSP 2.1 Benchmarks