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

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.

• Type: Conference
• Year: 2008
• Where: SODA
• Authors: Ulrich Faigle, Britta Peis
• Keywords: Algorithms, Greedy Algorithm, Lattice Polyhedra, Phase Monge Solutions, SODA 2008