Submitter Variables Constraints Density Status Group Objective MPS File
Falk Hueffner 2883 4408 1.04058e-03 easy huefner 610 toll-like.mps.gz

The NP-hard Balanced Subgraph problem (variant of MaxCut) encoded as ILPs. Real-world instances from two applications from bioinformatics, finding monotone subsystems in gene regulatory networks (http://dx.doi.org/10.1007/s10878-009-9212-2) and finding optimal layouts of tanglegrams (http://dx.doi.org/10.1007/978-3-642-11269-0). Solved by Gurobi 4.6 (8 threads) in about four days after a variable transformation reducing symmetry.

Imported from MIPLIB2010.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 2883 2883
Constraints 4408 4408
Binaries 2883 2883
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.00104058 0.00104058
Nonzeroes 13224 13224
Constraint Classification Properties
Original Presolved
Total 4408 4408
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 0 0
Set Partitioning 0 0
Set Packing 0 0
Set Covering 3253 1155
Cardinality 0 0
Invariant Knapsack 1155 3253
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 0 0
General Linear 0 0
Indicator 0 0

Structure

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

value min median mean max
Components 1.826075
Constraint % 0.022686 0.397005 0.0453721 10.8212
Variable % 0.104058 0.862948 0.1387440 24.6965
Score 0.221200

Best Known Solution(s)

No solution available for toll-like .

Similar instances in collection

The following instances are most similar to toll-like 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
tanglegram6 9182 9182 0 0 17712 53136 Falk Hueffner huefner easy 1224
tanglegram4 56048 56048 0 0 110404 331212 Falk Hueffner huefner easy 10696
neos18 3312 3312 0 0 11402 24614 NEOS Server Submission neos-pseudoapplication-49 easy 16
vpphard2 199999 199999 0 0 198450 648340 C. Cardonha easy 81
p0201 201 201 0 0 133 1923 MIPLIB submission pool pfour easy 7615

Reference

@incollection{BockerHuffnerTrussWahlstorm2009,
 author = {B{\"o}cker, Sebastian and H{\"u}ffner, Falk and Truss, Anke and
Wahlstr{\"o}m, Magnus},
 booktitle = {Parameterized and Exact Computation},
 editor = {Chen, Jianer and Fomin, Fedor},
 pages = {38-49},
 publisher = {Springer},
 series = {Lecture Notes in Computer Science},
 title = {A Faster Fixed-Parameter Approach to Drawing Binary Tanglegrams},
 volume = {5917},
 year = {2009}
}

@article{HerrRehnSchuermann2012,
 adsurl = {http://adsabs.harvard.edu/abs/2012arXiv1202.0435H},
 archiveprefix = {arXiv},
 author = {{Herr}, K. and {Rehn}, T. and {Sch{\"u}rmann}, A.},
 eprint = {1202.0435},
 journal = {ArXiv e-prints},
 primaryclass = {math.OC},
 title = {Exploiting Symmetry in Integer Convex Optimization using Core Points},
 year = {2012}
}

@article{HuffnerBetzlerNiedermeier2010,
 author = {H{\"u}ffner, Falk and Betzler, Nadja and Niedermeier, Rolf},
 issn = {1382-6905},
 issue = {4},
 journal = {Journal of Combinatorial Optimization},
 keyword = {Mathematics and Statistics},
 pages = {335-360},
 publisher = {Springer Netherlands},
 title = {Separator-based data reduction for signed graph balancing},
 volume = {20},
 year = {2010}
}

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