Instance: normalized-langford-3-3-ext
Number of variables: 9
Number of constraints: 36
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: 9
Number of constraints: 36
General features
Coarse blocks: 612
Value tables: 9
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Arity 2 2 2.00 2.00 72 6.87e+10 24.95 0.00 0.00 0.00
Coarse blocks size 1 8 7.18 8.00 4,392 MAX VALUE 1,122.90 2.26 0.31 0.36
Relational linkage 0.11 0.11 0.11 0.11 5.00 0.00 -98.88 0.00 0.00 0.00
Tightness 0.11 0.94 0.25 0.11 8.89 0.00 -66.38 0.30 1.23 0.63
Tuples 5 72 61.00 72.00 2,196 MAX VALUE 138.99 24.60 0.40 0.63
Values 9 9 9.00 9.00 81 387,420,000 19.77 0.00 0.00 0.00
Value table constraints 8 8 8.00 8.00 72 134,218,000 18.71 0.00 0.00 0.00
Value table partitions 9 9 9.00 9.00 81 387,420,000 19.77 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-3-3-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-ext/Tree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 36 36 36.00 36.00 36 36 3.58 0.00 0.00 0.00
Variables per cluster 9 9 9.00 9.00 9 9 2.20 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 9 1 0.00 0.00 0.00 0.00
Dual 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/langford3ExtConvert/normalized-langford-3-3-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-ext/DualTree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 63 127 83.00 63.00 581 2.01e+13 30.63 25.42 0.31 1.15
Variables per cluster 15 26 18.57 15.00 130 631,800,000 20.26 4.44 0.24 1.15
Separator constraints 0 70 47.00 49.00 329 0 None 20.74 0.44 1.15
Separator variables 0 20 13.43 14.00 94 0 None 5.92 0.44 1.15
Clusters per variable 1 5 3.61 4.00 130 4.89e+18 43.03 1.21 0.33 1.40
Primal graph
Density: 100.00%
MCB compute time (ms): 0
MCB cycles: 28
Triangles: 84
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-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 9.00 1.00 0.00 0.00 0.00 0.00
Degree 8 8 8.00 8.00 72 134,218,000 18.71 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 84 2.29e+13 30.76 0.00 0.00 0.00
Triangulated primal graph
Density: 100.00%
MCB compute time (ms): 0
MCB cycles: 28
Triangles: 84
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 1.00 1.00 1.00 1.00 9.00 1.00 0.00 0.00 0.00 0.00
Degree 8 8 8.00 8.00 72 134,218,000 18.71 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 84 2.29e+13 30.76 0.00 0.00 0.00
Dual graph
Density: 40.00%
MCB compute time (ms): 3
MCB cycles: 217
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-ext/Dual1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.54 0.54 0.54 0.54 19.38 0.00 -22.29 0.00 0.00 0.00
Degree 14 14 14.00 14.00 504 MAX VALUE 95.01 0.00 0.00 0.00
Eccentricity None None None None None None None None None None
MCB cycle size 3 3 3.00 3.00 651 MAX VALUE 238.40 0.00 0.00 0.00
Minimal dual graph
Density: 10.00%
MCB compute time (ms): 1
MCB cycles: 28
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.00 0.33 0.02 0.00 0.83 0.00 None 0.08 3.46 0.34
Degree 2 5 3.50 3.00 126 1.62e+19 44.23 0.76 0.22 1.12
Eccentricity None None None None None None None None None None
MCB cycle size 3 7 5.07 5.00 142 3.43e+19 44.98 0.92 0.18 1.32
Triangulated dual graph
Density: 80.00%
Triangles: 4,172
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.84 1.00 0.90 0.88 32.25 0.02 -4.01 0.05 0.06 1.97
Degree 14 33 28.00 31.00 1,008 MAX VALUE 118.86 5.98 0.21 1.97
Eccentricity None None None None None None None None None None
Triangulated minimal dual graph
Density: 24.76%
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.44 1.00 0.75 0.67 27.00 0.00 -11.61 0.20 0.26 2.55
Degree 2 19 8.67 6.50 312 8.66e+29 68.93 5.71 0.66 2.45
Eccentricity None None None None None None None None None None
Incidence graph
Density: 7.27%
MCB compute time (ms): 0
MCB cycles: 28
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-3-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 8 3.20 2.00 144 9.22e+18 43.67 2.40 0.75 0.50
Eccentricity None None None None None None None None None None
MCB cycle size 6 6 6.00 6.00 168 6.14e+21 50.17 0.00 0.00 0.00