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On Finite Dimension Exchange Algorithms

Abstract Load balancing on parallel computers aims at equilibrating some initial load which is different from one processor to another. We consider only nearest neighbour algorithms: in each step a processor communicates only with its direct neighbours. Such load balancing algorithms can be divided basically into two classes: diffusion and dimension exchange. Whereas the first is appropriate for the so-called all-port-model where a processor can send tokens to all its neighbours at a time, the latter relies on the one-port-model. Both kinds of algorithms can be viewed as methods for solving certain singular linear systems. Therefore, algorithms can be developed and analyzed using techniques from numerical linear algebra. In the last few years finite diffusion algorithms have been developed and it has been proven that they compute l 2 -minimal flows. In the paper new finite dimension exchange methods will be presented that are based on edge-colourings of the underlying graph. They are often faster and numerically more stable than their diffusion counterparts. The flows computed by the new methods are not minimal but it can be shown that they are bounded. For some special graphs these bounds can be explicitly determined by an analysis of the matrices representing the graph.