XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg15-17-ext
Number of variables: 255
Number of constraints: 32
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 255
Number of constraints: 32

General features

Coarse blocks: 4,758
Value tables: 255

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

Arity 15 17 15.94 15.00 510 2.82e+38 88.54 1.00 0.06 0.69

Coarse blocks size 1 17 2.73 2.00 13,005 MAX VALUE 3,509.08 2.25 0.82 1.77

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -53,278.40 0.00 0.44 0.80

Tightness 1.00 1.00 1.00 1.00 32.00 1.00 0.00 0.00 0.00 0.00

Tuples 7 44 26.66 44.00 853 MAX VALUE 93.52 18.46 0.69 0.69

Values 26 26 26.00 26.00 6,630 MAX VALUE 830.82 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 510 MAX VALUE 176.75 0.00 0.00 0.00

Value table partitions 11 18 14.63 14.00 3,731 MAX VALUE 682.61 1.65 0.11 1.84

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	15	17	15.94	15.00	510	2.82e+38	88.54	1.00	0.06	0.69
Coarse blocks size	1	17	2.73	2.00	13,005	MAX VALUE	3,509.08	2.25	0.82	1.77
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-53,278.40	0.00	0.44	0.80
Tightness	1.00	1.00	1.00	1.00	32.00	1.00	0.00	0.00	0.00	0.00
Tuples	7	44	26.66	44.00	853	MAX VALUE	93.52	18.46	0.69	0.69
Values	26	26	26.00	26.00	6,630	MAX VALUE	830.82	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	510	MAX VALUE	176.75	0.00	0.00	0.00
Value table partitions	11	18	14.63	14.00	3,731	MAX VALUE	682.61	1.65	0.11	1.84

Tree decomposition

Number of clusters: 30
Number of leaves: 15
Tree depth: 4
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/Tree1.json

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

Cluster constraints 0 2 1.07 1.50 32 0 None 0.96 0.90 0.89

Variables per cluster 31 163 56.77 37.50 1,703 MAX VALUE 116.38 36.67 0.65 1.60

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

Separator variables 0 127 48.27 30.00 1,448 0 None 27.90 0.58 1.60

Clusters per var 1 9 6.68 8.00 1,703 MAX VALUE 460.02 2.07 0.31 1.62

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.07	1.50	32	0	None	0.96	0.90	0.89
Variables per cluster	31	163	56.77	37.50	1,703	MAX VALUE	116.38	36.67	0.65	1.60
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	127	48.27	30.00	1,448	0	None	27.90	0.58	1.60
Clusters per var	1	9	6.68	8.00	1,703	MAX VALUE	460.02	2.07	0.31	1.62

Dual tree decomposition

Number of clusters: 17
Number of leaves: 2
Tree depth: 8
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/DualTree1.json

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

Cluster constraints 15 15 15.00 15.00 255 9.85e+19 46.04 0.00 0.00 0.00

Variables per cluster 16 16 16.00 16.00 272 2.95e+20 47.13 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 15 14.12 15.00 240 0 None 3.53 0.25 0.22

Clusters per variable 1 17 8.50 1.00 272 2.86e+18 42.50 7.98 0.94 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	15	15	15.00	15.00	255	9.85e+19	46.04	0.00	0.00	0.00
Variables per cluster	16	16	16.00	16.00	272	2.95e+20	47.13	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	15	14.12	15.00	240	0	None	3.53	0.25	0.22
Clusters per variable	1	17	8.50	1.00	272	2.86e+18	42.50	7.98	0.94	0.69

Primal graph

Density: 11.81%
MCB compute time (ms): 3,624
MCB cycles: 3,571
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/Primal1.json

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

Clustering coefficient 0.49 0.49 0.49 0.49 123.69 0.00 -184.49 0.00 0.00 0.00

Degree 30 30 30.00 30.00 7,650 MAX VALUE 867.30 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 10,937 MAX VALUE 3,987.59 0.24 0.08 0.23

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.49	0.49	0.49	0.49	123.69	0.00	-184.49	0.00	0.00	0.00
Degree	30	30	30.00	30.00	7,650	MAX VALUE	867.30	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	10,937	MAX VALUE	3,987.59	0.24	0.08	0.23

Triangulated primal graph

Density: 67.19%
MCB compute time (ms): 44,747
MCB cycles: 27,270
Triangles: None

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

Clustering coefficient 0.83 1.00 0.88 0.87 224.88 0.00 -32.47 0.05 0.06 3.24

Degree 30 216 170.66 188.00 43,518 MAX VALUE 1,283.73 58.00 0.34 2.91

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 81,810 MAX VALUE 29,959.20 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.83	1.00	0.88	0.87	224.88	0.00	-32.47	0.05	0.06	3.24
Degree	30	216	170.66	188.00	43,518	MAX VALUE	1,283.73	58.00	0.34	2.91
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	81,810	MAX VALUE	29,959.20	0.00	0.00	0.00

Dual graph

Density: 51.41%
MCB compute time (ms): 3
MCB cycles: 224
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-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 15 17 15.94 15.00 510 2.82e+38 88.54 1.00 0.06 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 896 MAX VALUE 310.53 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	15	17	15.94	15.00	510	2.82e+38	88.54	1.00	0.06	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	896	MAX VALUE	310.53	0.00	0.00	0.00

Minimal dual graph

Density: 51.41%
MCB compute time (ms): 3
MCB cycles: 224

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 15 17 15.94 15.00 510 2.82e+38 88.54 1.00 0.06 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 896 MAX VALUE 310.53 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	15	17	15.94	15.00	510	2.82e+38	88.54	1.00	0.06	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	896	MAX VALUE	310.53	0.00	0.00	0.00

Triangulated dual graph

Density: 72.58%
Triangles: 2,240

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

Clustering coefficient 0.71 1.00 0.86 1.00 27.61 0.01 -5.19 0.15 0.17 0.69

Degree 15 31 22.50 15.00 720 MAX VALUE 97.55 7.98 0.35 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	0.71	1.00	0.86	1.00	27.61	0.01	-5.19	0.15	0.17	0.69
Degree	15	31	22.50	15.00	720	MAX VALUE	97.55	7.98	0.35	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 72.58%

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

Clustering coefficient 0.71 1.00 0.86 1.00 27.61 0.01 -5.19 0.15 0.17 0.69

Degree 15 31 22.50 15.00 720 MAX VALUE 97.55 7.98 0.35 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	0.71	1.00	0.86	1.00	27.61	0.01	-5.19	0.15	0.17	0.69
Degree	15	31	22.50	15.00	720	MAX VALUE	97.55	7.98	0.35	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.24%
MCB compute time (ms): 105
MCB cycles: 224
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg15-17-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 17 3.55 2.00 1,020 MAX VALUE 265.29 4.40 1.24 0.43

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 1,792 MAX VALUE 465.80 0.00 0.00 0.00

XCSP 2.1 Benchmarks