Practical parallel algorithms for personalized communication and integer sorting
Journal of Experimental Algorithmics (JEA)
Hybrid Algorithms for Complete Exchange in 2D Meshes
IEEE Transactions on Parallel and Distributed Systems
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We study the complexity of permutation routing, sorting, and dynamic routing on meshes with row and column buses. We consider several variants of this model, with both fixed and reconfigurable buses. In the first part of the paper, we give improved deterministic algorithms for permutation routing and sorting. Among our results, we obtain two fairly simple algorithms for permutation routing on two-dimensional meshes with buses that achieve a running time of n+o(n) and a queue size of 2. We also describe an algorithm for routing on r-dimensional networks with a running time of (2-1/r)n+o(n) and a queue size of 2, and show how to obtain deterministic algorithms for sorting whose running times match those for permutation routing, within a lower order additive term. An interesting feature of our algorithms is that they can be efficiently implemented on a variety of different models of meshes with buses. The algorithms are obtained through a new technique that allows us to convert certain off-line routing schemes into deterministic on-line algorithms. In the second part of the paper, we study the performance of meshes with buses on dynamic routing problems. We analyze fast routing schemes under several different assumptions about the properties of the bus system. We observe that the time for the completion of a dynamic routing request can be significantly reduced by adding buses to the network.