Abstract
In a connected simple graph G the following random experiment is carried out: each node chooses one of its neighbors uniformly at random. We say a rendezvous occurs if there are adjacent nodes u and v such that u chooses v and v chooses u. Métivier et al. (2000) asked whether it is true that the probability for a rendezvous to occur in G is at least as large as the probability of a rendezvous if the same experiment is carried out in the complete graph on the same number of nodes. In this paper we show that this is the case.
Part of this work was done while the author was visiting the Max-Planck-Institut für Informatik, Saarbrücken, Germany.
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References
H. Austinat, Verteilte Algorithmen zur Koordinatorwahl in Netzwerken, Diplomarbeit Nr. 1727, Universität Stuttgart, Fakultät Informatik, 1999, 66 pages.
D.P. Dubhashi and D. Ranjan, Balls and bins: A study in negative dependence, Random Structures and Algorithms 13(2), 99–124 (1998).
Y. Métivier, N. Saheb, and A. Zemmari, Randomized rendezvous, in: G. Gardy and A. Mokkadem (Eds.), Algorithms, Trees, Combinatorics, and Probabilities, Trends in Mathematics, Birkhäuser, 2000, pp. 183–194. Also see the technical report version at ftp://ftp.labri.u-bordeaux.fr/pub/Local/Info/ Publications/Rapports-internes/RR-122800.ps.gz.
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© 2002 Springer-Verlag Berlin Heidelberg
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Dietzfelbinger, M. (2002). The Probability of a Rendezvous Is Minimal in Complete Graphs. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_6
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DOI: https://doi.org/10.1007/3-540-36136-7_6
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