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International Colloquium on Automata, Languages, and Programming

ICALP 2013: Automata, Languages, and Programming pp 533–544Cite as

Deterministic Polynomial Approach in the Plane

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7966))

Abstract

Two mobile agents with range of vision 1 start at arbitrary points in the plane and have to accomplish the task of approach, which consists in getting at distance at most one from each other, i.e., in getting within each other’s range of vision. An adversary chooses the initial positions of the agents, their possibly different starting times, and assigns a different positive integer label and a possibly different speed to each of them. Each agent is equipped with a compass showing the cardinal directions, with a measure of length and a clock. Each agent knows its label and speed but not those of the other agent and it does not know the initial position of the other agent relative to its own. Agents do not have any global system of coordinates and they cannot communicate. Our main result is a deterministic algorithm to accomplish the task of approach, working in time polynomial in the unknown initial distance between the agents, in the length of the smaller label and in the inverse of the larger speed. The distance travelled by each agent until approach is polynomial in the first two parameters and does not depend on the third. The problem of approach in the plane reduces to a network problem: that of rendezvous in an infinite grid.

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Author information

Authors and Affiliations

  1. MIS, Université de Picardie Jules Verne, France

    Yoann Dieudonné

  2. Département d’informatique, Université du Québec en Outaouais, Gatineau, Québec, Canada

    Andrzej Pelc

Authors
  1. Yoann Dieudonné
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  2. Andrzej Pelc
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Faculty of Computing, University of Latvia, Raina bulv. 19, 1586, Riga, Latvia

    Rūsiņš Freivalds

  3. Department of Computer Science, Wolfson Building, Parks Road, University of Oxford, OX1 3QD, Oxford, UK

    Marta Kwiatkowska

  4. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, 76100, Rehovot, Israel

    David Peleg

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Dieudonné, Y., Pelc, A. (2013). Deterministic Polynomial Approach in the Plane. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7966. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39212-2_47

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  • DOI: https://doi.org/10.1007/978-3-642-39212-2_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39211-5

  • Online ISBN: 978-3-642-39212-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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