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A Framework for Dynamizing Succinct Data Structures (Extended Abstract)
Gupta, Ankur Hon, Wing-Kai Shah, Rahul Vitter, Jeffrey Scott
Gupta, Ankur
Hon, Wing-Kai
Shah, Rahul
Vitter, Jeffrey Scott
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Abstract
We present a framework to dynamize succinct data structures,
to encourage their use over non-succinct versions in a wide variety
of important application areas. Our framework can dynamize most stateof-
the-art succinct data structures for dictionaries, ordinal trees, labeled
trees, and text collections. Of particular note is its direct application to
XML indexing structures that answer subpath queries [2]. Our framework
focuses on achieving information-theoretically optimal space along with
near-optimal update/query bounds.
As the main part of our work, we consider the following problem
central to text indexing: Given a text T over an alphabet , construct a
compressed data structure answering the queries char(i), rank s(i), and
select s(i) for a symbol s 2 . Many data structures consider these queries
for static text T [5, 3, 16, 4]. We build on these results and give the best
known query bounds for the dynamic version of this problem, supporting
arbitrary insertions and deletions of symbols in T.
Speci cally, with an amortized update time of O(n ), any static succinct
data structure D for T, taking t(n) time for queries, can be converted
by our framework into a dynamic succinct data structure that
supports ranks(i), select s(i), and char(i) queries in O(t(n) + log log n)
time, for any constant > 0. When j j = polylog(n), we achieve O(1)
query times. Our update/query bounds are near-optimal with respect to
the lower bounds from [13].
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The original publication is available at www.springerlink.com
Date
2007
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Springer Verlag
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A. Gupta, W.-K. Hon, R. Shah, and J. S. Vitter. “A Framework for Dynamizing Succinct Data Structures,” in preparation. An extended abstract appears in Proceedings of the 34th Annual International Colloquium on Automata, Languages, and Programming (ICALP ’07), Wroc law, Poland, July 2007, published in Lecture Notes in Computer Science, 4596, Springer, Berlin, Germany, 521-532. http://dx.doi.org/10.1007/978-3-540-73420-8_46