XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg12-15-ext
Number of variables: 180
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: 180
Number of constraints: 27

General features

Coarse blocks: 6,423
Value tables: 180

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

Arity 12 15 13.33 12.00 360 2.00e+30 69.77 1.49 0.11 0.69

Coarse blocks size 1 170 17.85 7.00 114,660 MAX VALUE 12,997.50 23.46 1.31 3.55

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -104,936.00 0.00 0.74 1.99

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

Tuples 44 593 349.00 593.00 9,423 MAX VALUE 141.19 272.80 0.78 0.69

Values 26 26 26.00 26.00 4,680 MAX VALUE 586.46 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Value table partitions 18 26 22.63 23.00 4,074 MAX VALUE 560.93 1.77 0.08 1.92

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	12	15	13.33	12.00	360	2.00e+30	69.77	1.49	0.11	0.69
Coarse blocks size	1	170	17.85	7.00	114,660	MAX VALUE	12,997.50	23.46	1.31	3.55
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-104,936.00	0.00	0.74	1.99
Tightness	1.00	1.00	1.00	1.00	27.00	1.00	-0.00	0.00	0.00	0.69
Tuples	44	593	349.00	593.00	9,423	MAX VALUE	141.19	272.80	0.78	0.69
Values	26	26	26.00	26.00	4,680	MAX VALUE	586.46	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	360	MAX VALUE	124.77	0.00	0.00	0.00
Value table partitions	18	26	22.63	23.00	4,074	MAX VALUE	560.93	1.77	0.08	1.92

Tree decomposition

Number of clusters: 25
Number of leaves: 12
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-ext/Tree1.json

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

Cluster constraints 0 2 1.08 1.00 27 0 None 0.93 0.87 0.97

Variables per cluster 26 114 45.08 36.00 1,127 MAX VALUE 91.86 26.25 0.58 1.62

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

Separator variables 0 90 37.88 25.00 947 0 None 20.18 0.53 1.62

Clusters per var 1 8 6.26 7.00 1,127 MAX VALUE 311.86 2.03 0.32 1.70

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.08	1.00	27	0	None	0.93	0.87	0.97
Variables per cluster	26	114	45.08	36.00	1,127	MAX VALUE	91.86	26.25	0.58	1.62
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	90	37.88	25.00	947	0	None	20.18	0.53	1.62
Clusters per var	1	8	6.26	7.00	1,127	MAX VALUE	311.86	2.03	0.32	1.70

Dual tree decomposition

Number of clusters: 15
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-vg12-15-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-ext/DualTree1.json

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

Cluster constraints 12 12 12.00 12.00 180 1.54e+16 37.27 0.00 0.00 0.00

Variables per cluster 13 13 13.00 13.00 195 5.12e+16 38.47 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 12 11.20 12.00 168 0 None 2.99 0.27 0.24

Clusters per variable 1 15 7.22 1.00 195 1.30e+14 32.50 6.96 0.96 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	12	12	12.00	12.00	180	1.54e+16	37.27	0.00	0.00	0.00
Variables per cluster	13	13	13.00	13.00	195	5.12e+16	38.47	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	12	11.20	12.00	168	0	None	2.99	0.27	0.24
Clusters per variable	1	15	7.22	1.00	195	1.30e+14	32.50	6.96	0.96	0.69

Primal graph

Density: 13.97%
MCB compute time (ms): 878
MCB cycles: 2,071
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-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 87.60 0.00 -129.63 0.00 0.00 0.00

Degree 25 25 25.00 25.00 4,500 MAX VALUE 579.40 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 6,367 MAX VALUE 2,319.53 0.26 0.09 0.26

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.49	0.49	0.49	87.60	0.00	-129.63	0.00	0.00	0.00
Degree	25	25	25.00	25.00	4,500	MAX VALUE	579.40	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	6,367	MAX VALUE	2,319.53	0.26	0.09	0.26

Triangulated primal graph

Density: 67.65%
MCB compute time (ms): 2,670
MCB cycles: 14,173
Triangles: None

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

Clustering coefficient 0.82 1.00 0.88 0.88 158.52 0.00 -23.20 0.05 0.06 2.82

Degree 25 155 121.10 136.00 21,798 MAX VALUE 845.76 40.38 0.33 2.64

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 42,519 MAX VALUE 15,570.60 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	0.88	158.52	0.00	-23.20	0.05	0.06	2.82
Degree	25	155	121.10	136.00	21,798	MAX VALUE	845.76	40.38	0.33	2.64
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	42,519	MAX VALUE	15,570.60	0.00	0.00	0.00

Dual graph

Density: 51.28%
MCB compute time (ms): 1
MCB cycles: 154
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-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 12 15 13.33 12.00 360 2.00e+30 69.77 1.49 0.11 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 616 MAX VALUE 213.49 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	12	15	13.33	12.00	360	2.00e+30	69.77	1.49	0.11	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	616	MAX VALUE	213.49	0.00	0.00	0.00

Minimal dual graph

Density: 51.28%
MCB compute time (ms): 1
MCB cycles: 154

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 12 15 13.33 12.00 360 2.00e+30 69.77 1.49 0.11 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 616 MAX VALUE 213.49 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	12	15	13.33	12.00	360	2.00e+30	69.77	1.49	0.11	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	616	MAX VALUE	213.49	0.00	0.00	0.00

Triangulated dual graph

Density: 70.09%
Triangles: 1,210

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

Clustering coefficient 0.68 1.00 0.86 1.00 23.12 0.01 -4.68 0.16 0.19 0.69

Degree 12 26 18.22 12.00 492 1.47e+33 76.37 6.96 0.38 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	23.12	0.01	-4.68	0.16	0.19	0.69
Degree	12	26	18.22	12.00	492	1.47e+33	76.37	6.96	0.38	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 70.09%

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

Clustering coefficient 0.68 1.00 0.86 1.00 23.12 0.01 -4.68 0.16 0.19 0.69

Degree 12 26 18.22 12.00 492 1.47e+33 76.37 6.96 0.38 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	23.12	0.01	-4.68	0.16	0.19	0.69
Degree	12	26	18.22	12.00	492	1.47e+33	76.37	6.96	0.38	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.69%
MCB compute time (ms): 47
MCB cycles: 154
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg12-15-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 15 3.48 2.00 720 MAX VALUE 194.54 3.85 1.11 0.48

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,232 MAX VALUE 320.23 0.00 0.00 0.00

XCSP 2.1 Benchmarks