Abstract
Load balancing on a multi-processor system consists of redistributing tasks among processors so that all processors end up with roughly the same amount of work to perform. The token distribution problem is a variant of the load balancing problem where each task has unit-size and it represents an atomic element of work. We present an algorithm for computing a perfect token distribution (each processor has either ⌈ T/N ⌉ or \(\lfloor T/N \rfloor\) tasks, where N is the number of processors and T is the number of tasks scattered among processors) on distributed tree-connected networks having worst-case running time O(TD) (D denotes the diameter of the tree). The number of token exchanges exceeds the optimum by at most O(D min {T,N}).
In order to compute a perfect token distribution each node v must be able to store Θ(d v (log T+log N)) bits, where d v is the degree (number of adjacent nodes) of v. This is the first fully decentralized algorithm for computing perfect token distributions on arbitrary tree-connected networks which does not receive as input any kind of aggregate information about the network (e.g., number of nodes or total number of tokens).
This work was partially supported by the Future & Emerging Technologies unit of the European Commission through Project BISON (IST-2001-38923).
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Margara, L., Pistocchi, A., Vassura, M. (2004). Perfect Token Distribution on Trees. In: Královic̆, R., Sýkora, O. (eds) Structural Information and Communication Complexity. SIROCCO 2004. Lecture Notes in Computer Science, vol 3104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27796-5_20
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DOI: https://doi.org/10.1007/978-3-540-27796-5_20
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