XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg14-16-ext
Number of variables: 224
Number of constraints: 30
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 224
Number of constraints: 30

General features

Coarse blocks: 6,090
Value tables: 224

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

Arity 14 16 14.93 14.00 448 1.57e+35 81.04 1.00 0.07 0.69

Coarse blocks size 1 40 4.89 3.00 29,792 MAX VALUE 6,870.49 5.15 1.05 2.40

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -94,544.40 0.00 0.60 1.21

Tightness 1.00 1.00 1.00 1.00 30.00 1.00 0.00 0.00 0.00 0.00

Tuples 17 116 69.80 116.00 2,094 MAX VALUE 115.72 49.39 0.71 0.69

Values 26 26 26.00 26.00 5,824 MAX VALUE 729.81 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 448 MAX VALUE 155.26 0.00 0.00 0.00

Value table partitions 14 22 18.47 19.00 4,138 MAX VALUE 652.46 1.55 0.08 1.83

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	14	16	14.93	14.00	448	1.57e+35	81.04	1.00	0.07	0.69
Coarse blocks size	1	40	4.89	3.00	29,792	MAX VALUE	6,870.49	5.15	1.05	2.40
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-94,544.40	0.00	0.60	1.21
Tightness	1.00	1.00	1.00	1.00	30.00	1.00	0.00	0.00	0.00	0.00
Tuples	17	116	69.80	116.00	2,094	MAX VALUE	115.72	49.39	0.71	0.69
Values	26	26	26.00	26.00	5,824	MAX VALUE	729.81	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	448	MAX VALUE	155.26	0.00	0.00	0.00
Value table partitions	14	22	18.47	19.00	4,138	MAX VALUE	652.46	1.55	0.08	1.83

Tree decomposition

Number of clusters: 28
Number of leaves: 14
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/Tree1.json

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

Cluster constraints 0 2 1.07 1.50 30 0 None 0.96 0.90 0.90

Variables per cluster 29 144 52.00 35.00 1,456 MAX VALUE 106.41 32.50 0.63 1.46

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

Separator variables 0 112 44.00 28.00 1,232 0 None 24.75 0.56 1.46

Clusters per var 1 8 6.50 7.00 1,456 MAX VALUE 397.69 2.02 0.31 1.50

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.07	1.50	30	0	None	0.96	0.90	0.90
Variables per cluster	29	144	52.00	35.00	1,456	MAX VALUE	106.41	32.50	0.63	1.46
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	112	44.00	28.00	1,232	0	None	24.75	0.56	1.46
Clusters per var	1	8	6.50	7.00	1,456	MAX VALUE	397.69	2.02	0.31	1.50

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/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/DualTree1.json

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

Cluster constraints 14 14 14.00 14.00 224 2.18e+18 42.22 0.00 0.00 0.00

Variables per cluster 15 15 15.00 15.00 240 6.57e+18 43.33 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 14 13.12 14.00 210 0 None 3.39 0.26 0.23

Clusters per variable 1 16 8.00 1.00 240 7.21e+16 38.82 7.48 0.94 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	14	14	14.00	14.00	224	2.18e+18	42.22	0.00	0.00	0.00
Variables per cluster	15	15	15.00	15.00	240	6.57e+18	43.33	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	14	13.12	14.00	210	0	None	3.39	0.26	0.23
Clusters per variable	1	16	8.00	1.00	240	7.21e+16	38.82	7.48	0.94	0.69

Primal graph

Density: 12.56%
MCB compute time (ms): 2,095
MCB cycles: 2,913
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/Primal1.json

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

Clustering coefficient 0.48 0.48 0.48 0.48 108.44 0.00 -162.49 0.00 0.00 0.00

Degree 28 28 28.00 28.00 6,272 MAX VALUE 746.41 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.07 3.00 8,934 MAX VALUE 3,256.36 0.25 0.08 0.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.48	0.48	0.48	108.44	0.00	-162.49	0.00	0.00	0.00
Degree	28	28	28.00	28.00	6,272	MAX VALUE	746.41	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.07	3.00	8,934	MAX VALUE	3,256.36	0.25	0.08	0.25

Triangulated primal graph

Density: 67.47%
MCB compute time (ms): 61,198
MCB cycles: 22,625
Triangles: None

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

Clustering coefficient 0.83 1.00 0.88 0.87 197.60 0.00 -28.46 0.05 0.06 2.11

Degree 28 189 150.46 174.00 33,704 MAX VALUE 1,099.99 50.78 0.34 2.11

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 67,875 MAX VALUE 24,856.10 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	0.87	197.60	0.00	-28.46	0.05	0.06	2.11
Degree	28	189	150.46	174.00	33,704	MAX VALUE	1,099.99	50.78	0.34	2.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	67,875	MAX VALUE	24,856.10	0.00	0.00	0.00

Dual graph

Density: 51.49%
MCB compute time (ms): 2
MCB cycles: 195
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-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 14 16 14.93 14.00 448 1.57e+35 81.04 1.00 0.07 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 780 MAX VALUE 270.33 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	14	16	14.93	14.00	448	1.57e+35	81.04	1.00	0.07	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	780	MAX VALUE	270.33	0.00	0.00	0.00

Minimal dual graph

Density: 51.49%
MCB compute time (ms): 2
MCB cycles: 195

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 14 16 14.93 14.00 448 1.57e+35 81.04 1.00 0.07 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 780 MAX VALUE 270.33 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	14	16	14.93	14.00	448	1.57e+35	81.04	1.00	0.07	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	780	MAX VALUE	270.33	0.00	0.00	0.00

Triangulated dual graph

Density: 72.41%
Triangles: 1,820

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

Clustering coefficient 0.70 1.00 0.86 1.00 25.86 0.01 -4.91 0.15 0.17 0.69

Degree 14 29 21.00 14.00 630 MAX VALUE 89.37 7.48 0.36 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	0.70	1.00	0.86	1.00	25.86	0.01	-4.91	0.15	0.17	0.69
Degree	14	29	21.00	14.00	630	MAX VALUE	89.37	7.48	0.36	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 72.41%

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

Clustering coefficient 0.70 1.00 0.86 1.00 25.86 0.01 -4.91 0.15 0.17 0.69

Degree 14 29 21.00 14.00 630 MAX VALUE 89.37 7.48 0.36 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	0.70	1.00	0.86	1.00	25.86	0.01	-4.91	0.15	0.17	0.69
Degree	14	29	21.00	14.00	630	MAX VALUE	89.37	7.48	0.36	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.39%
MCB compute time (ms): 68
MCB cycles: 195
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-16-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 3.53 2.00 896 MAX VALUE 236.31 4.19 1.19 0.44

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,560 MAX VALUE 405.49 0.00 0.00 0.00

XCSP 2.1 Benchmarks