Instance: normalized-rand-2-40-25-180-500-88-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:31
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0
Benchmark comments

Instance comments



Component #1 Number of variables: 40
Number of constraints: 180
General features
Coarse blocks: 9,000
Value tables: 40
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00
Coarse blocks size 4 21 12.53 13.00 112,796 MAX VALUE 22,564.80 2.50 0.20 2.33
Relational linkage 0.16 0.56 0.36 0.36 355.76 0.00 -1,049.57 0.06 0.17 1.84
Tightness 0.44 0.55 0.50 0.50 89.76 0.00 -125.41 0.02 0.04 3.83
Tuples 279 351 313.32 313.50 56,398 MAX VALUE 1,034.34 13.31 0.04 3.83
Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00
Value table constraints 4 15 9.00 8.50 360 2.56e+37 86.14 2.60 0.29 2.24
Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00
Tree decomposition
Number of clusters: 20
Number of leaves: 9
Tree depth: 4
CIR: 0.05
Independent Cluster Pairs: 9
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/Tree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 5 57 23.45 15.50 469 1.01e+25 57.58 17.74 0.76 2.65
Variables per cluster 5 21 11.60 9.50 232 2.84e+20 47.09 5.10 0.44 2.35
Separator constraints 0 49 14.45 7.00 289 0 None 16.04 1.11 2.60
Separator variables 0 19 9.60 8.00 192 0 None 5.12 0.53 2.35
Clusters per var 1 15 5.80 6.00 232 3.92e+24 56.63 3.97 0.68 2.26
Dual tree decomposition
Number of clusters: 38
Number of leaves: 16
Tree depth: 5
CIR: 0.19
Independent Cluster Pairs: 125
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/DualTree1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Cluster constraints 25 398 128.90 95.00 4,898 MAX VALUE 174.91 95.57 0.74 3.64
Variables per cluster 10 91 29.58 21.50 1,124 MAX VALUE 121.67 20.12 0.68 3.30
Separator constraints 0 217 87.45 74.00 3,323 0 None 58.44 0.67 3.48
Separator variables 0 69 24.84 20.00 944 0 None 15.44 0.62 3.16
Clusters per variable 1 10 6.24 7.00 1,124 MAX VALUE 300.77 2.67 0.43 2.12
Primal graph
Density: 23.08%
MCB compute time (ms): 5
MCB cycles: 149
Triangles: 110
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/Primal1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.00 0.67 0.21 0.21 8.51 0.00 None 0.10 0.48 3.21
Degree 4 15 9.00 8.50 360 2.56e+37 86.14 2.60 0.29 2.24
Eccentricity None None None None None None None None None None
MCB cycle size 3 4 3.35 3.00 499 MAX VALUE 178.65 0.48 0.14 0.65
Triangulated primal graph
Density: 51.54%
MCB compute time (ms): 16
MCB cycles: 370
Triangles: 2,418
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.60 1.00 0.84 0.82 33.52 0.00 -7.43 0.11 0.13 3.06
Degree 4 34 20.10 25.00 804 MAX VALUE 113.26 9.54 0.47 2.78
Eccentricity None None None None None None None None None None
MCB cycle size 3 3 3.00 3.00 1,110 MAX VALUE 406.49 0.00 0.00 0.00
Dual graph
Density: 9.78%
MCB compute time (ms): 246
MCB cycles: 1,963
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/Dual1.json
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.44 0.68 0.51 0.50 90.99 0.00 -123.12 0.03 0.06 4.24
Degree 9 27 17.50 17.00 3,150 MAX VALUE 511.03 3.66 0.21 2.68
Eccentricity None None None None None None None None None None
MCB cycle size 3 5 3.34 3.00 6,562 MAX VALUE 2,345.73 0.54 0.16 0.73
Minimal dual graph
Density: 1.99%
MCB compute time (ms): 67
MCB cycles: 141
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.00 0.33 0.00 0.00 0.77 0.00 None 0.04 8.37 0.10
Degree 2 5 3.56 3.00 640 MAX VALUE 224.15 0.77 0.22 1.11
Eccentricity None None None None None None None None None None
MCB cycle size 3 9 6.87 7.00 968 MAX VALUE 269.38 1.14 0.17 1.47
Triangulated dual graph
Density: 49.47%
Triangles: 226,932
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.72 1.00 0.84 0.82 151.91 0.00 -31.30 0.08 0.09 4.62
Degree 9 136 88.54 108.00 15,938 MAX VALUE 770.93 42.21 0.48 3.95
Eccentricity None None None None None None None None None None
Triangulated minimal dual graph
Density: 11.84%
Feature min max mean median sum prod ln(prod) std_dev COV ENT
Clustering coefficient 0.50 1.00 0.80 0.75 144.20 0.00 -43.25 0.15 0.19 3.24
Degree 2 65 21.20 7.00 3,816 MAX VALUE 422.27 23.24 1.10 3.06
Eccentricity None None None None None None None None None None
Incidence graph
Density: 1.49%
MCB compute time (ms): 43
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-88-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 15 3.27 2.00 720 MAX VALUE 210.90 2.92 0.89 0.88
Eccentricity None None None None None None None None None None
MCB cycle size 6 8 6.62 6.00 934 MAX VALUE 265.30 0.93 0.14 0.62