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

David Coudert (1) , Florian Huc (1, 2) , Dorian Mazauric (1)

1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
2 TCS-Sensor Lab [Genève]

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.

Domaines: Réseaux et télécommunications [cs.NI]; Algorithme et structure de données [cs.DS]

David Coudert, Florian Huc, Dorian Mazauric. A distributed algorithm for computing and updating the process number of a forest. 22nd International Symposium on Distributed Computing (DISC), 2008, Arcachon, France, France. pp.500-501. ⟨inria-00373850⟩