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Computing and updating the process number in trees

David Coudert 1 Florian Huc 1 Dorian Mazauric 1
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : 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(n log n), and n messages of size log3 n + 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(D log n), and O(D) messages of size log3 n + 3, where D is the diameter of the new connected component.
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David Coudert, Florian Huc, Dorian Mazauric. Computing and updating the process number in trees. 12th International Conference On Principles Of DIstributed Systems (OPODIS), Dec 2008, Luxor, Egypt. ⟨10.1007/978-3-540-92221-6_37⟩. ⟨inria-00429149⟩

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