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SCIENTIA SINICA Informationis, Volume 46, Issue 2: 228-243(2016) https://doi.org/10.1360/N112015-00154-93

Shortcuts and periodicity of networked max-plus system with ring topology

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  • AcceptedAug 21, 2015
  • PublishedJan 28, 2016

Abstract

This paper investigates the characteristics of cyclicity and cycle time after adding shortcuts to the networked max-plus system with ring topology. Both the lower bound expression of the probability of cyclicity being one and the sufficient and necessary condition for the cycle time being unchanged are established after adding k shortcuts with the same starting point. For two systems with the dimensions of a prime number and its power, it is discovered that the lower bounds of the probability of cyclicity being one is consistent after adding the shortcuts. The paper also investigates some situations of adding shortcuts under conditions with different starting points. The lower bound expression of the probability of cyclicity being one is given after adding k shortcuts with mutual disjoint. The method for algebra and combinatorics is constructive. The algorithm of the cycle time remaining unchanged is given after adding k shortcuts with the same starting point. It is proven that such algorithm has a polynomial bound. At the same time, the numerical example for cyclicity is also given.


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