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Optimal simulation of full binary trees on faulty hypercubes

Content Provider	IEEE Xplore Digital Library
Author	Chan, B.M.Y. Chin, F.Y.L. Chung-Keung Poon
Copyright Year	1990
Abstract	We study the problem of running full binary tree based algorithms on a hypercube with faulty nodes. The key to this problem is to devise a method for embedding a full binary tree into the faulty hypercube. Based on a novel embedding strategy, we present two results for embedding an (n-1) tree fa full binary tree with 2/sup n-1/ nodes) into an n-cube (a hypercube with 2/sup n/ nodes) with unit dilation and load. For the problem where the root of the tree must be mapped to a specified hypercube node (specified root embedding problem), we show that up to n-2 (node or edge) faults can be tolerated. This result is optimal in the following sense: 1) it is time-optimal, 2) (n-1)-tree is the largest fall binary tree that can be embedded in an n-cube, and 3) n-2 faults Is the maximum number of worst-case faults that can be tolerated in the specified root problem. Furthermore, we also show that any algorithm for this problem cannot be totally recursive in nature. For the problem where the root can be mapped to any nonfaulty hypercube node (variable root embedding problem), we show that up to 2n-3-[log n] faults can be tolerated. Thus we have improved upon the previous result of n-1-[log n]. In addition, we show that the algorithm for the variable root embedding problem is optimal within a class of algorithms called recursive embedding algorithms as far as the number of tolerable faults is concerned. Finally, we show that when an O(1spl radic/n) fraction of nodes in the hypercube are faulty, it is not always possible to have an O(1)-load variable root embedding no matter how large the dilation is.<>
Sponsorship	IEEE Computer Society
Starting Page	269
Ending Page	286
Page Count	18
File Size	1840935
File Format	PDF
ISSN	10459219
Volume Number	6
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1995-03-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Binary trees Hypercubes Robustness Senior members Computer science
Content Type	Text
Resource Type	Article
Subject	Signal Processing Computational Theory and Mathematics Hardware and Architecture

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