Submitter Variables Constraints Density Status Group Objective MPS File
Falk Hueffner 56048 110404 5.35255e-05 easy huefner 10696 tanglegram4.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).

Imported from the MIPLIB2010 submissions.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 56048 56048
Constraints 110404 110404
Binaries 56048 56048
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 5.35255e-05 5.35255e-05
Nonzeroes 331212 331212
Constraint Classification Properties
Original Presolved
Total 110404 110404
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 84761 25643
Cardinality 0 0
Invariant Knapsack 25643 84761
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 1.079181
Constraint % 0.000906 2.11150 0.00181 23.193
Variable % 0.005350 4.20305 0.00892 46.123
Score 0.125292

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 10696 10696 0 0 0 - 2018-10-12 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to tanglegram4 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
toll-like 2883 2883 0 0 4408 13224 Falk Hueffner huefner easy 610
vpphard2 199999 199999 0 0 198450 648340 C. Cardonha easy 81
vpphard 51471 51471 0 0 47280 372305 C. Cardonha easy 5
30_70_45_095_100 10976 10975 0 1 12526 46640 J. Walser 30_70 easy 3

Reference

No bibliographic information available

Last Update Nov 09, 2018 by Gregor Hendel
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