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New Results on Routing via Matchings on Graphs

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Fundamentals of Computation Theory (FCT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10472))

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Abstract

In this paper we present some new complexity results on the routing time of a graph under the routing via matching model. This is a parallel routing model which was introduced by Alon et al. [1]. The model can be viewed as a communication scheme on a distributed network. The nodes in the network can communicate via matchings (a step), where a node exchanges data (pebbles) with its matched partner. Let G be a connected graph with vertices labeled from \(\{1,...,n\}\) and the destination vertices of the pebbles are given by a permutation \(\pi \). The problem is to find a minimum step routing scheme for the input permutation \(\pi \). This is denoted as the routing time \(rt(G,\pi )\) of G given \(\pi \). In this paper we characterize the complexity of some known problems under the routing via matching model and discuss their relationship to graph connectivity and clique number. We also introduce some new problems in this domain, which may be of independent interest.

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Notes

  1. 1.

    The base case, which computes \(rt(Q_3)\) was determined to be 4 via a computer search [6].

  2. 2.

    After publication of our results to arXiv [16] a similar result was independently discovered in the context of parallel token swapping by Kawahara et al. [4].

  3. 3.

    We do not write the 1 cycles explicitly as is common.

References

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Authors and Affiliations

  1. Department of Computer Science, George Mason University, Fairfax, VA, 22030, USA

    Indranil Banerjee & Dana Richards

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  1. Indranil Banerjee
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  2. Dana Richards
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Correspondence to Indranil Banerjee .

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Editors and Affiliations

  1. CNRS, University of Bordeaux, Talence cedex, France

    Ralf Klasing

  2. LaBRI, University of Bordeaux, Talence cedex, France

    Marc Zeitoun

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Banerjee, I., Richards, D. (2017). New Results on Routing via Matchings on Graphs. In: Klasing, R., Zeitoun, M. (eds) Fundamentals of Computation Theory. FCT 2017. Lecture Notes in Computer Science(), vol 10472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55751-8_7

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  • DOI: https://doi.org/10.1007/978-3-662-55751-8_7

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