Submitter Variables Constraints Density Status Group Objective MPS File
Stephan Beyer 14380 94735 2.44351e-04 open genus -26 genus-g61-25.mps.gz

Minimum Genus instance of g.61.25 (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 14380 14379
Constraints 94735 94735
Binaries 14378 14378
Integers 1 1
Continuous 1 0
Implicit Integers 0 0
Fixed Variables 1 0
Nonzero Density 0.000244351 0.000244368
Nonzeroes 332877 332877
Constraint Classification Properties
Original Presolved
Total 94735 94735
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 0 0
Set Partitioning 540 540
Set Packing 0 0
Set Covering 20592 1104
Cardinality 3480 3480
Invariant Knapsack 70064 89552
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 58
Integer Knapsack 0 0
Mixed Binary 58 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 1.959041
Constraint % 0.006350 0.0503601 0.0635385 0.118605
Variable % 0.083455 1.1043900 1.6412800 1.641280
Score 0.044701

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 -26 1e+100 0 0 0 - 2018-10-12 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to genus-g61-25 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-sym-g62-2 12912 12910 1 1 78472 275855 Stephan Beyer genus open -20*
genus-sym-grafo5708-48 3379 3377 1 1 20538 72579 Stephan Beyer genus open -15*
neos-950242 5760 5520 240 0 34224 104160 NEOS Server Submission neos-pseudoapplication-72 easy 4
supportcase10 14770 14770 0 0 165684 555082 Michael Winkler hard 7
neos-3230376-yser 57000 56976 0 24 786916 2372590 Jeff Linderoth neos-pseudoapplication-4 easy Unbounded

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 09, 2018 by Gregor Hendel
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