Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. In this work, we identify submodular maximization problems for which one can get a better approximation for symmetric objectives compared to what is known for general submodular functions. For the problem of maximizing a non-negative symmetric submodular function f: 2 N → R+ subject to a down-monotone solvable polytope P ⊆ [0, 1] N, we describe an algorithm producing a fractional solution of value at least 0.432 · f(OPT), where OPT is the optimal integral solution. Our second result is a 0.432-approximation algorithm for the problem max{f(S): |S| = k} with a non-negative symmetric submodular function f: 2N → R+. Our method also applies to non-symmetric functions, in which case it produces 1/e − o(1) approximation. Finally, we describe a deterministic linear-time 1/2-approximation algorithm for unconstrained maximization of a non-negative symmetric submodular function.
CITATION STYLE
Feldman, M. (2015). Maximizing symmetric submodular functions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9294, pp. 521–532). Springer Verlag. https://doi.org/10.1007/978-3-662-48350-3_44
Mendeley helps you to discover research relevant for your work.