# Maximizing a Submodular Function with Viability Constraints

We study the problem of maximizing a monotone submodular function with viability constraints. This problem originates from computational biology, where we are given a phylogenetic tree over a set of species and a directed graph, the so-called food web, encoding viability constraints between these species. These food webs usually have constant depth. The goal is to select a subset of k species that satisfies the viability constraints and has maximal phylogenetic diversity. As this problem is known to be NP-hard, we investigate approximation algorithm. We present the first constant factor approximation algorithm if the depth is constant. Its approximation ratio is (1− 1/sqrt(e)). This algorithm not only applies to phylogenetic trees with viability constraints but for arbitrary monotone submodular set functions with viability constraints. Second, we show that there is no (1 − 1/e + \epsilon)-approximation algorithm for our problem setting (even for additive functions) and that there is no approximation algorithm for a slight extension of this setting.

Top- Dvořák, Wolfgang
- Henzinger, Monika
- Williamson, David P.

Category |
Paper in Conference Proceedings or in Workshop Proceedings (Paper) |

Event Title |
21st European Symposium on Algorithms (ESA 2013) |

Divisions |
Theory and Applications of Algorithms |

Event Location |
Sophia Antipolis, France |

Event Type |
Conference |

Event Dates |
02-04 Sep 2013 |

Series Name |
Lecture Notes in Computer Science |

ISSN/ISBN |
978-3-642-40449-8 |

Publisher |
Springer |

Page Range |
pp. 409-420 |

Date |
2013 |

Official URL |
http://dx.doi.org/10.1007/978-3-642-40450-4_35 |

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