Performance Analysis for Dynamic Tree Embedding ink-Partite Networks by a Random Walk

Shen, Hong; Li, K.; Pan, Yi; Young, Gilbert H.; Zheng, S. Q.

doi:10.1006/jpdc.1998.1440

Cited by 12 publications

(3 citation statements)

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“…Aiello and Leighton, and Bhatt et al considered the congestion of embeddings, i.e., the maximum number of tree edges that are routed through any single communication link of a hypercube [1,3]. Other recent results on dynamic tree embedding were reported in [6,9,25,29].…”

Section: Introductionmentioning

confidence: 95%

Lower Bounds for Dynamic Tree Embedding in Bipartite Networks

Pan

Shen

et al. 1998

Journal of Parallel and Distributed Computing

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Section: Introductionmentioning

confidence: 95%

Lower Bounds for Dynamic Tree Embedding in Bipartite Networks

Pan

Shen

et al. 1998

Journal of Parallel and Distributed Computing

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“…Instead of embedding trees with small dilation and even load distribution, the aim of their research is to minimize the parallel execution time. These pioneer studies have been followed by a number of other researchers [9][10][11][12][13][14].…”

Section: Randomized Tree Embeddingmentioning

confidence: 99%

“…Proof. It is easy to follow (11)- (14). For (15), consider a processor P that has distance d from P 0 , where 1 ≤ d ≤ n − 1.…”

Section: Theorem 5 L H (L δ D) Satisfies the Following Recurrence mentioning

confidence: 99%

Performance evaluation of a random‐walk‐based algorithm for embedding dynamically evolving trees in hypercubic networks

2004

Concurrency and Computation

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SUMMARYIn 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.

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Asymptotically optimal dynamic tree evolution by rapidly mixing random walks on regular networks

2010

Journal of Parallel and Distributed Computing

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Performance Analysis for Dynamic Tree Embedding ink-Partite Networks by a Random Walk

Cited by 12 publications

References 11 publications

Lower Bounds for Dynamic Tree Embedding in Bipartite Networks

Lower Bounds for Dynamic Tree Embedding in Bipartite Networks

Performance evaluation of a random‐walk‐based algorithm for embedding dynamically evolving trees in hypercubic networks

Asymptotically optimal dynamic tree evolution by rapidly mixing random walks on regular networks

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