Escape of resources in distributed clustering processes

Details Escape of resources in distributed clustering processes Escape of resources in distributed clustering processes

2010-08-14

arxiv.org/abs/1008.2426v1

Mathematics

Probability

8 pages

Scientific paper

In a distributed clustering algorithm introduced by Coffman, Courtois, Gilbert and Piret \cite{coffman91}, each vertex of $\mathbb{Z}^d$ 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 \cite{hlrnss} 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 \cite{berg91}. 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 \cite{hlrnss}.

Affiliated with

Also associated with

No associations

Rating

Escape of resources in distributed clustering processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Escape of resources in distributed clustering processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Escape of resources in distributed clustering processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-42344