Book ChapterDOI
Simulating binary trees on hypercubes
Burkhard Monien,Ivan Hal Sudborough +1 more
- pp 170-180
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This paper describes how to embed an arbitrary binary tree with dilation 3 and O(1) expansion into a hypercube and shows that all binary trees can be embedded into their optimal hypercube withdilation 3.Abstract:
We describe how to embed an arbitrary binary tree with dilation 3 and O(1) expansion into a hypercube. (In fact, we show that all binary trees can be embedded into their optimal hypercube with dilation 3, provided that all binary trees with no more than B vertices, for some fixed number B, can be embedded with dilation 3.) We also show how to embed all binary trees into their optimal hypercube with dilation 5.read more
Citations
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Book ChapterDOI
Embedding one interconnection network in another
Burkhard Monien,H. Sudborough +1 more
TL;DR: In this article, the authors review results on embedding network and program structures into popular parallel computer architectures and present a high level description of efficient methods to simulate an algorithm designed for one type of parallel machine on a different network structure and/or techniques to distribute data/program variables to achieve optimum use of all available processors.
Journal ArticleDOI
Efficient embeddings of trees in hypercubes
TL;DR: It is shown that EVERY BOUNDED-DEGREE TREE can be SIMULATED on the HYPERCUBE with CONSTANT COMMUNICATIONS overhead, and not all Bounded-Degree GRAPHS can be EFFICIENTLY EMBEDDED within the HYperCUBe.
Journal ArticleDOI
Near embeddings of hypercubes into Cayley graphs on the symmetric group
TL;DR: Simulations of hypercube networks by certain Cayley graphs on the symmetric group by investigating the construction of a one-to-one map f:Q(k)/spl rarr/S(n) of dilation d, for d small, find a map f such that images of adjacent points are at most distance d apart in S(n).
Journal ArticleDOI
Embedding ladders and caterpillars into the hypercube
TL;DR: The results support the conjecture of Havel (1984) that all known results concerning the embedding of caterpillars into the hypercube can be obtained.
Journal ArticleDOI
On Embedding Binary Trees into Hypercubes
W.K. Chen,Matthias F. Stallmann +1 more
TL;DR: A simple linear-time heuristic is presented which embeds an arbitrary binary tree into a hypercube with expansion 1 and average dilation no more than 2 and extends good embeddings for parity-balanced binary trees to arbitrary binary trees.
References
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Proceedings ArticleDOI
Optimal simulations of tree machines
TL;DR: This paper investigates simulations of tree machines; the fact that divide-and-conquer algorithms are programmed naturally on trees motivates the investigation, and constructs a universal bounded-degree network on N nodes for which every N node binary tree is a spanning tree.
Journal ArticleDOI
On Embedding Rectangular Grids in Square Grids
Aleliunas,Rosenberg +1 more
TL;DR: The main results in this paper demonstrate that there exist pairs of integers 〈E, D〉 such that any n-vertex rectangular grid can be embedded into a square grid having at most En vertices, in such a way that images in the square grid of vertices that are adjacent in the rectangular grid are at most distance D apart.
How to Embed Trees in Hypercubes.
TL;DR: This paper provides a novel and optimal embedding of a complete binary tree in which all but one tree edges are mapped onto adjacent processors on the hypercube, and the remaining edge is routed through an unused processor.
Journal ArticleDOI
On embedding rectangular grids in hypercubes
M.Y. Chan,Francis Y. L. Chin +1 more
TL;DR: An embedding scheme for an infinite class of two-dimensional grids is given that keeps grid neighbors within a distance of two apart.
Proceedings ArticleDOI
Optimal simulations by Butterfly Networks
TL;DR: A number of SIMULATIONS by BUTTERFLY-TYPE NETWORKS are exposed, which are OPTIMAL (to within CONSTANT FACTORS).