Computing and Updating the Process Number in Trees

The process number is the minimum number of requests that have to be simultaneously disturbed during a routing reconfiguration phase of a connection oriented network. From a graph theory point of view, it is similar to the node search number, and thus to the pathwidth, however they are not always equal. In general determining these parameters is NP-complete. In this paper, we present a distributed algorithm to compute these parameters as well as the edge search number. It can be executed in an asynchronous environment, requires n steps, an overall computation time of O(nlogn), and n messages of size log3 n+2. 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 addition or deletion of any edge. This second algorithm requires O(D) steps, an overall computation time of O(Dlogn), and O(D) messages of size log3 n+3, where D is the diameter of the new connected component.

• Type: Conference
• Year: 2008
• Where: OPODIS
• Authors: David Coudert, Florian Huc, Dorian Mazauric
• Keywords: Distributed And Parallel Computing, Edge Search Number, Node Search Number, OPODIS 2008, Search Number