XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-lex-vg10-12-ext
Number of variables: 120
Number of constraints: 22
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 120
Number of constraints: 22

General features

Coarse blocks: 5,626
Value tables: 120

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

Arity 10 12 10.91 10.00 240 6.19e+22 52.48 1.00 0.09 0.69

Coarse blocks size 1 538 54.69 31.00 307,680 MAX VALUE 17,962.20 67.47 1.23 4.63

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -85,621.90 0.00 0.95 4.06

Tightness 1.00 1.00 1.00 1.00 22.00 1.00 -0.00 0.00 0.00 0.69

Tuples 593 1,971 1,344.64 1,971.00 29,582 MAX VALUE 154.89 686.15 0.51 0.69

Values 26 26 26.00 26.00 3,120 MAX VALUE 390.97 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 240 1.33e+36 83.18 0.00 0.00 0.00

Value table partitions 22 26 25.32 26.00 3,039 MAX VALUE 387.72 1.01 0.04 1.09

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	10	12	10.91	10.00	240	6.19e+22	52.48	1.00	0.09	0.69
Coarse blocks size	1	538	54.69	31.00	307,680	MAX VALUE	17,962.20	67.47	1.23	4.63
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-85,621.90	0.00	0.95	4.06
Tightness	1.00	1.00	1.00	1.00	22.00	1.00	-0.00	0.00	0.00	0.69
Tuples	593	1,971	1,344.64	1,971.00	29,582	MAX VALUE	154.89	686.15	0.51	0.69
Values	26	26	26.00	26.00	3,120	MAX VALUE	390.97	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	240	1.33e+36	83.18	0.00	0.00	0.00
Value table partitions	22	26	25.32	26.00	3,039	MAX VALUE	387.72	1.01	0.04	1.09

Tree decomposition

Number of clusters: 20
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-vg10-12-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/Tree1.json

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

Cluster constraints 0 2 1.10 1.50 22 0 None 0.94 0.86 0.94

Variables per cluster 21 80 34.00 25.00 680 4.98e+29 68.38 17.38 0.51 1.43

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

Separator variables 0 56 28.00 20.00 560 0 None 13.51 0.48 1.43

Clusters per var 1 7 5.67 7.00 680 MAX VALUE 195.12 1.89 0.33 1.41

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.10	1.50	22	0	None	0.94	0.86	0.94
Variables per cluster	21	80	34.00	25.00	680	4.98e+29	68.38	17.38	0.51	1.43
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	56	28.00	20.00	560	0	None	13.51	0.48	1.43
Clusters per var	1	7	5.67	7.00	680	MAX VALUE	195.12	1.89	0.33	1.41

Dual tree decomposition

Number of clusters: 12
Number of leaves: 2
Tree depth: 6
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/DualTree1.json

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

Cluster constraints 10 10 10.00 10.00 120 1.00e+12 27.63 0.00 0.00 0.00

Variables per cluster 11 11 11.00 11.00 132 3.14e+12 28.77 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 9.17 10.00 110 0 None 2.76 0.30 0.29

Clusters per variable 1 12 6.00 1.00 132 6.19e+10 24.85 5.48 0.91 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	10	10	10.00	10.00	120	1.00e+12	27.63	0.00	0.00	0.00
Variables per cluster	11	11	11.00	11.00	132	3.14e+12	28.77	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	9.17	10.00	110	0	None	2.76	0.30	0.29
Clusters per variable	1	12	6.00	1.00	132	6.19e+10	24.85	5.48	0.91	0.69

Primal graph

Density: 16.81%
MCB compute time (ms): 228
MCB cycles: 1,081
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/Primal1.json

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

Clustering coefficient 0.48 0.48 0.48 0.48 57.47 0.00 -88.34 0.00 0.00 0.00

Degree 20 20 20.00 20.00 2,400 MAX VALUE 359.49 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.09 3.00 3,342 MAX VALUE 1,216.08 0.29 0.09 0.31

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.48	0.48	0.48	0.48	57.47	0.00	-88.34	0.00	0.00	0.00
Degree	20	20	20.00	20.00	2,400	MAX VALUE	359.49	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.09	3.00	3,342	MAX VALUE	1,216.08	0.29	0.09	0.31

Triangulated primal graph

Density: 68.04%
MCB compute time (ms): 3,154
MCB cycles: 5,637
Triangles: None

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

Clustering coefficient 0.83 1.00 0.88 0.85 105.48 0.00 -15.69 0.05 0.06 1.83

Degree 20 101 80.97 96.00 9,716 MAX VALUE 516.34 26.61 0.33 1.83

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 16,911 MAX VALUE 6,192.88 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	0.85	105.48	0.00	-15.69	0.05	0.06	1.83
Degree	20	101	80.97	96.00	9,716	MAX VALUE	516.34	26.61	0.33	1.83
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	16,911	MAX VALUE	6,192.88	0.00	0.00	0.00

Dual graph

Density: 51.95%
MCB compute time (ms): 1
MCB cycles: 99
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-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 12 10.91 10.00 240 6.19e+22 52.48 1.00 0.09 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 396 MAX VALUE 137.24 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	12	10.91	10.00	240	6.19e+22	52.48	1.00	0.09	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	396	MAX VALUE	137.24	0.00	0.00	0.00

Minimal dual graph

Density: 51.95%
MCB compute time (ms): 0
MCB cycles: 99

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 12 10.91 10.00 240 6.19e+22 52.48 1.00 0.09 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 396 MAX VALUE 137.24 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	12	10.91	10.00	240	6.19e+22	52.48	1.00	0.09	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	396	MAX VALUE	137.24	0.00	0.00	0.00

Triangulated dual graph

Density: 71.43%
Triangles: 660

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

Clustering coefficient 0.69 1.00 0.86 1.00 18.86 0.02 -3.77 0.16 0.18 0.69

Degree 10 21 15.00 10.00 330 1.67e+25 58.08 5.48 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	0.69	1.00	0.86	1.00	18.86	0.02	-3.77	0.16	0.18	0.69
Degree	10	21	15.00	10.00	330	1.67e+25	58.08	5.48	0.37	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 71.43%

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

Clustering coefficient 0.69 1.00 0.86 1.00 18.86 0.02 -3.77 0.16 0.18 0.69

Degree 10 21 15.00 10.00 330 1.67e+25 58.08 5.48 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	0.69	1.00	0.86	1.00	18.86	0.02	-3.77	0.16	0.18	0.69
Degree	10	21	15.00	10.00	330	1.67e+25	58.08	5.48	0.37	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 2.40%
MCB compute time (ms): 24
MCB cycles: 99
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg10-12-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 12 3.38 2.00 480 MAX VALUE 135.66 3.25 0.96 0.54

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 792 MAX VALUE 205.87 0.00 0.00 0.00

XCSP 2.1 Benchmarks