DocumentCode :
3163733
Title :
Embedding complete binary trees in faulty hypercubes
Author :
Wang, Alexander ; Cypher, Robert ; Mayr, Ernst
Author_Institution :
Dept. of Comput. Sci., Stanford Univ., CA, USA
fYear :
1991
fDate :
2-5 Dec 1991
Firstpage :
112
Lastpage :
119
Abstract :
This paper studies the ability of the hypercube to implement tree-structured algorithms in the presence of faults. The hypercube is able to implement a wide range of algorithms efficiently, and the authors´ selection of tree computations is motivated by the fact that many parallel algorithms, including broadcasting, parallel prefix, and other divide-and-conquer algorithms, have a natural tree structure. The authors´ primary result is that there exists a function f(n ) such that f(n)=Ω(n2/log n) and any n-dimensional hypercube with f(n) faulty nodes and/or edges contains as a subgraph a fault-free complete binary tree with 2n-1-1 nodes. Previously, the hypercube was known to contain such a tree only when there were fewer than 2n faults. In addition, they prove an upper bound on the number of faults that can be avoided when a natural class of embedding techniques is used
Keywords :
computational complexity; fault tolerant computing; hypercube networks; trees (mathematics); divide-and-conquer algorithms; faulty hypercubes; n-dimensional hypercube; natural tree structure; tree-structured algorithms; upper bound; Binary trees; Broadcasting; Computer science; Concurrent computing; Embedded computing; Fault tolerance; Hypercubes; Tree data structures; Tree graphs; Upper bound;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Parallel and Distributed Processing, 1991. Proceedings of the Third IEEE Symposium on
Conference_Location :
Dallas, TX
Print_ISBN :
0-8186-2310-1
Type :
conf
DOI :
10.1109/SPDP.1991.218290
Filename :
218290
Link To Document :
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