Instance: normalized-langford-3-19-ext
Number of variables: 57
Number of constraints: 1596
Satisfiable: True
Timestamp: 2025-07-27 21:35:00
Stampede: v1.0.0-797-g05e223c
Boost: 1.64.0
Benchmark comments

Instance comments



Component #1 Number of variables: 57
Number of constraints: 1596
General features
Coarse blocks: 181,108
Value tables: 57
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Arity 2 2 2.00 2.00 3,192 MAX VALUE 1,106.26 0.00 0.00 0.00
Coarse blocks size 1 56 54.94 56.00 9,949,770 MAX VALUE 714,951.00 7.57 0.14 0.10
Relational linkage 0.02 0.02 0.02 0.02 42.33 0.00 -9,755.88 0.00 0.00 0.00
Tightness 0.02 0.99 0.04 0.02 64.80 0.00 -6,299.62 0.15 3.64 0.18
Tuples 37 3,192 3,117.10 3,192.00 4,974,880 MAX VALUE 12,715.80 479.62 0.15 0.18
Values 57 57 57.00 57.00 3,249 MAX VALUE 230.45 0.00 0.00 0.00
Value table constraints 56 56 56.00 56.00 3,192 MAX VALUE 229.44 0.00 0.00 0.00
Value table partitions 57 57 57.00 57.00 3,249 MAX VALUE 230.45 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-3-19-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/Tree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 1,596 1,596 1,596.00 1,596.00 1,596 1,596 7.38 0.00 0.00 0.00
Variables per cluster 57 57 57.00 57.00 57 57 4.04 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 57 1 0.00 0.00 0.00 0.00
Dual tree decomposition
Number of clusters: 55
Number of leaves: 28
Tree depth: 5
CIR: 0.00
Independent Cluster Pairs: 0
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/DualTree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 3,135 38,640 7,501.00 3,135.00 412,555 MAX VALUE 473.74 7,568.22 1.01 1.45
Variables per cluster 111 1,056 243.75 111.00 13,406 MAX VALUE 288.16 215.16 0.88 1.45
Separator constraints 0 22,000 5,905.00 3,025.00 324,775 0 None 4,572.56 0.77 1.45
Separator variables 0 800 214.73 110.00 11,810 0 None 166.28 0.77 1.45
Clusters per variable 1 10 8.40 9.00 13,406 MAX VALUE 3,312.19 2.04 0.24 1.59
Primal graph
Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 29,260
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-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 57.00 1.00 0.00 0.00 0.00 0.00
Degree 56 56 56.00 56.00 3,192 MAX VALUE 229.44 0.00 0.00 0.00
Eccentricity 1 1 1.00 1.00 57 1 0.00 0.00 0.00 0.00
MCB cycle size None None None None None None None None None None
Triangulated primal graph
Density: 100.00%
MCB compute time (ms): None
MCB cycles: None
Triangles: 29,260
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 1.00 1.00 1.00 1.00 57.00 1.00 0.00 0.00 0.00 0.00
Degree 56 56 56.00 56.00 3,192 MAX VALUE 229.44 0.00 0.00 0.00
Eccentricity 1 1 1.00 1.00 57 1 0.00 0.00 0.00 0.00
MCB cycle size None None None None None None None None None None
Dual graph
Density: None%
MCB compute time (ms): 316,414
MCB cycles: 86,185
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/Dual1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient None None None None None None None None None None
Degree None None None None None None None None None None
Eccentricity None None None None None None None None None None
MCB cycle size 3 3 3.00 3.00 258,555 MAX VALUE 94,683.90 0.00 0.00 0.00
Minimal dual graph
Density: 0.25%
MCB compute time (ms): 77,979
MCB cycles: 1,543
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.00 0.33 0.00 0.00 0.83 0.00 None 0.01 23.95 0.01
Degree 2 7 3.93 4.00 6,270 MAX VALUE 2,136.73 0.98 0.25 1.27
Eccentricity 12 21 15.73 16.00 25,104 MAX VALUE 4,388.14 1.75 0.11 1.94
MCB cycle size 3 18 6.05 7.00 9,337 MAX VALUE 2,742.24 1.26 0.21 1.42
Triangulated dual graph
Density: None%
Triangles: None
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient None None None None None None None None None None
Degree None None None None None None None None None None
Eccentricity None None None None None None None None None None
Triangulated minimal dual graph
Density: 4.96%
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.47 1.00 0.82 0.78 1,303.03 0.00 -349.89 0.15 0.18 4.33
Degree 2 404 79.05 9.00 126,156 MAX VALUE 4,630.98 123.19 1.56 4.03
Eccentricity 3 6 4.61 5.00 7,351 MAX VALUE 2,424.32 0.59 0.13 0.89
Incidence graph
Density: 0.23%
MCB compute time (ms): 4,677
MCB cycles: 1,540
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/langford3ExtConvert/normalized-langford-3-19-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 56 3.86 2.00 6,384 MAX VALUE 1,335.71 9.85 2.55 0.15
Eccentricity 3 4 3.97 4.00 6,555 MAX VALUE 2,275.15 0.18 0.05 0.15
MCB cycle size 6 6 6.00 6.00 9,240 MAX VALUE 2,759.31 0.00 0.00 0.00