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Reports (Research Report) Year : 2008

A distributed algorithm for computing and updating the process number of a forest

Abstract

In this paper, we present a distributed algorithm to compute various parameters of a tree such as the process number, the edge search number or the node search number and so the pathwidth. This algorithm requires n steps, an overall computation time of O(n log(n)), and n messages of size log_3(n)+3. We then propose a distributed algorithm to update the process number (or the node search number, or the edge search number) of each component of a forest after adding or deleting an edge. This second algorithm requires O(D) steps, an overall computation time of O(D log(n)), and O(D) messages of size log_3(n)+3, where D is the diameter of the modified connected component. Finally, we show how to extend our algorithms to trees and forests of unknown size using messages of less than 2a+4+e bits, where a is the parameter to be determined and e=1 for updates algorithms.
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Dates and versions

inria-00288304 , version 1 (16-06-2008)
inria-00288304 , version 2 (18-06-2008)
inria-00288304 , version 3 (27-06-2008)

Identifiers

  • HAL Id : inria-00288304 , version 3
  • ARXIV : 0806.2710

Cite

David Coudert, Florian Huc, Dorian Mazauric. A distributed algorithm for computing and updating the process number of a forest. [Research Report] RR-6560, INRIA. 2008. ⟨inria-00288304v3⟩
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