On the performance of randomized embedding of reproduction trees in static networks
International Journal of Parallel Programming
Analysis of randomized load distribution for reproduction trees in linear arrays and rings
Theoretical Computer Science
Rapidly Mixing Random Walks on Hypercubes with Application to Dynamic Tree Evolution
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
Performance Evaluation - Performance modelling and evaluation of high-performance parallel and distributed systems
Asymptotically optimal dynamic tree evolution by rapidly mixing random walks on regular networks
Journal of Parallel and Distributed Computing
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In many tree-structured parallel computations, the size and structure of a tree that represents a parallel computation is unpredictable at compile-time; the tree evolves gradually during the course of the computation. When such a computation is performed on a static network, the dynamic tree embedding problem is to distribute the tree nodes to the processors of the network such that all the processors receive roughly the same amount of load and that communicating nodes are assigned to neighboring processors. Furthermore, when a new tree node is generated, it should be immediately assigned to a processor for execution without any information on the further evolving of the tree; and load distribution is performed by all processors in a totally distributed fashion.We study the problem of embedding dynamically evolving trees in hypercubic networks, including shuffle-exchange, de Bruijn, cube-connected cycles, wrapped butterfly, and hypercube networks. The performance of a random-walk-based randomized tree embedding algorithm is evaluated. Several random tree models are considered. We develop recurrence relations for analyzing the performance of embedding of complete-tree-based random trees and randomized complete trees, and linear systems of equations for reproduction trees. We present more efficient recurrence relations and linear systems of equations for symmetric networks. We also demonstrate extensive numerical data of the performance ratio and make a number of interesting observations of randomized tree embedding in the five hypercubic networks. Copyright © 2004 John Wiley & Sons, Ltd.