XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg13-14-ext
Number of variables: 182
Number of constraints: 27
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 182
Number of constraints: 27

General features

Coarse blocks: 6,867
Value tables: 182

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

Arity 13 14 13.48 13.00 364 3.13e+30 70.22 0.50 0.04 0.69

Coarse blocks size 1 79 10.47 7.00 71,890 MAX VALUE 12,642.70 10.87 1.04 3.22

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -119,963.00 0.00 0.82 2.78

Tightness 1.00 1.00 1.00 1.00 27.00 1.00 -0.00 0.00 0.00 0.69

Tuples 116 279 200.52 279.00 5,414 MAX VALUE 140.63 81.44 0.41 0.69

Values 26 26 26.00 26.00 4,732 MAX VALUE 592.97 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 364 MAX VALUE 126.15 0.00 0.00 0.00

Value table partitions 17 26 21.56 22.00 3,924 MAX VALUE 558.41 1.56 0.07 1.85

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	13	14	13.48	13.00	364	3.13e+30	70.22	0.50	0.04	0.69
Coarse blocks size	1	79	10.47	7.00	71,890	MAX VALUE	12,642.70	10.87	1.04	3.22
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-119,963.00	0.00	0.82	2.78
Tightness	1.00	1.00	1.00	1.00	27.00	1.00	-0.00	0.00	0.00	0.69
Tuples	116	279	200.52	279.00	5,414	MAX VALUE	140.63	81.44	0.41	0.69
Values	26	26	26.00	26.00	4,732	MAX VALUE	592.97	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	364	MAX VALUE	126.15	0.00	0.00	0.00
Value table partitions	17	26	21.56	22.00	3,924	MAX VALUE	558.41	1.56	0.07	1.85

Tree decomposition

Number of clusters: 25
Number of leaves: 13
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-ext/Tree1.json

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

Cluster constraints 0 2 1.08 2.00 27 0 None 0.98 0.90 0.83

Variables per cluster 26 118 45.24 26.00 1,131 MAX VALUE 91.82 26.73 0.59 1.40

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

Separator variables 0 90 37.96 25.00 949 0 None 20.63 0.54 1.40

Clusters per var 1 8 6.21 7.00 1,131 MAX VALUE 313.68 2.03 0.33 1.67

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.08	2.00	27	0	None	0.98	0.90	0.83
Variables per cluster	26	118	45.24	26.00	1,131	MAX VALUE	91.82	26.73	0.59	1.40
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	90	37.96	25.00	949	0	None	20.63	0.54	1.40
Clusters per var	1	8	6.21	7.00	1,131	MAX VALUE	313.68	2.03	0.33	1.67

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-vg13-14-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-ext/DualTree1.json

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

Cluster constraints 13 13 13.00 13.00 182 3.94e+15 35.91 0.00 0.00 0.00

Variables per cluster 14 14 14.00 14.00 196 1.11e+16 36.95 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 13 12.07 13.00 169 0 None 3.35 0.28 0.26

Clusters per variable 1 14 7.26 1.00 196 7.94e+14 34.31 6.50 0.89 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	13	13	13.00	13.00	182	3.94e+15	35.91	0.00	0.00	0.00
Variables per cluster	14	14	14.00	14.00	196	1.11e+16	36.95	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	13	12.07	13.00	169	0	None	3.35	0.28	0.26
Clusters per variable	1	14	7.26	1.00	196	7.94e+14	34.31	6.50	0.89	0.69

Primal graph

Density: 13.81%
MCB compute time (ms): 1,186
MCB cycles: 2,094
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-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 87.36 0.00 -133.58 0.00 0.00 0.00

Degree 25 25 25.00 25.00 4,550 MAX VALUE 585.84 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 6,438 MAX VALUE 2,345.37 0.26 0.09 0.27

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.48	0.48	0.48	87.36	0.00	-133.58	0.00	0.00	0.00
Degree	25	25	25.00	25.00	4,550	MAX VALUE	585.84	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	6,438	MAX VALUE	2,345.37	0.26	0.09	0.27

Triangulated primal graph

Density: 67.32%
MCB compute time (ms): 16,260
MCB cycles: 13,145
Triangles: None

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

Clustering coefficient 0.82 1.00 0.88 0.87 160.16 0.00 -23.60 0.05 0.06 2.62

Degree 25 155 121.86 137.00 22,178 MAX VALUE 855.95 40.97 0.34 2.62

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 39,435 MAX VALUE 14,441.30 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	0.87	160.16	0.00	-23.60	0.05	0.06	2.62
Degree	25	155	121.86	137.00	22,178	MAX VALUE	855.95	40.97	0.34	2.62
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	39,435	MAX VALUE	14,441.30	0.00	0.00	0.00

Dual graph

Density: 51.85%
MCB compute time (ms): 1
MCB cycles: 156
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-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 13 14 13.48 13.00 364 3.13e+30 70.22 0.50 0.04 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 624 MAX VALUE 216.26 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	13	14	13.48	13.00	364	3.13e+30	70.22	0.50	0.04	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	624	MAX VALUE	216.26	0.00	0.00	0.00

Minimal dual graph

Density: 51.85%
MCB compute time (ms): 1
MCB cycles: 156

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 13 14 13.48 13.00 364 3.13e+30 70.22 0.50 0.04 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 624 MAX VALUE 216.26 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	13	14	13.48	13.00	364	3.13e+30	70.22	0.50	0.04	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	624	MAX VALUE	216.26	0.00	0.00	0.00

Triangulated dual graph

Density: 74.07%
Triangles: 1,378

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

Clustering coefficient 0.72 1.00 0.87 1.00 23.36 0.01 -4.27 0.14 0.16 0.69

Degree 13 26 19.26 13.00 520 9.77e+33 78.26 6.50 0.34 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	0.72	1.00	0.87	1.00	23.36	0.01	-4.27	0.14	0.16	0.69
Degree	13	26	19.26	13.00	520	9.77e+33	78.26	6.50	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 74.07%

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

Clustering coefficient 0.72 1.00 0.87 1.00 23.36 0.01 -4.27 0.14 0.16 0.69

Degree 13 26 19.26 13.00 520 9.77e+33 78.26 6.50 0.34 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	0.72	1.00	0.87	1.00	23.36	0.01	-4.27	0.14	0.16	0.69
Degree	13	26	19.26	13.00	520	9.77e+33	78.26	6.50	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.67%
MCB compute time (ms): 56
MCB cycles: 156
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg13-14-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 3.48 2.00 728 MAX VALUE 196.37 3.86 1.11 0.47

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,248 MAX VALUE 324.39 0.00 0.00 0.00

XCSP 2.1 Benchmarks