License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2023.95
URN: urn:nbn:de:0030-drops-187489
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18748/
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Sonar, Chinmay ; Suri, Subhash ; Xue, Jie

Fault Tolerance in Euclidean Committee Selection

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Abstract

In the committee selection problem, the goal is to choose a subset of size k from a set of candidates C that collectively gives the best representation to a set of voters. We consider this problem in Euclidean d-space where each voter/candidate is a point and voters' preferences are implicitly represented by Euclidean distances to candidates. We explore fault-tolerance in committee selection and study the following three variants: (1) given a committee and a set of f failing candidates, find their optimal replacement; (2) compute the worst-case replacement score for a given committee under failure of f candidates; and (3) design a committee with the best replacement score under worst-case failures. The score of a committee is determined using the well-known (min-max) Chamberlin-Courant rule: minimize the maximum distance between any voter and its closest candidate in the committee. Our main results include the following: (1) in one dimension, all three problems can be solved in polynomial time; (2) in dimension d ≥ 2, all three problems are NP-hard; and (3) all three problems admit a constant-factor approximation in any fixed dimension, and the optimal committee problem has an FPT bicriterion approximation.

BibTeX - Entry

@InProceedings{sonar_et_al:LIPIcs.ESA.2023.95,
  author =	{Sonar, Chinmay and Suri, Subhash and Xue, Jie},
  title =	{{Fault Tolerance in Euclidean Committee Selection}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{95:1--95:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18748},
  URN =		{urn:nbn:de:0030-drops-187489},
  doi =		{10.4230/LIPIcs.ESA.2023.95},
  annote =	{Keywords: Multiwinner elections, Fault tolerance, Geometric Hitting Set, EPTAS}
}

Keywords: Multiwinner elections, Fault tolerance, Geometric Hitting Set, EPTAS
Collection: 31st Annual European Symposium on Algorithms (ESA 2023)
Issue Date: 2023
Date of publication: 30.08.2023

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