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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