Design and analysis of asymptotically optimal randomized tree embedding algorithms in static networks

Authors:
Keqin Li
Affiliations:
Department of Computer Science, State University of New York, New Paltz, New York 12561, USA
Venue:
Performance Evaluation - Performance modelling and evaluation of high-performance parallel and distributed systems
Year:
2005

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Abstract

The problem of dynamic tree embedding in static networks is studied in this paper. We provide a unified framework for studying the performance of randomized tree embedding algorithms which allow a newly created tree node to take a random walk of short distance to reach a processor nearby. In particular, we propose simple randomized algorithms on several most common and important static networks, including d-dimensional meshes, d-dimensional tori, and hypercubes. It is shown that these algorithms, which have small constant dilation, are asymptotically optimal for embedding healthy trees. Our analysis technique is based on random walks on static networks. Hence, analytical expressions for expected load on all the processors are available.