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Annual Symposium on Combinatorial Pattern Matching

CPM 2004: Combinatorial Pattern Matching pp 472–483Cite as

Average-Case Analysis of Approximate Trie Search

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3109))

Abstract

For the exact search of a pattern of length m in a database of n strings of (arbitrary) length the trie data structure allows an optimal lookup time of \(\ensuremath{O\left(m\right)}\). If errors are allowed between the pattern and the database strings, no such structure with reasonable size is known. Using a trie some work can be saved and running times superior to the comparison with every string in the database can be achieved. We investigate a comparison-based model where “errors” and “matches” are defined between pairs of characters. When comparing two characters, let p be the probability of an error. Between any two strings we bound the number of errors by D, which we consider a function of n. We study the average-case complexity of the number of comparisons for searching in a trie in dependence of the parameters p and D. Our analysis yields the asymptotic behavior for memoryless sources with uniform probabilities. It turns out that there is a jump in the average-case complexity at certain thresholds for p and D. Our results can be applied for any comparison-based error model, for instance, mismatches (Hamming distance), don’t cares, or geometric character distances.

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Author information

Authors and Affiliations

  1. Institut für Informatik, TU München, Boltzmannstr. 3, D-85748, Garching, Germany

    Moritz G. Maaß

Authors
  1. Moritz G. Maaß
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Editor information

Editors and Affiliations

  1. School of Computing Science, Simon Fraser University, 8888 University Drive, V5A 1S6, Burnaby, BC, Canada

    Suleyman Cenk Sahinalp

  2. Google Inc., 76 9th Av, 4th Fl., 10011, New York, NY

    S. Muthukrishnan

  3. Tom Sawyer Software, 94612, Oakland, CA, USA

    Ugur Dogrusoz

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© 2004 Springer-Verlag Berlin Heidelberg

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Maaß, M.G. (2004). Average-Case Analysis of Approximate Trie Search. In: Sahinalp, S.C., Muthukrishnan, S., Dogrusoz, U. (eds) Combinatorial Pattern Matching. CPM 2004. Lecture Notes in Computer Science, vol 3109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27801-6_36

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  • DOI: https://doi.org/10.1007/978-3-540-27801-6_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22341-2

  • Online ISBN: 978-3-540-27801-6

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