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

Authors:
Ulrich Faigle;Britta Peis
Affiliations:
Zentrum für Angewandte Informatik Köln, Germany;Universität Dortmund, Vogelpothsweg, Dortmund, Germany
Venue:
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2008

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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.