XCSP 2.1 Benchmark Database

Instance: normalized-crossword-m1c-words-vg9-10-ext
Number of variables: 90
Number of constraints: 19
Satisfiable: True
Timestamp: 2025-07-20 22:09:47
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 90
Number of constraints: 19

General features

Coarse blocks: 4,556
Value tables: 90

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

Arity 9 10 9.47 9.00 180 3.49e+18 42.70 0.50 0.05 0.69

Coarse blocks size 1 1,620 210.78 124.00 960,300 MAX VALUE 20,535.40 242.06 1.15 5.48

Relational linkage 0.00 0.00 0.00 0.00 0.00 0.00 -55,550.00 0.00 1.13 5.07

Tightness 1.00 1.00 1.00 1.00 19.00 1.00 -0.00 0.00 0.00 0.69

Tuples 4,591 6,079 5,374.16 6,079.00 102,109 MAX VALUE 163.01 742.97 0.14 0.69

Values 26 26 26.00 26.00 2,340 MAX VALUE 293.23 0.00 0.00 0.00

Value table constraints 2 2 2.00 2.00 180 1.24e+27 62.38 0.00 0.00 0.00

Value table partitions 24 26 25.88 26.00 2,329 MAX VALUE 292.79 0.44 0.02 0.33

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	9	10	9.47	9.00	180	3.49e+18	42.70	0.50	0.05	0.69
Coarse blocks size	1	1,620	210.78	124.00	960,300	MAX VALUE	20,535.40	242.06	1.15	5.48
Relational linkage	0.00	0.00	0.00	0.00	0.00	0.00	-55,550.00	0.00	1.13	5.07
Tightness	1.00	1.00	1.00	1.00	19.00	1.00	-0.00	0.00	0.00	0.69
Tuples	4,591	6,079	5,374.16	6,079.00	102,109	MAX VALUE	163.01	742.97	0.14	0.69
Values	26	26	26.00	26.00	2,340	MAX VALUE	293.23	0.00	0.00	0.00
Value table constraints	2	2	2.00	2.00	180	1.24e+27	62.38	0.00	0.00	0.00
Value table partitions	24	26	25.88	26.00	2,329	MAX VALUE	292.79	0.44	0.02	0.33

Tree decomposition

Number of clusters: 17
Number of leaves: 9
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/Tree1.json

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

Cluster constraints 0 2 1.12 2.00 19 0 None 0.96 0.86 0.87

Variables per cluster 18 58 27.82 18.00 473 7.53e+23 54.98 12.94 0.47 1.34

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

Separator variables 0 44 22.53 17.00 383 0 None 10.43 0.46 1.34

Clusters per var 1 7 5.26 6.00 473 MAX VALUE 138.82 1.85 0.35 1.59

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	0	2	1.12	2.00	19	0	None	0.96	0.86	0.87
Variables per cluster	18	58	27.82	18.00	473	7.53e+23	54.98	12.94	0.47	1.34
Separator constraints	0	0	0.00	0.00	0	0	None	0.00	None	0.00
Separator variables	0	44	22.53	17.00	383	0	None	10.43	0.46	1.34
Clusters per var	1	7	5.26	6.00	473	MAX VALUE	138.82	1.85	0.35	1.59

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/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/DualTree1.json

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

Cluster constraints 9 9 9.00 9.00 90 3.49e+09 21.97 0.00 0.00 0.00

Variables per cluster 10 10 10.00 10.00 100 1.00e+10 23.03 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 9 8.10 9.00 81 0 None 2.70 0.33 0.33

Clusters per variable 1 10 5.26 1.00 100 1.00e+09 20.72 4.49 0.85 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	9	9	9.00	9.00	90	3.49e+09	21.97	0.00	0.00	0.00
Variables per cluster	10	10	10.00	10.00	100	1.00e+10	23.03	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	9	8.10	9.00	81	0	None	2.70	0.33	0.33
Clusters per variable	1	10	5.26	1.00	100	1.00e+09	20.72	4.49	0.85	0.69

Primal graph

Density: 19.10%
MCB compute time (ms): 78
MCB cycles: 676
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-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 42.35 0.00 -67.84 0.00 0.00 0.00

Degree 17 17 17.00 17.00 1,530 MAX VALUE 254.99 0.00 0.00 0.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.11 3.00 2,100 MAX VALUE 763.38 0.31 0.10 0.34

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.47	0.47	0.47	0.47	42.35	0.00	-67.84	0.00	0.00	0.00
Degree	17	17	17.00	17.00	1,530	MAX VALUE	254.99	0.00	0.00	0.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.11	3.00	2,100	MAX VALUE	763.38	0.31	0.10	0.34

Triangulated primal graph

Density: 67.94%
MCB compute time (ms): 715
MCB cycles: 2,783
Triangles: None

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

Clustering coefficient 0.81 1.00 0.88 0.86 78.75 0.00 -12.20 0.06 0.07 2.34

Degree 17 77 60.47 69.00 5,442 MAX VALUE 361.48 19.63 0.32 2.34

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 8,349 MAX VALUE 3,057.44 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.81	1.00	0.88	0.86	78.75	0.00	-12.20	0.06	0.07	2.34
Degree	17	77	60.47	69.00	5,442	MAX VALUE	361.48	19.63	0.32	2.34
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	8,349	MAX VALUE	3,057.44	0.00	0.00	0.00

Dual graph

Density: 52.63%
MCB compute time (ms): 0
MCB cycles: 72
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-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 9 10 9.47 9.00 180 3.49e+18 42.70 0.50 0.05 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 288 MAX VALUE 99.81 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	9	10	9.47	9.00	180	3.49e+18	42.70	0.50	0.05	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	288	MAX VALUE	99.81	0.00	0.00	0.00

Minimal dual graph

Density: 52.63%
MCB compute time (ms): 0
MCB cycles: 72

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 9 10 9.47 9.00 180 3.49e+18 42.70 0.50 0.05 0.69

Eccentricity None None None None None None None None None None

MCB cycle size 4 4 4.00 4.00 288 MAX VALUE 99.81 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	9	10	9.47	9.00	180	3.49e+18	42.70	0.50	0.05	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	4	4	4.00	4.00	288	MAX VALUE	99.81	0.00	0.00	0.00

Triangulated dual graph

Density: 73.68%
Triangles: 444

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

Clustering coefficient 0.71 1.00 0.86 1.00 16.35 0.04 -3.13 0.15 0.17 0.69

Degree 9 18 13.26 9.00 252 6.92e+20 47.99 4.49 0.34 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	16.35	0.04	-3.13	0.15	0.17	0.69
Degree	9	18	13.26	9.00	252	6.92e+20	47.99	4.49	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 73.68%

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

Clustering coefficient 0.71 1.00 0.86 1.00 16.35 0.04 -3.13 0.15 0.17 0.69

Degree 9 18 13.26 9.00 252 6.92e+20 47.99 4.49 0.34 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	16.35	0.04	-3.13	0.15	0.17	0.69
Degree	9	18	13.26	9.00	252	6.92e+20	47.99	4.49	0.34	0.69
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 3.06%
MCB compute time (ms): 11
MCB cycles: 72
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/wordsVg/normalized-crossword-m1c-words-vg9-10-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 3.30 2.00 360 MAX VALUE 105.08 2.84 0.86 0.58

Eccentricity None None None None None None None None None None

MCB cycle size 8 8 8.00 8.00 576 MAX VALUE 149.72 0.00 0.00 0.00

XCSP 2.1 Benchmarks