Submitter Variables Constraints Density Status Group Objective MPS File
Stephan Beyer 3484 32073 3.59039e-03 open genus -19 genus-sym-g31-8.mps.gz

Minimum Genus instance, with symmetry breaking constraints, of g.31.8 (undirected) of the AT&T Graphs by Stephen C. North.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 3484 3483
Constraints 32073 32073
Binaries 3482 3482
Integers 1 1
Continuous 1 0
Implicit Integers 0 0
Fixed Variables 1 0
Nonzero Density 0.00359039 0.00359142
Nonzeroes 401199 401199
Constraint Classification Properties
Original Presolved
Total 32073 32073
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 26 26
Variable Bound 0 0
Set Partitioning 234 234
Set Packing 0 0
Set Covering 14532 8376
Cardinality 837 837
Invariant Knapsack 16416 22572
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 27
Integer Knapsack 0 0
Mixed Binary 27 0
General Linear 1 1
Indicator 0 0

Structure

Available nonzero structure and decomposition information. Further information can be found here.

value min median mean max
Components 1.612784
Constraint % 0.0436504 0.720232 0.0966545 25.5355
Variable % 0.3445310 2.486360 3.3304600 4.4789
Score 0.275756

Best Known Solution(s)

Find solutions below. Download the archive containing all solutions from the Download page.

ID Objective Exact Int. Viol Cons. Viol Obj. Viol Submitter Date Description
1 -19 0 0 0 - 2018-10-12 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to genus-sym-g31-8 in the collection. This similarity analysis is based on 100 scaled instance features describing properties of the variables, objective function, bounds, constraints, and right hand sides.

Instance Variables Binaries Integers Continuous Constraints Nonz. Submitter Group Status Objective
genus-g31-8 3484 3482 1 1 32047 401147 Stephan Beyer genus open -19*
genus-sym-grafo5708-48 3379 3377 1 1 20538 72579 Stephan Beyer genus open -15*
graph20-80-1rand 16263 16263 0 0 55107 191997 Michael Bastubbe graphs open -6*
genus-sym-g62-2 12912 12910 1 1 78472 275855 Stephan Beyer genus open -20*
graph40-20-1rand 31243 31243 0 0 99067 345557 Michael Bastubbe graphs open -14*

Reference

@inproceedings{BCHK16,
 author    = {Stephan Beyer and Markus Chimani and Ivo Hedtke and Michal Kotrbc{\'{\i}}k},
 title     = {{A} {Practical} {Method} for the {Minimum} {Genus} of a {Graph}: {Models} and {Experiments}},
 booktitle = {Experimental Algorithms---Proceedings 15th {SEA} 2016, St. Petersburg},
 editor    = {Andrew V. Goldberg and Alexander S. Kulikov},
 pages     = {75--88},
 year      = {2016},
 series    = {LNCS},
 volume    = {9685},
 publisher = {Springer},
 doi       = {10.1007/978-3-319-38851-9_6}
}

@article{DBLP:journals/comgeo/WelzlBGLTTV97,
author    = {Giuseppe {Di Battista} and Ashim Garg and Giuseppe Liotta and Roberto Tamassia and Emanuele Tassinari and Francesco Vargiu},
title     = {An Experimental Comparison of Four Graph Drawing Algorithms},
journal   = {Comput. Geom.},
volume    = {7},
pages     = {303--325},
year      = {1997},
url       = {https://doi.org/10.1016/S0925-7721(96)00005-3},
doi       = {10.1016/S0925-7721(96)00005-3}
}

Last Update Nov 17, 2018 by Gregor Hendel
generated with R Markdown
© 2018 by Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)
Imprint