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Two-phase greedy algorithms for some classes of combinatorial linear programs

Published: 03 September 2010 Publication History

Abstract

We present greedy algorithms for some classes of combinatorial packing and cover problems within the general formal framework of Hoffman and Schwartz' lattice polyhedra. Our algorithms compute in a first phase Monge solutions for the associated dual cover and packing problems and then proceed to construct greedy solutions for the primal problems in a second phase. We show optimality of the algorithms under certain sub- and supermodular assumptions and monotone constraints. For supermodular lattice polyhedra with submodular constraints, our algorithms offer the farthest reaching generalization of Edmonds' polymatroid greedy algorithm currently known.

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  1. Two-phase greedy algorithms for some classes of combinatorial linear programs

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    Published In

    cover image ACM Transactions on Algorithms
    ACM Transactions on Algorithms  Volume 6, Issue 4
    August 2010
    308 pages
    ISSN:1549-6325
    EISSN:1549-6333
    DOI:10.1145/1824777
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 03 September 2010
    Accepted: 01 July 2009
    Received: 01 March 2009
    Published in TALG Volume 6, Issue 4

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    Author Tags

    1. Lattices
    2. submodularity

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