Maximizing a submodular function with viability constraints

Dvořák W, Henzinger MH, Williamson DP. 2017. Maximizing a submodular function with viability constraints. Algorithmica. 77(1), 152–172.

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Author
Dvořák, Wolfgang; Henzinger, MonikaISTA ; Williamson, David P.
Abstract
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 algorithms. We present the first constant factor approximation algorithm if the depth is constant. Its approximation ratio is (1−1e√). 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+ϵ)-approximation algorithm for our problem setting (even for additive functions) and that there is no approximation algorithm for a slight extension of this setting.
Publishing Year
Date Published
2017-01-01
Journal Title
Algorithmica
Publisher
Springer Nature
Acknowledgement
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 340506.
Volume
77
Issue
1
Page
152-172
ISSN
eISSN
IST-REx-ID

Cite this

Dvořák W, Henzinger MH, Williamson DP. Maximizing a submodular function with viability constraints. Algorithmica. 2017;77(1):152-172. doi:10.1007/s00453-015-0066-y
Dvořák, W., Henzinger, M. H., & Williamson, D. P. (2017). Maximizing a submodular function with viability constraints. Algorithmica. Springer Nature. https://doi.org/10.1007/s00453-015-0066-y
Dvořák, Wolfgang, Monika H Henzinger, and David P. Williamson. “Maximizing a Submodular Function with Viability Constraints.” Algorithmica. Springer Nature, 2017. https://doi.org/10.1007/s00453-015-0066-y.
W. Dvořák, M. H. Henzinger, and D. P. Williamson, “Maximizing a submodular function with viability constraints,” Algorithmica, vol. 77, no. 1. Springer Nature, pp. 152–172, 2017.
Dvořák W, Henzinger MH, Williamson DP. 2017. Maximizing a submodular function with viability constraints. Algorithmica. 77(1), 152–172.
Dvořák, Wolfgang, et al. “Maximizing a Submodular Function with Viability Constraints.” Algorithmica, vol. 77, no. 1, Springer Nature, 2017, pp. 152–72, doi:10.1007/s00453-015-0066-y.
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