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Asynchronous Deterministic Rendezvous on the Line

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SOFSEM 2009: Theory and Practice of Computer Science (SOFSEM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5404))

Abstract

We study the rendezvous problem in the asynchronous setting in the graph of infinite line following the model introduced in [13]. We formulate general lemmas about deterministic rendezvous algorithms in this setting which characterize the algorithms in which the agents have the shortest routes. We also improve rendezvous algorithms in the infinite line which formulated in [13]. Two agents have distinct labels L m in,L m ax and |L m in |leq |L m ax |. When the initial distance D between the agents is known, our algorithm has cost \(D |L_min|^2\) which is an improvement in the constant. If the initial distance is unknown we give an algorithm of cost \(O(D\log^2 D+D log D|L_max |+D|L_min |^2+|L_max ||L_min |log|L_min |)\) which is an asymptotic improvement.

Supported by MNiSW grants N206 001 31/0436, 2006–2008 and N N206 1723 33, 2007–2010.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Joliot-Curie 15, 50-383, Wrocław, Poland

    Grzegorz Stachowiak

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  1. Grzegorz Stachowiak
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Editor information

Editors and Affiliations

  1. Aarhus Graduate School of Science, University of Aarhus, Ny Munkegade Bldg 1521-110, DK-8000, Aarhus C, Denmark

    Mogens Nielsen

  2. Faculty of Informatics, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic

    Antonín Kučera

  3. Department of Computer Science, University of Aarhus, IT-parken, Aabogade 34, DK-8200, Aarhus N., Denmark

    Peter Bro Miltersen

  4. Ecole Polytechnique, Rue de Saclay, 91128, Palaiseau Cedex, France

    Catuscia Palamidessi  & Frank Valencia  & 

  5. Faculty of Mathematics and Physics, Charles University, Malostranské námestí 25, 118 00, Prague 1, Malá Strana, Czech Republic

    Petr Tůma

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© 2009 Springer-Verlag Berlin Heidelberg

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Stachowiak, G. (2009). Asynchronous Deterministic Rendezvous on the Line. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds) SOFSEM 2009: Theory and Practice of Computer Science. SOFSEM 2009. Lecture Notes in Computer Science, vol 5404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95891-8_45

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  • DOI: https://doi.org/10.1007/978-3-540-95891-8_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-95890-1

  • Online ISBN: 978-3-540-95891-8

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