eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-08-30
95:1
95:14
10.4230/LIPIcs.ESA.2023.95
article
Fault Tolerance in Euclidean Committee Selection
Sonar, Chinmay
1
https://orcid.org/0000-0003-0026-4455
Suri, Subhash
1
Xue, Jie
2
Department of Computer Science, University of California, Santa Barbara, CA, USA
Department of Computer Science, New York University, Shanghai, China
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol274-esa2023/LIPIcs.ESA.2023.95/LIPIcs.ESA.2023.95.pdf
Multiwinner elections
Fault tolerance
Geometric Hitting Set
EPTAS