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Escape of resources in a distributed clustering process
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Jacob van den Berg, CWI and VU University Amsterdam
Marcelo Richard Hilário, IMPA
Alexander E. Holroyd, Microsoft Research and University of British Columbia
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Abstract
In a distributed clustering algorithm introduced by Coffman, Courtois,
Gilbert and Piret [1], each vertex of Zd receives an
initial amount of a resource, and, at each iteration, transfers all of its
resource to the neighboring vertex which currently holds the maximum amount
of resource. In [4] it was shown that, if the distribution of the
initial quantities of resource is invariant under lattice translations, then
the flow of resource at each vertex eventually stops almost surely, thus
solving a problem posed in [2]. In this article we prove the
existence of translation-invariant initial distributions for which resources
nevertheless escape to infinity, in the sense that the the final amount of
resource at a given vertex is strictly smaller in expectation than the
initial amount. This answers a question posed in [4].
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Full text: PDF
Pages: 442-448
Published on: September 30, 2010
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Electronic Communications in Probability. ISSN: 1083-589X |
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