Instance: normalized-2-insertions-4-4-ext
Number of variables: 149
Number of constraints: 541
Satisfiable: True
Timestamp: 2025-07-27 21:34:49
Stampede: v1.0.0-1618-gfb467d2
Boost: 1.64.0
Benchmark comments

Instance comments



Component #1 Number of variables: 149
Number of constraints: 541
General features
Coarse blocks: 4,328
Value tables: 149
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Arity 2 2 2.00 2.00 1,082 MAX VALUE 374.99 0.00 0.00 0.00
Coarse blocks size 3 3 3.00 3.00 12,984 MAX VALUE 4,754.79 0.00 0.00 0.00
Relational linkage 0.75 0.75 0.75 0.75 447.00 0.00 -171.46 0.00 0.00 0.00
Tightness 0.25 0.25 0.25 0.25 135.25 0.00 -749.99 0.00 0.00 0.00
Tuples 12 12 12.00 12.00 6,492 MAX VALUE 1,344.33 0.00 0.00 0.00
Values 4 4 4.00 4.00 596 MAX VALUE 206.56 0.00 0.00 0.00
Value table constraints 4 37 7.26 8.00 1,082 MAX VALUE 287.33 3.23 0.45 1.27
Value table partitions 4 4 4.00 4.00 596 MAX VALUE 206.56 0.00 0.00 0.00
Tree decomposition
Number of clusters: 106
Number of leaves: 72
Tree depth: 12
CIR: 0.34
Independent Cluster Pairs: 1,830
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Tree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 0 37 9.94 6.00 1,054 0 None 8.65 0.87 2.41
Variables per cluster 5 39 11.97 7.00 1,269 MAX VALUE 241.24 8.87 0.74 2.41
Separator constraints 0 32 4.84 0.00 513 0 None 9.01 1.86 1.25
Separator variables 0 34 10.57 6.00 1,120 0 None 8.41 0.80 2.40
Clusters per var 1 68 8.52 3.00 1,269 MAX VALUE 197.90 9.91 1.16 2.23
Dual tree decomposition
Number of clusters: 147
Number of leaves: 62
Tree depth: 8
CIR: 0.68
Independent Cluster Pairs: 7,153
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/DualTree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 25 738 91.13 56.00 13,396 MAX VALUE 613.76 115.01 1.26 3.56
Variables per cluster 10 174 27.73 17.00 4,077 MAX VALUE 448.43 27.64 1.00 3.26
Separator constraints 0 561 62.78 42.00 9,229 0 None 75.49 1.20 3.39
Separator variables 0 130 24.05 16.00 3,536 0 None 21.61 0.90 3.24
Clusters per variable 1 14 7.54 8.00 4,077 MAX VALUE 961.65 4.07 0.54 2.56
Primal graph
Density: 4.91%
MCB compute time (ms): None
MCB cycles: None
Triangles: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Primal1.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 37 7.26 8.00 1,082 MAX VALUE 287.33 3.23 0.45 1.27
Eccentricity 4 4 4.00 4.00 596 MAX VALUE 206.56 0.00 0.00 0.00
MCB cycle size None None None None None None None None None None
Triangulated primal graph
Density: 18.38%
MCB compute time (ms): None
MCB cycles: None
Triangles: 20,931
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.27 1.00 0.83 0.85 124.08 0.00 -31.13 0.18 0.21 2.81
Degree 4 110 27.21 12.00 4,054 MAX VALUE 414.13 24.74 0.91 3.12
Eccentricity 2 3 2.66 3.00 396 MAX VALUE 143.01 0.47 0.18 0.64
MCB cycle size None None None None None None None None None None
Dual graph
Density: 2.85%
MCB compute time (ms): 8,664
MCB cycles: 5,052
Triangles: 15,720
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Dual1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.44 0.85 0.51 0.47 277.85 0.00 -368.85 0.10 0.20 1.76
Degree 9 45 15.40 14.00 8,334 MAX VALUE 1,440.43 7.31 0.47 1.69
Eccentricity 5 5 5.00 5.00 2,705 MAX VALUE 870.71 0.00 0.00 0.00
MCB cycle size 3 9 3.57 3.00 18,029 MAX VALUE 6,299.47 0.88 0.25 0.93
Minimal dual graph
Density: 0.64%
MCB compute time (ms): 3,073
MCB cycles: 393
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 3.45 3.00 1,866 MAX VALUE 660.09 0.67 0.19 0.97
Eccentricity 8 12 9.74 10.00 5,271 MAX VALUE 1,230.46 0.64 0.07 0.97
MCB cycle size 4 12 7.21 7.00 2,834 MAX VALUE 767.99 1.49 0.21 1.73
Triangulated dual graph
Density: 24.36%
Triangles: 1,787,410
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.65 1.00 0.82 0.79 441.44 0.00 -113.99 0.10 0.12 5.36
Degree 9 283 131.56 109.00 71,174 MAX VALUE 2,380.87 100.53 0.76 4.70
Eccentricity 2 3 2.70 3.00 1,460 MAX VALUE 528.26 0.46 0.17 0.61
Triangulated minimal dual graph
Density: 6.13%
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.45 1.00 0.80 0.75 433.21 0.00 -130.41 0.16 0.19 3.63
Degree 2 141 33.08 7.00 17,898 MAX VALUE 1,330.05 46.20 1.40 3.40
Eccentricity 3 6 4.67 5.00 2,528 MAX VALUE 829.88 0.57 0.12 0.85
Incidence graph
Density: 0.46%
MCB compute time (ms): 2,807
MCB cycles: 393
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/graphColoring-insertion-k-insertionExtConvert/normalized-2-insertions-4-4-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 37 3.14 2.00 2,164 MAX VALUE 662.32 2.64 0.84 0.80
Eccentricity 9 10 9.78 10.00 6,751 MAX VALUE 1,573.08 0.41 0.04 0.52
MCB cycle size 8 18 8.03 8.00 3,154 MAX VALUE 818.03 0.50 0.06 0.02