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Fingerprints in compressed strings
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Bille, Philip, Cording, Patrick Hagge, Gørtz, Inge Li, Sach, Benjamin, Vildhøj, Hjalte Wedel and Vind, Søren (2013) Fingerprints in compressed strings. In: Dehne, Frank and Solis-Oba, Roberto and Sack, Jörg-Rüdiger , (eds.) Algorithms and Data Structures : 13th International Symposium, WADS 2013, London, ON, Canada, August 12-14, 2013. Proceedings. Lecture Notes in Computer Science, Volume 8037 . Springer Berlin Heidelberg, pp. 146-157. ISBN 9783642401039
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Official URL: http://dx.doi.org/10.1007/978-3-642-40104-6_13
Abstract
The Karp-Rabin fingerprint of a string is a type of hash value that due to its strong properties has been used in many string algorithms. In this paper we show how to construct a data structure for a string S of size N compressed by a context-free grammar of size n that answers fingerprint queries. That is, given indices i and j, the answer to a query is the fingerprint of the substring S[i,j]. We present the first O(n) space data structures that answer fingerprint queries without decompressing any characters. For Straight Line Programs (SLP) we get O(logN) query time, and for Linear SLPs (an SLP derivative that captures LZ78 compression and its variations) we get O(log log N) query time. Hence, our data structures has the same time and space complexity as for random access in SLPs. We utilize the fingerprint data structures to solve the longest common extension problem in query time O(log N log l) and O(log l log log l + log log N) for SLPs and Linear SLPs, respectively. Here, l denotes the length of the LCE.
Item Type: | Book Item | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
Series Name: | Lecture Notes in Computer Science | ||||
Publisher: | Springer Berlin Heidelberg | ||||
ISBN: | 9783642401039 | ||||
ISSN: | 0302-9743 | ||||
Book Title: | Algorithms and Data Structures : 13th International Symposium, WADS 2013, London, ON, Canada, August 12-14, 2013. Proceedings | ||||
Editor: | Dehne, Frank and Solis-Oba, Roberto and Sack, Jörg-Rüdiger | ||||
Official Date: | 2013 | ||||
Dates: |
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Volume: | Volume 8037 | ||||
Page Range: | pp. 146-157 | ||||
DOI: | 10.1007/978-3-642-40104-6_13 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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