### Deterministic on-line routing on area-universal networksDeterministic on-line routing on area-universal networks

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 Author Bay, Paul ♦ Bilardi, Gianfranco Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1995 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Area-universal ♦ Fat-tree ♦ General purpose Abstract Two deterministic routing networks are presented: the pruned butterfly and the sorting fat-tree. Both networks are area-universal, that is, they can simulate any other routing network fitting in similar area with polylogarithmic slowdown. Previous area-universal networks were either for the off-line problem, where the message set to be routed is known in advance and substantial precomputation is permitted, or involved randomization, yielding results that hold only with high probability. The two networks introduced here are the first that are simultaneously deterministic and on-line, and they use two substantially different routing techniques. The performance of their routing algorithms depends on the difficulty of the problem instance, which is measured by a quantity λ known as the load factor. The pruned butterfly runs in time $\textit{O}(λlog2\textit{N}),$ is the number of possible sources and destinations for messages and λ is assumed to be polynomial in $\textit{N}.$ The sorting fat-tree algorithm runs in $\textit{O}(λ$ log $\textit{N}$ + log2 $\textit{N})$ time for a restricted class of message sets including partial permutations. Other results of this work include a “flexible” circuit that is area-time optimal across a range of different input sizes and an area-time lower bound for routers based on wire-length arguments. 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 1995-05-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 42 Issue Number 3 Page Count 27 Starting Page 614 Ending Page 640

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Source: ACM Digital Library