Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing

Authors Petr Kolman, Christian Scheideler



PDF
Thumbnail PDF

File

LIPIcs.STACS.2011.129.pdf
  • Filesize: 0.61 MB
  • 12 pages

Document Identifiers

Author Details

Petr Kolman
Christian Scheideler

Cite AsGet BibTex

Petr Kolman and Christian Scheideler. Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 129-140, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)
https://doi.org/10.4230/LIPIcs.STACS.2011.129

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.
Keywords
  • Multicommodity flow
  • Multiroute flow
  • Cuts
  • Duality

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail