Permutation routing in all-optical product networks

In this paper we study permutation routing techniques for all-optical networks. Firstly, we show some lower bounds on the number of wavelengths needed for implementing any permutation on an alloptical network in terms of bisection of the network. Secondly, we study permutation routing on product networks by giving a lower bound on the number of wavelengths needed, and presenting permutation routing algorithms for the wavelength non-conversion and conversion models, respectively. Finally, we investigate permutation routing on a cube-connectedcycles network by showing that the number of wavelengths needed for implementing any permutation in one round is [2 log n], which improves on a previously known general result for bounded degree graphs by a factor of O(log3n) for this special case.