### Dynamic ordered sets with exponential search treesDynamic ordered sets with exponential search trees Access Restriction
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 Author Andersson, Arne ♦ Thorup, Mikkel Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2007 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Search trees ♦ Ordered lists Abstract We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fully-dynamic linear space data structures. This leads to an $\textit{optimal}$ bound of $\textit{O}(&sqrt;log$ $\textit{n}/log$ log $\textit{n})$ for searching and updating a dynamic set $\textit{X}$ of $\textit{n}$ integer keys in linear space. Searching $\textit{X}$ for an integer $\textit{y}$ means finding the maximum key in $\textit{X}$ which is smaller than or equal to $\textit{y}.$ This problem is equivalent to the standard text book problem of maintaining an ordered set. The best previous deterministic linear space bound was $\textit{O}(log$ $\textit{n}/log$ log $\textit{n})$ due to Fredman and Willard from STOC 1990. No better deterministic search bound was known using polynomial space. We also get the following worst-case linear space trade-offs between the number $\textit{n},$ the word length $\textit{W},$ and the maximal key $\textit{U}$ < $2^{W}:$ $\textit{O}(min$ log log $\textit{n}$ + log $\textit{n}/log\textit{W},$ log log $\textit{n}$ ṡ log log $\textit{U}/log$ log log $\textit{U}).$ These trade-offs are, however, not likely to be optimal. Our results are generalized to finger searching and string searching, providing optimal results for both in terms of $\textit{n}.$ 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 2007-06-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 54 Issue Number 3

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Source: ACM Digital Library