XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg10-10-ext
Number of variables: 100
Number of constraints: 20
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 100
Number of constraints: 20

General features

Coarse blocks: 4,960
Value tables: 100

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

Arity 10 10 10.00 10.00 200 1.00e+20 46.05 0.00 0.00 0.00

Coarse blocks size 1 538 79.48 53.00 394,200 MAX VALUE 17,998.70 81.86 1.03 4.75

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -62,148.20 0.00 1.01 4.49

Tightness 1.00 1.00 1.00 1.00 20.00 1.00 -0.00 0.00 0.00 0.00

Tuples 1,971 1,971 1,971.00 1,971.00 39,420 MAX VALUE 151.73 0.00 0.00 0.00

Values 26 26 26.00 26.00 2,600 MAX VALUE 325.81 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 200 1.27e+30 69.31 0.00 0.00 0.00

Value table partitions 22 26 25.70 26.00 2,570 MAX VALUE 324.60 0.77 0.03 0.62

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	10	10	10.00	10.00	200	1.00e+20	46.05	0.00	0.00	0.00
Coarse blocks size	1	538	79.48	53.00	394,200	MAX VALUE	17,998.70	81.86	1.03	4.75
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-62,148.20	0.00	1.01	4.49
Tightness	1.00	1.00	1.00	1.00	20.00	1.00	-0.00	0.00	0.00	0.00
Tuples	1,971	1,971	1,971.00	1,971.00	39,420	MAX VALUE	151.73	0.00	0.00	0.00
Values	26	26	26.00	26.00	2,600	MAX VALUE	325.81	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	200	1.27e+30	69.31	0.00	0.00	0.00
Value table partitions	22	26	25.70	26.00	2,570	MAX VALUE	324.60	0.77	0.03	0.62

Tree decomposition

Number of clusters: 18
Number of leaves: 10
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-ext/Tree1.json

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

Cluster constraints 0 2 1.11 2.00 20 0 None 0.99 0.89 0.69

Variables per cluster 19 64 29.78 19.00 536 5.59e+25 59.29 14.52 0.49 1.09

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

Separator variables 0 48 24.22 18.00 436 0 None 11.56 0.48 1.09

Clusters per var 1 7 5.36 6.00 536 MAX VALUE 156.34 1.86 0.35 1.48

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.11	2.00	20	0	None	0.99	0.89	0.69
Variables per cluster	19	64	29.78	19.00	536	5.59e+25	59.29	14.52	0.49	1.09
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	48	24.22	18.00	436	0	None	11.56	0.48	1.09
Clusters per var	1	7	5.36	6.00	536	MAX VALUE	156.34	1.86	0.35	1.48

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-vg10-10-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-ext/DualTree1.json

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

Cluster constraints 10 10 10.00 10.00 100 1.00e+10 23.03 0.00 0.00 0.00

Variables per cluster 11 11 11.00 11.00 110 2.59e+10 23.98 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 10 9.00 10.00 90 0 None 3.00 0.33 0.33

Clusters per variable 1 10 5.50 5.50 110 1.00e+10 23.03 4.50 0.82 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	10	10	10.00	10.00	100	1.00e+10	23.03	0.00	0.00	0.00
Variables per cluster	11	11	11.00	11.00	110	2.59e+10	23.98	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	10	9.00	10.00	90	0	None	3.00	0.33	0.33
Clusters per variable	1	10	5.50	5.50	110	1.00e+10	23.03	4.50	0.82	0.69

Primal graph

Density: 18.18%
MCB compute time (ms): 133
MCB cycles: 837
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-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 47.06 0.00 -75.38 0.00 0.00 0.00

Degree 18 18 18.00 18.00 1,800 MAX VALUE 289.04 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.14 3.00 2,628 MAX VALUE 953.20 0.35 0.11 0.40

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.47	0.47	0.47	47.06	0.00	-75.38	0.00	0.00	0.00
Degree	18	18	18.00	18.00	1,800	MAX VALUE	289.04	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.14	3.00	2,628	MAX VALUE	953.20	0.35	0.11	0.40

Triangulated primal graph

Density: 67.58%
MCB compute time (ms): 444
MCB cycles: 4,337
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 87.54 0.00 -13.51 0.06 0.07 1.48

Degree 18 85 66.90 77.00 6,690 MAX VALUE 411.40 22.00 0.33 1.48

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 13,011 MAX VALUE 4,764.68 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	87.54	0.00	-13.51	0.06	0.07	1.48
Degree	18	85	66.90	77.00	6,690	MAX VALUE	411.40	22.00	0.33	1.48
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	13,011	MAX VALUE	4,764.68	0.00	0.00	0.00

Dual graph

Density: 52.63%
MCB compute time (ms): 1
MCB cycles: 81
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-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 10 10 10.00 10.00 200 1.00e+20 46.05 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 324 MAX VALUE 112.29 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	10	10	10.00	10.00	200	1.00e+20	46.05	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	324	MAX VALUE	112.29	0.00	0.00	0.00

Minimal dual graph

Density: 52.63%
MCB compute time (ms): 0
MCB cycles: 81

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 10 10 10.00 10.00 200 1.00e+20 46.05 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 324 MAX VALUE 112.29 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	10	10	10.00	10.00	200	1.00e+20	46.05	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	324	MAX VALUE	112.29	0.00	0.00	0.00

Triangulated dual graph

Density: 76.32%
Triangles: 570

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

Clustering coefficient 0.74 1.00 0.87 0.87 17.37 0.05 -3.05 0.13 0.15 0.69

Degree 10 19 14.50 14.50 290 6.13e+22 52.47 4.50 0.31 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	0.74	1.00	0.87	0.87	17.37	0.05	-3.05	0.13	0.15	0.69
Degree	10	19	14.50	14.50	290	6.13e+22	52.47	4.50	0.31	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 76.32%

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

Clustering coefficient 0.74 1.00 0.87 0.87 17.37 0.05 -3.05 0.13 0.15 0.69

Degree 10 19 14.50 14.50 290 6.13e+22 52.47 4.50 0.31 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	0.74	1.00	0.87	0.87	17.37	0.05	-3.05	0.13	0.15	0.69
Degree	10	19	14.50	14.50	290	6.13e+22	52.47	4.50	0.31	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.80%
MCB compute time (ms): 15
MCB cycles: 81
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-10-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 3.33 2.00 400 MAX VALUE 115.37 2.98 0.89 0.45

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 648 MAX VALUE 168.44 0.00 0.00 0.00

XCSP 2.1 Benchmarks