New transience bounds for long walks in weighted digraphs

Bernadette Charron-Bost 1 Matthias Függer 2 Thomas Nowak 3
3 DYOGENE - Dynamics of Geometric Networks
CNRS - Centre National de la Recherche Scientifique : UMR8548, Inria Paris-Rocquencourt, DI-ENS - Département d'informatique de l'École normale supérieure
Abstract : We consider the sequence of maximal weights of walks of lengt n between two fixed nodes in a weighted digraph. It is known that these sequences show a periodic behavior after an initial transient. We identify relevant graph parameters and propose a modular strategy to derive new upper bounds on the transient. To the best of our knowledge, our bounds are the first that are both asymptotically tight and potentially subquadratic. In particular, the new bounds show that the transient is linear in the number of nodes in bi-directional trees. Besides, our results enable a fine-grained performance analysis and give guidelines for the design of distributed systems based on max-plus recursions.
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Submitted on : Wednesday, May 21, 2014 - 9:46:16 AM
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Bernadette Charron-Bost, Matthias Függer, Thomas Nowak. New transience bounds for long walks in weighted digraphs. Eurocomb 2013, Sep 2013, Pise, Italy. pp.623-624, ⟨10.1007/978-88-7642-475-5_103⟩. ⟨hal-00993814⟩



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