### A trade-off between space and efficiency for routing tablesA trade-off between space and efficiency for routing tables

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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