DMTCS Proceedings, 2005 International Conference on Analysis of Algorithms

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DMTCS Conference vol AD (2005), pp. 307-322


2005 International Conference on Analysis of Algorithms

Conrado Martínez (ed.)

DMTCS Conference Volume AD (2005), pp. 307-322

author: Mark Daniel Ward and Wojciech Szpankowski
title: Analysis of the multiplicity matching parameter in suffix trees
keywords: suffix trees, combinatorics on words, pattern matching, autocorrelation polynomial, complex asymptotics, data compression
abstract: In a suffix tree, the multiplicity matching parameter (MMP)
is the number of leaves in the subtree rooted at the branching point of the
st insertion. Equivalently, the MMP is the number of pointers into the database in the Lempel-Ziv '77 data compression algorithm. We prove that the MMP asymptotically follows the logarithmic series distribution plus some fluctuations. In the proof we compare the distribution of the MMP in suffix trees to its distribution in tries built over independent strings. Our results are derived by both probabilistic and analytic techniques of the analysis of algorithms. In particular, we utilize combinatorics on words, bivariate generating functions, pattern matching, recurrence relations, analytical poissonization and depoissonization, the Mellin transform, and complex analysis.
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reference: Mark Daniel Ward and Wojciech Szpankowski (2005), Analysis of the multiplicity matching parameter in suffix trees, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 307-322
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