Instance: normalized-langford-3-4-ext
Number of variables: 12
Number of constraints: 66
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: 12
Number of constraints: 66
General features
Coarse blocks: 1,528
Value tables: 12
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Arity 2 2 2.00 2.00 132 7.38e+19 45.75 0.00 0.00 0.00
Coarse blocks size 1 11 10.11 11.00 15,448 MAX VALUE 3,337.87 2.85 0.28 0.30
Relational linkage 0.08 0.08 0.08 0.08 7.33 0.00 -218.67 0.00 0.00 0.00
Tightness 0.08 0.95 0.19 0.08 12.36 0.00 -144.61 0.28 1.49 0.54
Tuples 7 132 117.03 132.00 7,724 MAX VALUE 300.25 40.31 0.34 0.54
Values 12 12 12.00 12.00 144 8.92e+12 29.82 0.00 0.00 0.00
Value table constraints 11 11 11.00 11.00 132 3.14e+12 28.77 0.00 0.00 0.00
Value table partitions 12 12 12.00 12.00 144 8.92e+12 29.82 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-3-4-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/Tree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 66 66 66.00 66.00 66 66 4.19 0.00 0.00 0.00
Variables per cluster 12 12 12.00 12.00 12 12 2.48 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 12 1 0.00 0.00 0.00 0.00
Dual tree decomposition
Number of clusters: 10
Number of leaves: 6
Tree depth: 3
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/DualTree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 120 292 176.00 120.00 1,760 1.32e+22 50.94 71.51 0.41 0.95
Variables per cluster 21 44 28.60 21.00 286 2.15e+14 33.00 9.65 0.34 0.95
Separator constraints 0 180 110.00 100.00 1,100 0 None 47.54 0.43 1.09
Separator variables 0 36 22.00 20.00 220 0 None 9.51 0.43 1.09
Clusters per variable 1 6 4.33 4.00 286 MAX VALUE 90.93 1.43 0.33 1.52
Primal graph
Density: 100.00%
MCB compute time (ms): 0
MCB cycles: 55
Triangles: 220
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-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 12.00 1.00 0.00 0.00 0.00 0.00
Degree 11 11 11.00 11.00 132 3.14e+12 28.77 0.00 0.00 0.00
Eccentricity None None None None None None None None None None
MCB cycle size 3 3 3.00 3.00 165 1.74e+26 60.42 0.00 0.00 0.00
Triangulated primal graph
Density: 100.00%
MCB compute time (ms): 0
MCB cycles: 55
Triangles: 220
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 1.00 1.00 1.00 1.00 12.00 1.00 0.00 0.00 0.00 0.00
Degree 11 11 11.00 11.00 132 3.14e+12 28.77 0.00 0.00 0.00
Eccentricity None None None None None None None None None None
MCB cycle size 3 3 3.00 3.00 165 1.74e+26 60.42 0.00 0.00 0.00
Dual graph
Density: 30.77%
MCB compute time (ms): 15
MCB cycles: 595
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/Dual1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.53 0.53 0.53 0.53 34.74 0.00 -42.36 0.00 0.00 0.00
Degree 20 20 20.00 20.00 1,320 MAX VALUE 197.72 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 1,785 MAX VALUE 653.67 0.00 0.00 0.00
Minimal dual graph
Density: 5.59%
MCB compute time (ms): 4
MCB cycles: 60
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.00 0.33 0.01 0.00 0.83 0.00 None 0.06 4.77 0.21
Degree 2 5 3.64 3.00 240 1.99e+36 83.58 0.81 0.22 1.13
Eccentricity None None None None None None None None None None
MCB cycle size 3 7 5.48 5.00 329 MAX VALUE 101.07 0.99 0.18 1.37
Triangulated dual graph
Density: 76.92%
Triangles: 24,848
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.82 1.00 0.89 0.91 58.82 0.00 -7.72 0.05 0.06 1.67
Degree 20 61 50.00 53.00 3,300 MAX VALUE 255.47 12.01 0.24 1.67
Eccentricity None None None None None None None None None None
Triangulated minimal dual graph
Density: 18.97%
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.50 1.00 0.76 0.69 50.31 0.00 -19.61 0.17 0.23 2.97
Degree 2 29 12.33 7.50 814 MAX VALUE 141.66 9.80 0.79 2.71
Eccentricity None None None None None None None None None None
Incidence graph
Density: 4.40%
MCB compute time (ms): 2
MCB cycles: 55
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-4-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 11 3.38 2.00 264 2.32e+32 74.52 3.25 0.96 0.43
Eccentricity None None None None None None None None None None
MCB cycle size 6 6 6.00 6.00 330 MAX VALUE 98.55 0.00 0.00 0.00