XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg14-18-ext
Number of variables: 252
Number of constraints: 32
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 252
Number of constraints: 32

General features

Coarse blocks: 5,348
Value tables: 252

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

Arity 14 18 15.75 14.00 504 1.60e+38 87.97 1.98 0.13 0.69

Coarse blocks size 1 40 5.65 4.00 30,240 MAX VALUE 6,760.44 5.56 0.98 2.53

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -48,251.60 0.00 0.25 0.27

Tightness 1.00 1.00 1.00 1.00 32.00 1.00 0.00 0.00 0.00 0.00

Tuples 4 116 67.00 116.00 2,144 MAX VALUE 104.97 55.56 0.83 0.69

Values 26 26 26.00 26.00 6,552 MAX VALUE 821.04 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 504 MAX VALUE 174.67 0.00 0.00 0.00

Value table partitions 14 21 17.76 18.00 4,476 MAX VALUE 723.91 1.64 0.09 1.82

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	14	18	15.75	14.00	504	1.60e+38	87.97	1.98	0.13	0.69
Coarse blocks size	1	40	5.65	4.00	30,240	MAX VALUE	6,760.44	5.56	0.98	2.53
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-48,251.60	0.00	0.25	0.27
Tightness	1.00	1.00	1.00	1.00	32.00	1.00	0.00	0.00	0.00	0.00
Tuples	4	116	67.00	116.00	2,144	MAX VALUE	104.97	55.56	0.83	0.69
Values	26	26	26.00	26.00	6,552	MAX VALUE	821.04	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	504	MAX VALUE	174.67	0.00	0.00	0.00
Value table partitions	14	21	17.76	18.00	4,476	MAX VALUE	723.91	1.64	0.09	1.82

Tree decomposition

Number of clusters: 30
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-vg14-18-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/Tree1.json

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

Cluster constraints 0 2 1.07 1.00 32 0 None 0.93 0.87 0.99

Variables per cluster 31 164 56.53 43.00 1,696 MAX VALUE 116.36 36.25 0.64 1.62

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

Separator variables 0 124 48.13 36.00 1,444 0 None 27.60 0.57 1.62

Clusters per var 1 9 6.73 8.00 1,696 MAX VALUE 456.78 2.08 0.31 1.73

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.07	1.00	32	0	None	0.93	0.87	0.99
Variables per cluster	31	164	56.53	43.00	1,696	MAX VALUE	116.36	36.25	0.64	1.62
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	124	48.13	36.00	1,444	0	None	27.60	0.57	1.62
Clusters per var	1	9	6.73	8.00	1,696	MAX VALUE	456.78	2.08	0.31	1.73

Dual tree decomposition

Number of clusters: 18
Number of leaves: 2
Tree depth: 9
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/DualTree1.json

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

Cluster constraints 14 14 14.00 14.00 252 4.27e+20 47.50 0.00 0.00 0.00

Variables per cluster 15 15 15.00 15.00 270 1.48e+21 48.74 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 13.22 14.00 238 0 None 3.21 0.24 0.21

Clusters per variable 1 18 8.44 1.00 270 3.75e+17 40.47 8.43 1.00 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	14	14	14.00	14.00	252	4.27e+20	47.50	0.00	0.00	0.00
Variables per cluster	15	15	15.00	15.00	270	1.48e+21	48.74	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	13.22	14.00	238	0	None	3.21	0.24	0.21
Clusters per variable	1	18	8.44	1.00	270	3.75e+17	40.47	8.43	1.00	0.69

Primal graph

Density: 11.95%
MCB compute time (ms): 3,043
MCB cycles: 3,529
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/Primal1.json

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

Clustering coefficient 0.49 0.49 0.49 0.49 123.97 0.00 -178.76 0.00 0.00 0.00

Degree 30 30 30.00 30.00 7,560 MAX VALUE 857.10 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 10,808 MAX VALUE 3,940.58 0.24 0.08 0.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.49	0.49	0.49	123.97	0.00	-178.76	0.00	0.00	0.00
Degree	30	30	30.00	30.00	7,560	MAX VALUE	857.10	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	10,808	MAX VALUE	3,940.58	0.24	0.08	0.23

Triangulated primal graph

Density: 67.49%
MCB compute time (ms): 9,166
MCB cycles: 31,698
Triangles: None

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

Clustering coefficient 0.82 1.00 0.88 0.86 222.35 0.00 -31.96 0.05 0.06 2.98

Degree 30 216 169.41 192.00 42,690 MAX VALUE 1,267.27 57.08 0.34 2.98

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 95,094 MAX VALUE 34,823.80 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	0.88	0.86	222.35	0.00	-31.96	0.05	0.06	2.98
Degree	30	216	169.41	192.00	42,690	MAX VALUE	1,267.27	57.08	0.34	2.98
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	95,094	MAX VALUE	34,823.80	0.00	0.00	0.00

Dual graph

Density: 50.81%
MCB compute time (ms): 3
MCB cycles: 221
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-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 18 15.75 14.00 504 1.60e+38 87.97 1.98 0.13 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 884 MAX VALUE 306.37 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	18	15.75	14.00	504	1.60e+38	87.97	1.98	0.13	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	884	MAX VALUE	306.37	0.00	0.00	0.00

Minimal dual graph

Density: 50.81%
MCB compute time (ms): 2
MCB cycles: 221

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 18 15.75 14.00 504 1.60e+38 87.97 1.98 0.13 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 884 MAX VALUE 306.37 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	18	15.75	14.00	504	1.60e+38	87.97	1.98	0.13	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	884	MAX VALUE	306.37	0.00	0.00	0.00

Triangulated dual graph

Density: 69.15%
Triangles: 2,002

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

Clustering coefficient 0.67 1.00 0.86 1.00 27.39 0.00 -5.59 0.16 0.19 0.69

Degree 14 31 21.44 14.00 686 MAX VALUE 95.58 8.43 0.39 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	0.67	1.00	0.86	1.00	27.39	0.00	-5.59	0.16	0.19	0.69
Degree	14	31	21.44	14.00	686	MAX VALUE	95.58	8.43	0.39	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 69.15%

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

Clustering coefficient 0.67 1.00 0.86 1.00 27.39 0.00 -5.59 0.16 0.19 0.69

Degree 14 31 21.44 14.00 686 MAX VALUE 95.58 8.43 0.39 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	0.67	1.00	0.86	1.00	27.39	0.00	-5.59	0.16	0.19	0.69
Degree	14	31	21.44	14.00	686	MAX VALUE	95.58	8.43	0.39	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.25%
MCB compute time (ms): 101
MCB cycles: 221
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg14-18-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 18 3.55 2.00 1,008 MAX VALUE 262.64 4.40 1.24 0.43

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,768 MAX VALUE 459.56 0.00 0.00 0.00

XCSP 2.1 Benchmarks