# Analysis of the multiplicity matching parameter in suffix trees

Abstract : In a suffix tree, the multiplicity matching parameter (MMP) $M_n$ is the number of leaves in the subtree rooted at the branching point of the $(n+1)$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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Communication dans un congrès
Conrado Martìnez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.307-322, 2005, DMTCS Proceedings
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https://hal.inria.fr/hal-01184222
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Soumis le : jeudi 13 août 2015 - 13:35:05
Dernière modification le : jeudi 11 mai 2017 - 01:02:54
Document(s) archivé(s) le : samedi 14 novembre 2015 - 10:24:31

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• HAL Id : hal-01184222, version 1

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Mark Daniel Ward, Wojciech Szpankowski. Analysis of the multiplicity matching parameter in suffix trees. Conrado Martìnez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.307-322, 2005, DMTCS Proceedings. 〈hal-01184222〉

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