Kernelization for Spreading Points

Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider the following problem about dispersing points. Given a set of points in the plane, the task is to identify whether by moving a small number of points by small distance, we can obtain an arrangement of points such that no pair of points is “close” to each other. More precisely, for a family of n points, an integer k, and a real number d > 0, we ask whether at most k points could be relocated, each point at distance at most d from its original location, such that the distance between each pair of points is at least a fixed constant, say 1. A number of approximation algorithms for variants of this problem, under different names like distant representatives, disk dispersing, or point spreading, are known in the literature. However, to the best of our knowledge, the parameterized complexity of this problem remains widely unexplored. We make the first step in this direction by providing a kernelization algorithm that, in polynomial time, produces an equivalent instance with O(d2k3) points. As a byproduct of this result, we also design a non-trivial fixed-parameter tractable (FPT) algorithm for the problem, parameterized by k and d. Finally, we complement the result about polynomial kernelization by showing a lower bound that rules out the existence of a kernel whose size is polynomial in k alone, unless NP ⊆ coNP /poly.

Original languageEnglish
Title of host publication31st Annual European Symposium on Algorithms, ESA 2023
EditorsInge Li Gortz, Martin Farach-Colton, Simon J. Puglisi, Grzegorz Herman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772952
DOIs
StatePublished - 1 Sep 2023
Event31st Annual European Symposium on Algorithms, ESA 2023 - Amsterdam, Netherlands
Duration: 4 Sep 20236 Sep 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume274
ISSN (Print)1868-8969

Conference

Conference31st Annual European Symposium on Algorithms, ESA 2023
Country/TerritoryNetherlands
CityAmsterdam
Period4/09/236/09/23

Keywords

  • distant representatives
  • kernelization
  • parameterized algorithms
  • spreading points
  • unit disk packing

ASJC Scopus subject areas

  • Software

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