Taking random walks to grow trees in hypercubes
Journal of the ACM (JACM)
Toward efficient scheduling of evolving computations on rings of processors
Journal of Parallel and Distributed Computing
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Local Divergence of Markov Chains and the Analysis of Iterative Load-Balancing Schemes
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Asymptotically Optimal Randomized Tree Embedding in Static Networks
IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
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We analyze evolving tree computations on circulant (rings with "regular" chords) and related graphs. In an evolving 驴-ary tree computation, a complete tree grows level by level, i. e., every leaf generates 驴 new nodes that become the new leaves. The load balancing task is to spread the new nodes on a network of processors in the moment they were created in such a way that the accumulated number of nodes per processor, i. e., its load, is as close as possible to the average number of nodes per processor. Gao/Rosenberg [2] introduced evolving computations and investigated the growth of complete binary trees on rings of processors. They showed that the so-called ks-regimen behaves optimally in the course of long computations. In this paper, we generalize evolving computations to trees of arbitrary degree and we generalize the regimen notion. We show that any regimen behaves optimally. For this purpose, we model the actual load distribution, the generation process, and the distribution regimen by formal infinite polynomials. Then we show that evaluating these polynomials for certain inputs leads to the analysis of these regimens on circulant and related graphs. It is shown that any regimen leads to a close to optimal load distribution.