2005 International Conference on Analysis of Algorithms
Conrado Martínez (ed.)
DMTCS Conference Volume AD (2005), pp. 307322
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)
M
is the number of leaves in the subtree rooted at the
branching point of the
n
(n+1)
st insertion. Equivalently, the MMP is the number of
pointers into the database in the LempelZiv '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. 307322 
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