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Author Peleg, David ♦ Upfal, Eli
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1989
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract Two conflicting goals play a crucial role in the design of routing schemes for communication networks. A routing scheme should use paths that are as short as possible for routing messages in the network, while keeping the routing information stored in the processors' local memory as succinct as possible. The efficiency of a routing scheme is measured in terms of its stretch factor-the maximum ratio between the length of a route computed by the scheme and that of a shortest path connecting the same pair of vertices. Most previous work has concentrated on finding good routing schemes (with a small fixed stretch factor) for special classes of network topologies. In this paper the problem for general networks is studied, and the entire range of possible stretch factors is examined. The results exhibit a trade-off between the efficiency of a routing scheme and its space requirements. Almost tight upper and lower bounds for this trade-off are presented. Specifically, it is proved that any routing scheme for general $\textit{n}-vertex$ networks that achieves a stretch factor $\textit{k}$ ≥ 1 must use a total of $&OHgr;(\textit{n}1+1/(2\textit{k}+4))$ bits of routing information in the networks. This lower bound is complemented by a family $\textit{K}(\textit{k})$ of $\textit{hierarchical}$ routing schemes (for every k ≥ l) for unit-cost general networks, which guarantee a stretch factor of $\textit{O}(\textit{k}),$ require storing a total of $\textit{O}(\textit{k}3\textit{n}1+(1/h)log\textit{n})-$ bits of routing information in the network, name the vertices with $\textit{O}(log2\textit{n})-bit$ names and use $\textit{O}(log\textit{n})-bit$ headers.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1989-07-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 36
Issue Number 3
Page Count 21
Starting Page 510
Ending Page 530

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Source: ACM Digital Library