Algorithms and complexity for the almost equal maximum flow problem

In the equal maximum flow problem (EMFP), we aim for a maximum flow where we require the same flow value on all arcs in some given subsets of the arc set, so called homologous arc sets. In this article, we study the closely related almost equal maximum flow problems (AEMFP) where the flow values on...

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Veröffentlicht in:Networks Jg. 83; H. 4; S. 642 - 652
Hauptverfasser: Haese, Rebekka, Heller, Till, Krumke, Sven O.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Wiley Subscription Services, Inc 01.06.2024
Schlagworte:
Algorithms
Deviation
Homology
Mathematical analysis
Polynomials
ISSN:0028-3045, 1097-0037
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Zusammenfassung:In the equal maximum flow problem (EMFP), we aim for a maximum flow where we require the same flow value on all arcs in some given subsets of the arc set, so called homologous arc sets. In this article, we study the closely related almost equal maximum flow problems (AEMFP) where the flow values on arcs of one homologous arc set differ at most by the valuation of a so called deviation function . We prove that the integer AEMFP is in general ‐complete, and show that even the problem of finding a fractional maximum flow in the case of convex deviation functions is also ‐complete. This is in contrast to the EMFP, which is polynomial time solvable in the fractional case. Additionally, we provide inapproximability results for the integral AEMFP. For the (fractional) concave AEMFP we state a strongly polynomial algorithm for the linear and concave piecewise polynomial deviation function case for a fixed number of homologous sets using a parametric search approach.
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ISSN:0028-3045
1097-0037
DOI:10.1002/net.22209