New Results on Routing via Matchings on Graphs


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 π. The problem is to find a minimum step routing scheme for the input permutation π. This is denoted as the routing time rt(G, π) of G given π. 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.

Meeting Name

21st International Symposium on Fundamentals of Computation Theory, FCT 2017 (2017: Sep. 11-13, Bordeaux, France)


Computer Science


Published as Indranil Banerjee.

Keywords and Phrases

Complex Networks; Computation Theory, Communication Schemes; Complexity Results; Connected Graph; Distributed Networks; Graph Connectivity; Matching Models; Parallel Routing; Routing Scheme, Graph Theory

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International Standard Serial Number (ISSN)


Document Type

Article - Conference proceedings

Document Version


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© 2017 Springer Verlag, All rights reserved.

Publication Date

13 Sep 2017