Instance: normalized-crossword-m1c-lex-vg4-5-ext
Number of variables: 20
Number of constraints: 9
Satisfiable: True
Timestamp: 2025-07-20 22:08:35
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0
Benchmark comments

Instance comments



Component #1 Number of variables: 20
Number of constraints: 9
General features
Coarse blocks: 1,018
Value tables: 20
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Arity 4 5 4.44 4.00 40 640,000 13.37 0.50 0.11 0.69
Coarse blocks size 1 566 104.54 69.00 106,420 MAX VALUE 4,063.42 105.55 1.01 4.87
Relational linkage 0.00 0.00 0.00 0.00 0.14 0.00 -4,405.40 0.00 0.94 4.57
Tightness 1.00 1.00 1.00 1.00 8.98 0.98 -0.02 0.00 0.00 0.69
Tuples 2,176 3,145 2,606.67 2,176.00 23,460 4.77e+30 70.64 481.50 0.18 0.69
Values 26 26 26.00 26.00 520 1.99e+28 65.16 0.00 0.00 0.00
Value table constraints 2 2 2.00 2.00 40 1,048,580 13.86 0.00 0.00 0.00
Value table partitions 25 26 25.90 26.00 518 1.84e+28 65.08 0.30 0.01 0.33
Tree decomposition
Number of clusters: 7
Number of leaves: 4
Tree depth: 2
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/Tree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 0 2 1.29 2.00 9 0 None 0.88 0.68 0.96
Variables per cluster 8 13 9.57 8.00 67 6,389,760 15.67 1.99 0.21 1.15
Separator constraints 0 0 0.00 0.00 0 0 None 0.00 None 0.00
Separator variables 0 10 6.71 7.00 47 0 None 2.96 0.44 1.15
Clusters per var 1 5 3.35 4.00 67 2.21e+09 21.52 1.39 0.41 1.44
Dual tree decomposition
Number of clusters: 5
Number of leaves: 2
Tree depth: 2
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/DualTree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 4 4 4.00 4.00 20 1,024 6.93 0.00 0.00 0.00
Variables per cluster 5 5 5.00 5.00 25 3,125 8.05 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 4 3.20 4.00 16 0 None 1.60 0.50 0.50
Clusters per variable 1 5 2.78 1.00 25 625 6.44 1.99 0.72 0.69
Primal graph
Density: 36.84%
MCB compute time (ms): 0
MCB cycles: 51
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/Primal1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.43 0.43 0.43 0.43 8.57 0.00 -16.95 0.00 0.00 0.00
Degree 7 7 7.00 7.00 140 7.98e+16 38.92 0.00 0.00 0.00
Eccentricity None None None None None None None None None None
MCB cycle size 3 4 3.24 3.00 165 6.80e+25 59.48 0.42 0.13 0.55
Triangulated primal graph
Density: 71.58%
MCB compute time (ms): 1
MCB cycles: 144
Triangles: None
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.77 1.00 0.86 0.82 17.14 0.04 -3.17 0.08 0.09 1.96
Degree 7 17 13.60 15.50 272 1.79e+22 51.24 3.69 0.27 1.77
Eccentricity None None None None None None None None None None
MCB cycle size 3 3 3.00 3.00 432 MAX VALUE 158.20 0.00 0.00 0.00
Dual graph
Density: 55.56%
MCB compute time (ms): 0
MCB cycles: 12
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-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 4 5 4.44 4.00 40 640,000 13.37 0.50 0.11 0.69
Eccentricity None None None None None None None None None None
MCB cycle size 4 4 4.00 4.00 48 16,777,200 16.64 0.00 0.00 0.00
Minimal dual graph
Density: 55.56%
MCB compute time (ms): 0
MCB cycles: 12
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 4 5 4.44 4.00 40 640,000 13.37 0.50 0.11 0.69
Eccentricity None None None None None None None None None None
MCB cycle size 4 4 4.00 4.00 48 16,777,200 16.64 0.00 0.00 0.00
Triangulated dual graph
Density: 72.22%
Triangles: 34
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.64 1.00 0.84 1.00 7.57 0.17 -1.77 0.18 0.21 0.69
Degree 4 8 5.78 4.00 52 4,194,300 15.25 1.99 0.34 0.69
Eccentricity None None None None None None None None None None
Triangulated minimal dual graph
Density: 72.22%
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.64 1.00 0.84 1.00 7.57 0.17 -1.77 0.18 0.21 0.69
Degree 4 8 5.78 4.00 52 4,194,300 15.25 1.99 0.34 0.69
Eccentricity None None None None None None None None None None
Incidence graph
Density: 9.85%
MCB compute time (ms): 0
MCB cycles: 12
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/lexVg/normalized-crossword-m1c-lex-vg4-5-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 5 2.76 2.00 80 6.71e+11 27.23 1.16 0.42 0.83
Eccentricity None None None None None None None None None None
MCB cycle size 8 8 8.00 8.00 96 6.87e+10 24.95 0.00 0.00 0.00