### An Optimal Permutation Routing Algorithm on Full-Duplex Hexagonal Networks

*Janez Zerovnik, Ignasi Sau*

#### Abstract

In the permutation routing problem, each processor is the origin of at most one packet and the destination of no more than one packet. The goal is to minimize the number of time steps required to route all packets to their respective destinations, under the constraint that each link can be crossed simultaneously by no more than one packet. We study this problem in a hexagonal network, i.e. a finite subgraph of a triangular grid, which is a widely used network in practical applications.
We present an optimal distributed permutation routing algorithm for full-duplex hexagonal networks, using the addressing scheme described by Nocetti et al. Furthermore, we prove that this algorithm is oblivious and translation invariant.

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