Maximum bipartite flow in networks with adaptive channel width

Yossi Azar, Aleksander Ma̧dry, Thomas Moscibroda, Debmalya Panigrahi, Aravind Srinivasan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Traditionally, combinatorial optimization problems (such as maximum flow, maximum matching, etc.) have been studied for networks where each link has a fixed capacity. Recent research in wireless networking has shown that it is possible to design networks where the capacity of the links can be changed adaptively to suit the needs of specific applications. In particular, one gets a choice of having few high capacity outgoing links or many low capacity ones at any node of the network. This motivates us to have a re-look at the traditional combinatorial optimization problems and design algorithms to solve them in this new framework. In particular, we consider the problem of maximum bipartite flow, which has been studied extensively in the traditional network model. One of the motivations for studying this problem arises from the need to maximize the throughput of an infrastructure wireless network comprising base-stations (one set of vertices in the bipartition) and clients (the other set of vertices in the bipartition). We show that this problem has a significantly different combinatorial structure in this new network model from the classical one. While there are several polynomial time algorithms solving the maximum bipartite flow problem in traditional networks, we show that the problem is NP-hard in the new model. In fact, our proof extends to showing that the problem is APX-hard. We complement our lower bound by giving two algorithms for solving the problem approximately. The first algorithm is deterministic and achieves an approximation factor of O(logN), where there are N nodes in the network, while the second algorithm (which is our main contribution) is randomized and achieves an approximation factor of .

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings
Pages351-362
Number of pages12
EditionPART 2
DOIs
StatePublished - 2009
Event36th International Colloquium on Automata, Languages and Programming, ICALP 2009 - Rhodes, Greece
Duration: 5 Jul 200912 Jul 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume5556 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference36th International Colloquium on Automata, Languages and Programming, ICALP 2009
Country/TerritoryGreece
CityRhodes
Period5/07/0912/07/09

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