Dispersion on trees

Pawel Gawrychowski, Nadav Krasnopolsky, Shay Mozes, Oren Weimann

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


In the k-dispersion problem, we need to select k nodes of a given graph so as to maximize the minimum distance between any two chosen nodes. This can be seen as a generalization of the independent set problem, where the goal is to select nodes so that the minimum distance is larger than 1. We design an optimal O(n) time algorithm for the dispersion problem on trees consisting of n nodes, thus improving the previous O(n log n) time solution from 1997. We also consider the weighted case, where the goal is to choose a set of nodes of total weight at least W. We present an O(n log2 n) algorithm improving the previous O(n log4 n) solution. Our solution builds on the search version (where we know the minimum distance λ between the chosen nodes) for which we present tight ϵ(n log n) upper and lower bounds.

Original languageEnglish
Title of host publication25th European Symposium on Algorithms, ESA 2017
EditorsChristian Sohler, Christian Sohler, Kirk Pruhs
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770491
StatePublished - 1 Sep 2017
Event25th European Symposium on Algorithms, ESA 2017 - Vienna, Austria
Duration: 4 Sep 20176 Sep 2017

Publication series

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


Conference25th European Symposium on Algorithms, ESA 2017

Bibliographical note

Funding Information:
∗ The research was supported in part by Israel Science Foundation grant 794/13. † The full version of this paper, containing missing proofs and supplementary figures, is available at http://arxiv.org/abs/1706.09185.


  • Dispersion
  • Dynamic programming
  • K-center
  • Parametric search

ASJC Scopus subject areas

  • Software

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