Computing and Updating the Process Number in Trees

  • David Coudert
  • Florian Huc
  • Dorian Mazauric
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5401)


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.

We present a distributed algorithm to compute these parameters and the edge search number, in trees. It can be executed in an asynchronous environment, requires n steps, an overall computation time of O(nlogn), and n messages of size log3n + 2. Then, we propose a distributed algorithm to update these parameters on each component of a forest after addition or deletion of any tree edge. This second algorithm requires O(D) steps, an overall computation time of O(Dlogn), and O(D) messages of size log3n + 3, where D is the diameter of the new connected component.


Pathwidth process number distributed algorithm 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • David Coudert
    • 1
  • Florian Huc
    • 1
  • Dorian Mazauric
    • 1
  1. 1.Mascotte, INRIA, I3S, CNRSUniversity of Nice Sophia AntipolisFrance

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