Abstract
We discuss iterative nearest neighbor load balancing schemes on processor networks which are represented by a cartesian product of graphs like e.g. tori or hypercubes. By the use of the Alternating-Direction Loadbalancing scheme, the number of load balance iterations decreases by a factor of 2 for this type of graphs. The resulting flow is analyzed theoretically and it can be very high for certain cases. Therefore, we furthermore present the Mixed-Direction scheme which needs the same number of iterations but results in a much smaller flow.
Apart from that, we present a simple optimal diffusion scheme for general graphs which calculates a minimal balancing flow in the l 2 norm. The scheme is based on the spectrum of the graph representing the network and needs only m-1 iterations in order to balance the load with m being the number of distinct eigenvalues.
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Elsässer⋆, R., Monien*, B., Preis*, R., Frommer, A. (1999). Optimal and Alternating-Direction Load Balancing Schemes. In: Amestoy, P., et al. Euro-Par’99 Parallel Processing. Euro-Par 1999. Lecture Notes in Computer Science, vol 1685. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48311-X_36
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DOI: https://doi.org/10.1007/3-540-48311-X_36
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