Elsevier

Discrete Applied Mathematics

Volume 219, 11 March 2017, Pages 83-99
Discrete Applied Mathematics

New transience bounds for max-plus linear systems

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Abstract

Linear max-plus systems describe the behavior of a large variety of complex systems. It is known that these systems show a periodic behavior after an initial transient phase. Assessment of the length of this transient phase provides important information on complexity measures of such systems, and so is crucial in system design. We identify relevant parameters in a graph representation of these systems and propose a modular strategy to derive new upper bounds on the length of the transient phase. By that we are the first to give asymptotically tight and potentially subquadratic transience bounds. We use our bounds to derive new complexity results, in particular in distributed computing.

Keywords

Transience bounds
Max-plus systems
Cyclic scheduling
Network synchronizers
Link-reversal algorithms

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