Group search on the line

Marek Chrobak, Leszek Gąsieniec, Thomas Gorry, Russell Martin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

31 Scopus citations

Abstract

In this paper we consider the group search problem, or evacuation problem, in which k mobile entities (Mεs) located on the line perform search for a specific destination. The Mεs are initially placed at the same origin on the line L and the target is located at an unknown distance d, either to the left or to the right from the origin. All Mεs must simultaneously occupy the destination, and the goal is to minimize the time necessary for this to happen. The problem with k = 1 is known as the cow-path problem, and the time required for this problem is known to be 9d - o(d) in the worst case (when the cow moves at unit speed); it is also known that this is the case for k ≥ 1 unit-speed Mεs. In this paper we present a clear argument for this claim by showing a rather counter-intuitive result. Namely, independent of the number of Mεs, group search cannot be performed faster than in time 9d - o(d). We also examine the case of k = 2 Mεs with different speeds, showing a surprising result that the bound of 9d can be achieved when one Mε has unit speed, and the other Mε moves with speed at least 1/3.

Original languageEnglish (US)
Title of host publicationSOFSEM 2015
Subtitle of host publicationTheory and Practice of Computer Science - 41st International Conference on Current Trends in Theory and Practice of Computer Science,
EditorsGiuseppe F. Italiano, Tiziana Margaria-Steffen, Jaroslav Pokorný, Jean-Jacques Quisquater, Roger Wattenhofer
PublisherSpringer Verlag
Pages164-176
Number of pages13
ISBN (Electronic)9783662460771
DOIs
StatePublished - Jan 1 2015
Event41st International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2015 - Pec pod Sněžkou, Czech Republic
Duration: Jan 24 2015Jan 29 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8939
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference41st International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2015
CountryCzech Republic
CityPec pod Sněžkou
Period1/24/151/29/15

Keywords

  • Evacuation
  • Group search
  • Mobile entity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Chrobak, M., Gąsieniec, L., Gorry, T., & Martin, R. (2015). Group search on the line. In G. F. Italiano, T. Margaria-Steffen, J. Pokorný, J-J. Quisquater, & R. Wattenhofer (Eds.), SOFSEM 2015: Theory and Practice of Computer Science - 41st International Conference on Current Trends in Theory and Practice of Computer Science, (pp. 164-176). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8939). Springer Verlag. https://doi.org/10.1007/978-3-662-46078-8_14