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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2011.129
URN: urn:nbn:de:0030-drops-30051
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2011/3005/
Kolman, Petr ;
Scheideler, Christian
Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing
Abstract
An elementary h-route flow, for an integer h >= 1, is a set of h edge-disjoint paths between a source and a sink, each path carrying a unit of flow, and an h-route flow is a non-negative linear combination of elementary h-route flows. An h-route cut is a set of edges whose removal decreases the maximum h-route flow between a given source-sink pair (or between every source-sink pair in the multicommodity setting) to zero. The main result of this paper is an approximate duality theorem for multicommodity
$h$-route cuts and flows, for h <= 3: The size of a minimum h-route cut is at least f/h and at most O(log^3(k)f) where f is the size of the maximum h-route flow and k is the number of commodities. The main step towards the proof of this duality is the design and analysis of a polynomial-time approximation algorithm for the minimum h-route cut problem for h=3 that has an approximation ratio of O(log^3 k). Previously, polylogarithmic approximation was known only for $h$-route cuts for h <= 2.
A key ingredient of our algorithm is a novel rounding technique that we call multilevel ball-growing. Though the proof of the duality relies on this algorithm, it is not a straightforward corollary of it as in the case of classical multicommodity flows and cuts. Similar results are shown also for the sparsest multiroute cut problem.
BibTeX - Entry
@InProceedings{kolman_et_al:LIPIcs:2011:3005,
author = {Petr Kolman and Christian Scheideler},
title = {{Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing}},
booktitle = {28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) },
pages = {129--140},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-25-5},
ISSN = {1868-8969},
year = {2011},
volume = {9},
editor = {Thomas Schwentick and Christoph D{\"u}rr},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2011/3005},
URN = {urn:nbn:de:0030-drops-30051},
doi = {10.4230/LIPIcs.STACS.2011.129},
annote = {Keywords: Multicommodity flow, Multiroute flow, Cuts, Duality}
}
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Keywords: |
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Multicommodity flow, Multiroute flow, Cuts, Duality |
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Collection: |
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28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) |
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Issue Date: |
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2011 |
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Date of publication: |
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11.03.2011 |
