---
_id: '11792'
abstract:
- lang: eng
  text: "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\U0001D452√). 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."
alternative_title:
- LNCS
article_processing_charge: No
arxiv: 1
author:
- first_name: Wolfgang
  full_name: Dvořák, Wolfgang
  last_name: Dvořák
- first_name: Monika H
  full_name: Henzinger, Monika H
  id: 540c9bbd-f2de-11ec-812d-d04a5be85630
  last_name: Henzinger
  orcid: 0000-0002-5008-6530
- first_name: David P.
  full_name: Williamson, David P.
  last_name: Williamson
citation:
  ama: 'Dvořák W, Henzinger MH, Williamson DP. Maximizing a submodular function with
    viability constraints. In: <i>21st Annual European Symposium on Algorithms</i>.
    Vol 8125. Springer Nature; 2013:409-420. doi:<a href="https://doi.org/10.1007/978-3-642-40450-4_35">10.1007/978-3-642-40450-4_35</a>'
  apa: 'Dvořák, W., Henzinger, M. H., &#38; Williamson, D. P. (2013). Maximizing a
    submodular function with viability constraints. In <i>21st Annual European Symposium
    on Algorithms</i> (Vol. 8125, pp. 409–420). Sophia Antipolis, France: Springer
    Nature. <a href="https://doi.org/10.1007/978-3-642-40450-4_35">https://doi.org/10.1007/978-3-642-40450-4_35</a>'
  chicago: Dvořák, Wolfgang, Monika H Henzinger, and David P. Williamson. “Maximizing
    a Submodular Function with Viability Constraints.” In <i>21st Annual European
    Symposium on Algorithms</i>, 8125:409–20. Springer Nature, 2013. <a href="https://doi.org/10.1007/978-3-642-40450-4_35">https://doi.org/10.1007/978-3-642-40450-4_35</a>.
  ieee: W. Dvořák, M. H. Henzinger, and D. P. Williamson, “Maximizing a submodular
    function with viability constraints,” in <i>21st Annual European Symposium on
    Algorithms</i>, Sophia Antipolis, France, 2013, vol. 8125, pp. 409–420.
  ista: 'Dvořák W, Henzinger MH, Williamson DP. 2013. Maximizing a submodular function
    with viability constraints. 21st Annual European Symposium on Algorithms. ESA:
    European Symposium on Algorithms, LNCS, vol. 8125, 409–420.'
  mla: Dvořák, Wolfgang, et al. “Maximizing a Submodular Function with Viability Constraints.”
    <i>21st Annual European Symposium on Algorithms</i>, vol. 8125, Springer Nature,
    2013, pp. 409–20, doi:<a href="https://doi.org/10.1007/978-3-642-40450-4_35">10.1007/978-3-642-40450-4_35</a>.
  short: W. Dvořák, M.H. Henzinger, D.P. Williamson, in:, 21st Annual European Symposium
    on Algorithms, Springer Nature, 2013, pp. 409–420.
conference:
  end_date: 2013-09-04
  location: Sophia Antipolis, France
  name: 'ESA: European Symposium on Algorithms'
  start_date: 2013-09-02
date_created: 2022-08-11T11:18:19Z
date_published: 2013-09-01T00:00:00Z
date_updated: 2023-02-21T16:28:24Z
day: '01'
doi: 10.1007/978-3-642-40450-4_35
extern: '1'
external_id:
  arxiv:
  - '1611.05753'
intvolume: '      8125'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1611.05753
month: '09'
oa: 1
oa_version: Preprint
page: 409 - 420
publication: 21st Annual European Symposium on Algorithms
publication_identifier:
  isbn:
  - '9783642404498'
  issn:
  - 1611-3349
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  record:
  - id: '11792'
    relation: later_version
    status: public
scopus_import: '1'
status: public
title: Maximizing a submodular function with viability constraints
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8125
year: '2013'
...