XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg8-10-ext
Number of variables: 80
Number of constraints: 18
Satisfiable: True
Timestamp: 2025-07-20 22:08:36
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 80
Number of constraints: 18

General features

Coarse blocks: 4,004
Value tables: 80

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

Arity 8 10 8.89 8.00 160 1.07e+17 39.22 0.99 0.11 0.69

Coarse blocks size 1 861 111.45 75.00 446,240 MAX VALUE 15,802.80 120.09 1.08 5.15

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -49,748.90 0.00 1.01 4.77

Tightness 1.00 1.00 1.00 1.00 18.00 1.00 -0.00 0.00 0.00 0.69

Tuples 1,971 3,607 2,879.89 3,607.00 51,838 MAX VALUE 142.60 812.93 0.28 0.69

Values 26 26 26.00 26.00 2,080 MAX VALUE 260.65 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 160 1.21e+24 55.45 0.00 0.00 0.00

Value table partitions 23 26 25.80 26.00 2,064 MAX VALUE 260.01 0.60 0.02 0.46

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	8	10	8.89	8.00	160	1.07e+17	39.22	0.99	0.11	0.69
Coarse blocks size	1	861	111.45	75.00	446,240	MAX VALUE	15,802.80	120.09	1.08	5.15
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-49,748.90	0.00	1.01	4.77
Tightness	1.00	1.00	1.00	1.00	18.00	1.00	-0.00	0.00	0.00	0.69
Tuples	1,971	3,607	2,879.89	3,607.00	51,838	MAX VALUE	142.60	812.93	0.28	0.69
Values	26	26	26.00	26.00	2,080	MAX VALUE	260.65	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	160	1.21e+24	55.45	0.00	0.00	0.00
Value table partitions	23	26	25.80	26.00	2,064	MAX VALUE	260.01	0.60	0.02	0.46

Tree decomposition

Number of clusters: 16
Number of leaves: 8
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/Tree1.json

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

Cluster constraints 0 2 1.12 1.50 18 0 None 0.93 0.82 0.97

Variables per cluster 17 52 25.75 20.00 412 9.95e+21 50.65 11.37 0.44 1.44

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

Separator variables 0 40 20.75 16.00 332 0 None 9.27 0.45 1.44

Clusters per var 1 7 5.15 6.00 412 MAX VALUE 121.75 1.82 0.35 1.60

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.12	1.50	18	0	None	0.93	0.82	0.97
Variables per cluster	17	52	25.75	20.00	412	9.95e+21	50.65	11.37	0.44	1.44
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	40	20.75	16.00	332	0	None	9.27	0.45	1.44
Clusters per var	1	7	5.15	6.00	412	MAX VALUE	121.75	1.82	0.35	1.60

Dual tree decomposition

Number of clusters: 10
Number of leaves: 2
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/DualTree1.json

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

Cluster constraints 8 8 8.00 8.00 80 1.07e+09 20.79 0.00 0.00 0.00

Variables per cluster 9 9 9.00 9.00 90 3.49e+09 21.97 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 7.20 8.00 72 0 None 2.40 0.33 0.33

Clusters per variable 1 10 5.00 1.00 90 100,000,000 18.42 4.47 0.89 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	8	8	8.00	8.00	80	1.07e+09	20.79	0.00	0.00	0.00
Variables per cluster	9	9	9.00	9.00	90	3.49e+09	21.97	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	7.20	8.00	72	0	None	2.40	0.33	0.33
Clusters per variable	1	10	5.00	1.00	90	100,000,000	18.42	4.47	0.89	0.69

Primal graph

Density: 20.25%
MCB compute time (ms): 38
MCB cycles: 561
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/Primal1.json

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

Clustering coefficient 0.47 0.47 0.47 0.47 38.00 0.00 -59.56 0.00 0.00 0.00

Degree 16 16 16.00 16.00 1,280 MAX VALUE 221.81 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.11 3.00 1,746 MAX VALUE 634.45 0.32 0.10 0.35

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.47	0.47	0.47	38.00	0.00	-59.56	0.00	0.00	0.00
Degree	16	16	16.00	16.00	1,280	MAX VALUE	221.81	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.11	3.00	1,746	MAX VALUE	634.45	0.32	0.10	0.35

Triangulated primal graph

Density: 68.58%
MCB compute time (ms): 283
MCB cycles: 2,296
Triangles: None

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

Clustering coefficient 0.82 1.00 0.88 0.85 70.06 0.00 -10.77 0.06 0.06 2.19

Degree 16 68 54.17 62.50 4,334 MAX VALUE 312.82 17.32 0.32 2.19

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 6,888 MAX VALUE 2,522.41 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	0.85	70.06	0.00	-10.77	0.06	0.06	2.19
Degree	16	68	54.17	62.50	4,334	MAX VALUE	312.82	17.32	0.32	2.19
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	6,888	MAX VALUE	2,522.41	0.00	0.00	0.00

Dual graph

Density: 52.29%
MCB compute time (ms): 0
MCB cycles: 63
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-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 10 8.89 8.00 160 1.07e+17 39.22 0.99 0.11 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 252 8.51e+37 87.34 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	10	8.89	8.00	160	1.07e+17	39.22	0.99	0.11	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	252	8.51e+37	87.34	0.00	0.00	0.00

Minimal dual graph

Density: 52.29%
MCB compute time (ms): 0
MCB cycles: 63

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 10 8.89 8.00 160 1.07e+17 39.22 0.99 0.11 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 252 8.51e+37 87.34 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	10	8.89	8.00	160	1.07e+17	39.22	0.99	0.11	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	252	8.51e+37	87.34	0.00	0.00	0.00

Triangulated dual graph

Density: 70.59%
Triangles: 336

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

Clustering coefficient 0.67 1.00 0.85 1.00 15.35 0.04 -3.21 0.16 0.19 0.69

Degree 8 17 12.00 8.00 216 7.49e+18 43.46 4.47 0.37 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	15.35	0.04	-3.21	0.16	0.19	0.69
Degree	8	17	12.00	8.00	216	7.49e+18	43.46	4.47	0.37	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 70.59%

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

Clustering coefficient 0.67 1.00 0.85 1.00 15.35 0.04 -3.21 0.16 0.19 0.69

Degree 8 17 12.00 8.00 216 7.49e+18 43.46 4.47 0.37 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	15.35	0.04	-3.21	0.16	0.19	0.69
Degree	8	17	12.00	8.00	216	7.49e+18	43.46	4.47	0.37	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 3.37%
MCB compute time (ms): 7
MCB cycles: 63
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg8-10-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 10 3.27 2.00 320 MAX VALUE 94.67 2.70 0.83 0.60

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 504 MAX VALUE 131.00 0.00 0.00 0.00

XCSP 2.1 Benchmarks