Abstract
We design a general mathematical framework to analyze the properties of nearest neighbor balancing algorithms of the diffusion type. Within this framework we develop a new optimal polynomial scheme (OPS) which we show to terminate within a finite number m of steps, where m only depends on the graph and not on the initial load distribution.
We show that all existing diffusion load balancing algorithms, including OPS determine a flow of load on the edges of the graph which is uniquely defined, independent of the method and minimal in the l 2-norm. This result can also be extended to edge weighted graphs.
The l 2-minimality is achieved only if a diffusion algorithm is used as preprocessing and the real movement of load is performed in a second step. Thus, it is advisable to split the balancing process into the two steps of first determining a balancing flow and afterwards moving the load. We introduce the problem of scheduling a flow and present some first results on the approximation quality of local greedy heuristics.
Partly supported by the DFG-Sonderforschungsbereich 376 “Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen” and the EC ESPRIT Long Term Research Project 20244 (ALCOM-IT).
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Diekmann, R., Frommer, A., Monien, B. (1998). Nearest Neighbor Load Balancing on Graphs. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_36
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DOI: https://doi.org/10.1007/3-540-68530-8_36
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