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Distributed Computing

, Volume 24, Issue 1, pp 45–63 | Cite as

Distributed algorithms for covering, packing and maximum weighted matching

  • Christos KoufogiannakisEmail author
  • Neal E. Young
Article

Abstract

This paper gives poly-logarithmic-round, distributed δ-approximation algorithms for covering problems with submodular cost and monotone covering constraints (Submodular-cost Covering). The approximation ratio δ is the maximum number of variables in any constraint. Special cases include Covering Mixed Integer Linear Programs (CMIP), and Weighted Vertex Cover (with δ = 2). Via duality, the paper also gives poly-logarithmic-round, distributed δ-approximation algorithms for Fractional Packing linear programs (where δ is the maximum number of constraints in which any variable occurs), and for Max Weighted c-Matching in hypergraphs (where δ is the maximum size of any of the hyperedges; for graphs δ = 2). The paper also gives parallel (RNC) 2-approximation algorithms for CMIP with two variables per constraint and Weighted Vertex Cover. The algorithms are randomized. All of the approximation ratios exactly match those of comparable centralized algorithms.

Keywords

Approximation algorithms Integer linear programming Packing and covering Vertex cover Matching 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringUniversity of CaliforniaRiversideUSA

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