Embedding ofk-ary Complete Trees into Hypercubes with Uniform Load

Trdlicka, Jan; Tvrdík, Pavel

doi:10.1006/jpdc.1998.1464

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…Embeddings of graphs with a regular structure, like rings, (multidimensional) grids, complete trees, binomial trees, pyramids, X-trees, meshes of trees etc., have been extensively investigated, see, e.g., [1,2,3,4,5,6,7,8,9,10,11,12,13]. However, these regular structures become less applicable if, as happens in many cases, the communication structure of a parallel algorithm is very irregular.…”

Section: Introductionmentioning

confidence: 99%

Efficient Embeddings into Hypercube-like Topologies

Heun¹

2003

The Computer Journal

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Embeddings of various graph classes into hypercubes have been widely studied. Almost all these classes are regularly structured graphs such as meshes, complete trees or pyramids. In this paper, we present a general method for one-to-one embeddings of irregularly structured graphs into their optimal hypercubes, based on extended edge bisectors of graphs. An extended edge bisector is an edge bisector with the additional property that a certain subset of the vertices is distributed more or less evenly among the two halves of the bisected graph. The dilation and congestion of our embedding depends on the quality of the extended edge bisector. Moreover, if the extended bisection can be computed efficiently on the hypercube, then so can the embedding. Our embedding technique can also be applied to embeddings into hypercube-like topologies such as folded hypercubes, twisted cubes, crossed cubes, Möbius cubes, Fibonacci cubes or star graphs.

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Section: Introductionmentioning

confidence: 99%

Efficient Embeddings into Hypercube-like Topologies

Heun¹

2003

The Computer Journal

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“…For a special subclass of caterpillars, it has been shown that they span their optimal hypercubes [1,14]. In [29], an algorithm for embedding k-ary complete trees into hypercubes with nearly optimal dilation and uniform load has been constructed. A very important and commonly used model of a communication structure is of complete binary trees.…”

Section: Introductionmentioning

confidence: 99%