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The all-or-nothing flow problem in directed graphs with symmetric demand pairs
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Chekuri, Chandra and Ene, Alina (2014) The all-or-nothing flow problem in directed graphs with symmetric demand pairs. Mathematical Programming Series B . doi:10.1007/978-3-319-07557-0-19
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Official URL: http://dx.doi.org/10.1007/s10107-014-0856-z
Abstract
We study the approximability of the All-or-Nothing multicommodity flow problem in directed graphs with symmetric demand pairs (SymANF). The input consists of a directed graph G = (V, E) and a collection of (unordered) pairs of nodes M = {s1t1,s2t2,...,sk tk }. A subset M of the pairs is routable if there is a feasible multicommodity flow in G such that, for each pair si ti ∈ M, the amount of flow from si to ti is at least one and the amount of flow from ti to si is at least one. The goal is to find a maximum cardinality subset of the given pairs that can be routed. Our main result is a poly-logarithmic approximation with constant congestion for SymANF. We obtain this result by extending the well-linked decomposition framework of Chekuri et al. (2005) to the directed graph setting with symmetric demand pairs. We point out the importance of studying routing problems in this setting and the relevance of our result to future work.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science > Computer Science | ||||||||
| Library of Congress Subject Headings (LCSH): | Directed graphs | ||||||||
| Journal or Publication Title: | Mathematical Programming Series B | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0025-5610 | ||||||||
| Official Date: | 21 December 2014 | ||||||||
| Dates: |
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| DOI: | 10.1007/978-3-319-07557-0-19 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Funder: | National Science Foundation (U.S.) (NSF), Toyota Technological Institute at Chicago (TTI) | ||||||||
| Grant number: | CCF-1016684 (NSF), CCF-1319376 (NSF), CCF-0844872 (NSF) | ||||||||
| Version or Related Resource: | Chekuri, C. and Ene, A. (2014). The all-or-nothing flow problem in directed graphs with symmetric demand pairs. In: Lee, J. and Vygen, J., (eds.) Integer Programming and Combinatorial Optimization : 17th International Conference, IPCO 2014, Bonn, Germany, June 23-25, 2014 : proceedings. Lecture notes in computer science, 8494. Springer International Publishing, pp. 222-233. | ||||||||
| Embodied As: | 1 | ||||||||
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