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Fault Tolerance in Euclidean Committee Selection

Authors Chinmay Sonar , Subhash Suri, Jie Xue

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Author Details

Chinmay Sonar
  • Department of Computer Science, University of California, Santa Barbara, CA, USA
Subhash Suri
  • Department of Computer Science, University of California, Santa Barbara, CA, USA
Jie Xue
  • Department of Computer Science, New York University, Shanghai, China

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Chinmay Sonar, Subhash Suri, and Jie Xue. Fault Tolerance in Euclidean Committee Selection. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 95:1-95:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ESA.2023.95

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Randomness, geometry and discrete structures
Keywords
  • Multiwinner elections
  • Fault tolerance
  • Geometric Hitting Set
  • EPTAS

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