Instance: normalized-langford-3-2-ext
Number of variables: 6
Number of constraints: 15
Satisfiable: True
Timestamp: 2025-07-20 22:08:33
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0
Benchmark comments

Instance comments



Component #1 Number of variables: 6
Number of constraints: 15
General features
Coarse blocks: 160
Value tables: 6
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Arity 2 2 2.00 2.00 30 32,768 10.40 0.00 0.00 0.00
Coarse blocks size 1 5 4.30 5.00 688 MAX VALUE 212.45 1.52 0.35 0.46
Relational linkage 0.17 0.17 0.17 0.17 2.67 0.00 -28.67 0.00 0.00 0.00
Tightness 0.17 0.92 0.36 0.17 5.44 0.00 -20.12 0.33 0.90 0.76
Tuples 3 30 22.93 30.00 344 2.55e+18 42.38 11.72 0.51 0.76
Values 6 6 6.00 6.00 36 46,656 10.75 0.00 0.00 0.00
Value table constraints 5 5 5.00 5.00 30 15,625 9.66 0.00 0.00 0.00
Value table partitions 6 6 6.00 6.00 36 46,656 10.75 0.00 0.00 0.00
Tree decomposition
Number of clusters: 1
Number of leaves: 1
Tree depth: 0
CIR: None
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/Tree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 15 15 15.00 15.00 15 15 2.71 0.00 0.00 0.00
Variables per cluster 6 6 6.00 6.00 6 6 1.79 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 0 0.00 0.00 0 0 None 0.00 None 0.00
Clusters per var 1 1 1.00 1.00 6 1 0.00 0.00 0.00 0.00
Dual tree decomposition
Number of clusters: 4
Number of leaves: 3
Tree depth: 1
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/DualTree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 24 36 27.00 24.00 108 497,664 13.12 5.20 0.19 0.56
Variables per cluster 9 12 9.75 9.00 39 8,748 9.08 1.30 0.13 0.56
Separator constraints 0 16 12.00 16.00 48 0 None 6.93 0.58 0.56
Separator variables 0 8 6.00 8.00 24 0 None 3.46 0.58 0.56
Clusters per variable 1 3 2.60 3.00 39 531,441 13.18 0.80 0.31 0.50
Primal graph
Density: 100.00%
MCB compute time (ms): 0
MCB cycles: 10
Triangles: 20
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/Primal1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 1.00 1.00 1.00 1.00 6.00 1.00 0.00 0.00 0.00 0.00
Degree 5 5 5.00 5.00 30 15,625 9.66 0.00 0.00 0.00
Eccentricity None None None None None None None None None None
MCB cycle size 3 3 3.00 3.00 30 59,049 10.99 0.00 0.00 0.00
Triangulated primal graph
Density: 100.00%
MCB compute time (ms): 0
MCB cycles: 10
Triangles: 20
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 1.00 1.00 1.00 1.00 6.00 1.00 0.00 0.00 0.00 0.00
Degree 5 5 5.00 5.00 30 15,625 9.66 0.00 0.00 0.00
Eccentricity None None None None None None None None None None
MCB cycle size 3 3 3.00 3.00 30 59,049 10.99 0.00 0.00 0.00
Dual graph
Density: 57.14%
MCB compute time (ms): 0
MCB cycles: 46
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/Dual1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.57 0.57 0.57 0.57 8.57 0.00 -8.39 0.00 0.00 0.00
Degree 8 8 8.00 8.00 120 3.52e+13 31.19 0.00 0.00 0.00
Eccentricity None None None None None None None None None None
MCB cycle size 3 3 3.00 3.00 138 8.86e+21 50.54 0.00 0.00 0.00
Minimal dual graph
Density: 22.86%
MCB compute time (ms): 0
MCB cycles: 10
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.00 0.33 0.06 0.00 0.83 0.00 None 0.12 2.10 0.63
Degree 2 4 3.20 3.00 48 26,873,900 17.11 0.65 0.20 0.97
Eccentricity None None None None None None None None None None
MCB cycle size 3 5 4.50 5.00 45 3,000,000 14.91 0.67 0.15 0.90
Triangulated dual graph
Density: 85.71%
Triangles: 304
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.88 1.00 0.91 0.88 13.62 0.23 -1.47 0.05 0.05 0.50
Degree 8 13 12.00 13.00 180 1.19e+16 37.02 2.00 0.17 0.50
Eccentricity None None None None None None None None None None
Triangulated minimal dual graph
Density: 37.14%
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.47 1.00 0.72 0.67 10.81 0.00 -5.47 0.20 0.27 2.06
Degree 2 9 5.20 5.00 78 1.06e+10 23.09 2.32 0.45 1.71
Eccentricity None None None None None None None None None None
Incidence graph
Density: 14.29%
MCB compute time (ms): 0
MCB cycles: 10
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-2-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 2.86 2.00 60 512,000,000 20.05 1.36 0.47 0.60
Eccentricity None None None None None None None None None None
MCB cycle size 6 6 6.00 6.00 60 60,466,200 17.92 0.00 0.00 0.00