XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg16-20-ext
Number of variables: 320
Number of constraints: 36
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 320
Number of constraints: 36

General features

Coarse blocks: 3,420
Value tables: 320

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

Arity 16 20 17.78 16.00 640 MAX VALUE 103.38 1.99 0.11 0.69

Coarse blocks size 1 6 1.68 1.00 5,760 MAX VALUE 1,291.90 1.03 0.61 1.12

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -12,504.60 0.00 0.00 0.00

Tightness 1.00 1.00 1.00 1.00 36.00 1.00 0.00 0.00 0.00 0.00

Tuples 1 17 9.89 17.00 356 4.06e+24 56.66 7.95 0.80 0.69

Values 26 26 26.00 26.00 8,320 MAX VALUE 1,042.59 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 640 MAX VALUE 221.81 0.00 0.00 0.00

Value table partitions 7 14 10.06 10.00 3,218 MAX VALUE 734.13 1.69 0.17 1.88

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	16	20	17.78	16.00	640	MAX VALUE	103.38	1.99	0.11	0.69
Coarse blocks size	1	6	1.68	1.00	5,760	MAX VALUE	1,291.90	1.03	0.61	1.12
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-12,504.60	0.00	0.00	0.00
Tightness	1.00	1.00	1.00	1.00	36.00	1.00	0.00	0.00	0.00	0.00
Tuples	1	17	9.89	17.00	356	4.06e+24	56.66	7.95	0.80	0.69
Values	26	26	26.00	26.00	8,320	MAX VALUE	1,042.59	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	640	MAX VALUE	221.81	0.00	0.00	0.00
Value table partitions	7	14	10.06	10.00	3,218	MAX VALUE	734.13	1.69	0.17	1.88

Tree decomposition

Number of clusters: 34
Number of leaves: 16
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/Tree1.json

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

Cluster constraints 0 2 1.06 1.00 36 0 None 0.94 0.89 0.97

Variables per cluster 35 208 66.35 49.00 2,256 MAX VALUE 136.67 45.86 0.69 1.60

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

Separator variables 0 160 56.94 41.00 1,936 0 None 34.94 0.61 1.60

Clusters per var 1 9 7.05 8.00 2,256 MAX VALUE 596.66 2.10 0.30 1.68

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.06	1.00	36	0	None	0.94	0.89	0.97
Variables per cluster	35	208	66.35	49.00	2,256	MAX VALUE	136.67	45.86	0.69	1.60
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	160	56.94	41.00	1,936	0	None	34.94	0.61	1.60
Clusters per var	1	9	7.05	8.00	2,256	MAX VALUE	596.66	2.10	0.30	1.68

Dual tree decomposition

Number of clusters: 20
Number of leaves: 2
Tree depth: 10
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/DualTree1.json

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

Cluster constraints 16 16 16.00 16.00 320 1.21e+24 55.45 0.00 0.00 0.00

Variables per cluster 17 17 17.00 17.00 340 4.06e+24 56.66 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 16 15.20 16.00 304 0 None 3.49 0.23 0.20

Clusters per variable 1 20 9.44 1.00 340 6.55e+20 47.93 9.44 1.00 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	16	16.00	16.00	320	1.21e+24	55.45	0.00	0.00	0.00
Variables per cluster	17	17	17.00	17.00	340	4.06e+24	56.66	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	16	15.20	16.00	304	0	None	3.49	0.23	0.20
Clusters per variable	1	20	9.44	1.00	340	6.55e+20	47.93	9.44	1.00	0.69

Primal graph

Density: 10.66%
MCB compute time (ms): 7,834
MCB cycles: 5,121
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/Primal1.json

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

Clustering coefficient 0.49 0.49 0.49 0.49 157.43 0.00 -226.98 0.00 0.00 0.00

Degree 34 34 34.00 34.00 10,880 MAX VALUE 1,128.44 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 15,648 MAX VALUE 5,707.98 0.23 0.08 0.21

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.49	0.49	0.49	157.43	0.00	-226.98	0.00	0.00	0.00
Degree	34	34	34.00	34.00	10,880	MAX VALUE	1,128.44	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	15,648	MAX VALUE	5,707.98	0.23	0.08	0.21

Triangulated primal graph

Density: 67.72%
MCB compute time (ms): 635,317
MCB cycles: 38,768
Triangles: None

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

Clustering coefficient 0.84 1.00 0.89 0.87 283.23 0.00 -39.55 0.05 0.06 2.30

Degree 34 272 216.04 250.50 69,132 MAX VALUE 1,685.67 73.15 0.34 2.30

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 116,304 MAX VALUE 42,591.00 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.84	1.00	0.89	0.87	283.23	0.00	-39.55	0.05	0.06	2.30
Degree	34	272	216.04	250.50	69,132	MAX VALUE	1,685.67	73.15	0.34	2.30
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	116,304	MAX VALUE	42,591.00	0.00	0.00	0.00

Dual graph

Density: 50.79%
MCB compute time (ms): 5
MCB cycles: 285
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-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 16 20 17.78 16.00 640 MAX VALUE 103.38 1.99 0.11 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 1,140 MAX VALUE 395.09 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	16	20	17.78	16.00	640	MAX VALUE	103.38	1.99	0.11	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	1,140	MAX VALUE	395.09	0.00	0.00	0.00

Minimal dual graph

Density: 50.79%
MCB compute time (ms): 5
MCB cycles: 285

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 16 20 17.78 16.00 640 MAX VALUE 103.38 1.99 0.11 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 1,140 MAX VALUE 395.09 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	16	20	17.78	16.00	640	MAX VALUE	103.38	1.99	0.11	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	1,140	MAX VALUE	395.09	0.00	0.00	0.00

Triangulated dual graph

Density: 69.84%
Triangles: 2,960

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

Clustering coefficient 0.68 1.00 0.86 1.00 30.89 0.00 -6.15 0.16 0.18 0.69

Degree 16 35 24.44 16.00 880 MAX VALUE 112.34 9.44 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	0.68	1.00	0.86	1.00	30.89	0.00	-6.15	0.16	0.18	0.69
Degree	16	35	24.44	16.00	880	MAX VALUE	112.34	9.44	0.39	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 69.84%

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

Clustering coefficient 0.68 1.00 0.86 1.00 30.89 0.00 -6.15 0.16 0.18 0.69

Degree 16 35 24.44 16.00 880 MAX VALUE 112.34 9.44 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	0.68	1.00	0.86	1.00	30.89	0.00	-6.15	0.16	0.18	0.69
Degree	16	35	24.44	16.00	880	MAX VALUE	112.34	9.44	0.39	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.01%
MCB compute time (ms): 181
MCB cycles: 285
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg16-20-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 20 3.60 2.00 1,280 MAX VALUE 325.19 4.80 1.33 0.40

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 2,280 MAX VALUE 592.64 0.00 0.00 0.00

XCSP 2.1 Benchmarks