Online Hitting Sets for Disks of Bounded Radii

Loading...
Thumbnail Image

Access rights

openAccess
CC BY
publishedVersion

URL

Journal Title

Journal ISSN

Volume Title

A4 Artikkeli konferenssijulkaisussa

Major/Subject

Mcode

Degree programme

Language

en

Pages

16

Series

33rd Annual European Symposium on Algorithms, ESA 2025, pp. 1-16, Leibniz International Proceedings in Informatics, LIPIcs ; Volume 351

Abstract

We present algorithms for the online minimum hitting set problem in geometric range spaces: Given a set P of n points in the plane and a sequence of geometric objects that arrive one-by-one, we need to maintain a hitting set at all times. For disks of radii in the interval [1, M], we present an O(log M log n)-competitive algorithm. This result generalizes from disks to positive homothets of any convex body in the plane with scaling factors in the interval [1, M]. As a main technical tool, we reduce the problem to the online hitting set problem for a finite subset of integer points and bottomless rectangles. Specifically, for a given N > 1, we present an O(log N)-competitive algorithm for the variant where P is a subset of an N × N section of the integer lattice, and the geometric objects are bottomless rectangles.

Description

Publisher Copyright: © Minati De, Satyam Singh, and Csaba D. Tóth;

Other note

Citation

De, M, Singh, S & Tóth, C D 2025, Online Hitting Sets for Disks of Bounded Radii. in A Benoit, H Kaplan, S Wild, S Wild & G Herman (eds), 33rd Annual European Symposium on Algorithms, ESA 2025., 50, Leibniz International Proceedings in Informatics, LIPIcs, vol. 351, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, pp. 1-16, European Symposium on Algorithms, Warsaw, Poland, 15/09/2025. https://doi.org/10.4230/LIPIcs.ESA.2025.50