XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg11-14-ext
Number of variables: 154
Number of constraints: 25
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 154
Number of constraints: 25

General features

Coarse blocks: 6,307
Value tables: 154

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

Arity 11 14 12.32 11.00 308 1.54e+27 62.60 1.49 0.12 0.69

Coarse blocks size 1 338 30.18 11.00 190,344 MAX VALUE 15,572.90 43.02 1.43 3.97

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -107,947.00 0.00 0.84 2.76

Tightness 1.00 1.00 1.00 1.00 25.00 1.00 -0.00 0.00 0.00 0.69

Tuples 116 1,120 678.24 1,120.00 16,956 MAX VALUE 150.59 498.37 0.73 0.69

Values 26 26 26.00 26.00 4,004 MAX VALUE 501.75 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 308 MAX VALUE 106.75 0.00 0.00 0.00

Value table partitions 20 26 23.78 24.00 3,662 MAX VALUE 487.79 1.21 0.05 1.54

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	11	14	12.32	11.00	308	1.54e+27	62.60	1.49	0.12	0.69
Coarse blocks size	1	338	30.18	11.00	190,344	MAX VALUE	15,572.90	43.02	1.43	3.97
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-107,947.00	0.00	0.84	2.76
Tightness	1.00	1.00	1.00	1.00	25.00	1.00	-0.00	0.00	0.00	0.69
Tuples	116	1,120	678.24	1,120.00	16,956	MAX VALUE	150.59	498.37	0.73	0.69
Values	26	26	26.00	26.00	4,004	MAX VALUE	501.75	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	308	MAX VALUE	106.75	0.00	0.00	0.00
Value table partitions	20	26	23.78	24.00	3,662	MAX VALUE	487.79	1.21	0.05	1.54

Tree decomposition

Number of clusters: 23
Number of leaves: 11
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/Tree1.json

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

Cluster constraints 0 2 1.09 1.00 25 0 None 0.93 0.85 0.99

Variables per cluster 24 102 40.48 33.00 931 5.58e+35 82.31 22.32 0.55 1.60

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

Separator variables 0 74 33.78 23.00 777 0 None 17.17 0.51 1.60

Clusters per var 1 8 6.05 7.00 931 MAX VALUE 261.01 1.99 0.33 1.65

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.09	1.00	25	0	None	0.93	0.85	0.99
Variables per cluster	24	102	40.48	33.00	931	5.58e+35	82.31	22.32	0.55	1.60
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	74	33.78	23.00	777	0	None	17.17	0.51	1.60
Clusters per var	1	8	6.05	7.00	931	MAX VALUE	261.01	1.99	0.33	1.65

Dual tree decomposition

Number of clusters: 14
Number of leaves: 2
Tree depth: 7
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/DualTree1.json

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

Cluster constraints 11 11 11.00 11.00 154 3.80e+14 33.57 0.00 0.00 0.00

Variables per cluster 12 12 12.00 12.00 168 1.28e+15 34.79 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 11 10.21 11.00 143 0 None 2.83 0.28 0.26

Clusters per variable 1 14 6.72 1.00 168 4.05e+12 29.03 6.45 0.96 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	11	11	11.00	11.00	154	3.80e+14	33.57	0.00	0.00	0.00
Variables per cluster	12	12	12.00	12.00	168	1.28e+15	34.79	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	11	10.21	11.00	143	0	None	2.83	0.28	0.26
Clusters per variable	1	14	6.72	1.00	168	4.05e+12	29.03	6.45	0.96	0.69

Primal graph

Density: 15.03%
MCB compute time (ms): 422
MCB cycles: 1,618
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-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 74.87 0.00 -111.07 0.00 0.00 0.00

Degree 23 23 23.00 23.00 3,542 MAX VALUE 482.87 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.08 3.00 4,984 MAX VALUE 1,814.95 0.27 0.09 0.28

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.49	0.49	0.49	74.87	0.00	-111.07	0.00	0.00	0.00
Degree	23	23	23.00	23.00	3,542	MAX VALUE	482.87	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.08	3.00	4,984	MAX VALUE	1,814.95	0.27	0.09	0.28

Triangulated primal graph

Density: 67.76%
MCB compute time (ms): 8,079
MCB cycles: 10,438
Triangles: None

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

Clustering coefficient 0.83 1.00 0.88 0.85 135.49 0.00 -19.98 0.05 0.06 2.94

Degree 23 130 103.67 121.00 15,966 MAX VALUE 700.10 34.40 0.33 2.80

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 31,314 MAX VALUE 11,467.30 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	0.85	135.49	0.00	-19.98	0.05	0.06	2.94
Degree	23	130	103.67	121.00	15,966	MAX VALUE	700.10	34.40	0.33	2.80
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	31,314	MAX VALUE	11,467.30	0.00	0.00	0.00

Dual graph

Density: 51.33%
MCB compute time (ms): 1
MCB cycles: 130
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-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 11 14 12.32 11.00 308 1.54e+27 62.60 1.49 0.12 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 520 MAX VALUE 180.22 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	11	14	12.32	11.00	308	1.54e+27	62.60	1.49	0.12	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	520	MAX VALUE	180.22	0.00	0.00	0.00

Minimal dual graph

Density: 51.33%
MCB compute time (ms): 1
MCB cycles: 130

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 11 14 12.32 11.00 308 1.54e+27 62.60 1.49 0.12 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 520 MAX VALUE 180.22 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	11	14	12.32	11.00	308	1.54e+27	62.60	1.49	0.12	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	520	MAX VALUE	180.22	0.00	0.00	0.00

Triangulated dual graph

Density: 69.67%
Triangles: 935

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

Clustering coefficient 0.67 1.00 0.85 1.00 21.37 0.01 -4.40 0.16 0.19 0.69

Degree 11 24 16.72 11.00 418 5.78e+29 68.53 6.45 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	0.85	1.00	21.37	0.01	-4.40	0.16	0.19	0.69
Degree	11	24	16.72	11.00	418	5.78e+29	68.53	6.45	0.39	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 69.67%

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

Clustering coefficient 0.67 1.00 0.85 1.00 21.37 0.01 -4.40 0.16 0.19 0.69

Degree 11 24 16.72 11.00 418 5.78e+29 68.53 6.45 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	0.85	1.00	21.37	0.01	-4.40	0.16	0.19	0.69
Degree	11	24	16.72	11.00	418	5.78e+29	68.53	6.45	0.39	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.93%
MCB compute time (ms): 29
MCB cycles: 130
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg11-14-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 14 3.44 2.00 616 MAX VALUE 169.34 3.62 1.05 0.50

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,040 MAX VALUE 270.33 0.00 0.00 0.00

XCSP 2.1 Benchmarks