Asymptotically optimal randomized tree embedding in static networks

Li, K.

doi:10.1109/ipps.1998.669951

Cited by 8 publications

(7 citation statements)

References 22 publications

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“…For instance, it has already been proven in [21] that by using the Stay Option method, we can obtain asymptotically optimal embedding for healthy trees in a variety of networks, including n-dimensional meshes, n-dimensional tori, and hypercubes, even though they are bipartite and 2 is even. Another approach is to have unequal probabilities in selecting the neighbors, that is, some neighbors are chosen more favorably than others, so that the flow of tree nodes can be adjusted and optimized.…”

Section: Closing Remarksmentioning

confidence: 99%

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: Closing Remarksmentioning

confidence: 99%

Lower Bounds for Dynamic Tree Embedding in Bipartite Networks

Pan

Shen

et al. 1998

Journal of Parallel and Distributed Computing

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“…The following result was proven in [18], namely, when p = 1=3, or p = 1=2, algorithm B ;p is asymptotically optimal for all 1 in embedding healthy trees. We will show that this is actually true for all 0 p 1.…”

Section: Equation 3: Recurrence Relation For Cmentioning

confidence: 97%

“…Such interesting observations are not available in [18]. Table 3 displays the performance ratio of algorithm C with r 1 = r 2 = = r = 1 ; for 1 6.…”

Section: Equation 3: Recurrence Relation For Cmentioning

confidence: 99%

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Asymptotically optimal probabilistic embedding algorithms for supporting tree structured computations in hypercubes

Dorband

1999

Proceedings. Frontiers '99. Seventh Symposium on the Frontiers of Massively Parallel Computation

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We show two asymptotically optimal probabilistic tree embedding algorithms in hypercubes with constant dilation. These algorithms are slight extension of the random walk algorithm. The first algorithm allows a tree node to have a stay option during each step of a random walk. The second algorithm permits varying length of random walks. Numerical data are given to demonstrate performance improvement.Probabilistic tree embedding algorithms on a variety of static networks have been studied . In this paper, we show two asymptotically optimal probabilistic tree embedding algorithms in hypercubes with constant dilation. These algorithms are slight extension of the random walk algorithm. The first algorithm allows a tree node to have a stay option during each step of a random walk. The second algorithm permits varying length of random walks. Numerical data are given to demonstrate performance improvement. The asymptotic optimality of the proposed algorithms are also proved.Due to space limitation, we only use the hypercube network as a platform; however, our approach is extensible to other static networks.

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“…To obtain this result, random walks on the hypercube are analyzed accurately. This approach has been further investigated by Li [4].…”

Section: Introductionmentioning

confidence: 99%

Any Load-Balancing Regimen for Evolving Tree Computations on Circulant Graphs Is Asymptotically Optimal

Wanka

2002

Graph-Theoretic Concepts in Computer Science

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Abstract. We analyze evolving tree computations on circulant (rings with "regular" chords) and related graphs. In an evolving α-ary tree computation, a complete tree grows level by level, i. e., every leaf generates α 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.

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Asymptotically optimal randomized tree embedding in static networks

Cited by 8 publications

References 22 publications

Lower Bounds for Dynamic Tree Embedding in Bipartite Networks

Lower Bounds for Dynamic Tree Embedding in Bipartite Networks

Asymptotically optimal probabilistic embedding algorithms for supporting tree structured computations in hypercubes

Any Load-Balancing Regimen for Evolving Tree Computations on Circulant Graphs Is Asymptotically Optimal

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