DMTCS Proceedings, 2005 International Conference on Analysis of Algorithms

Font Size:  Small  Medium  Large

Analysis of the multiplicity matching parameter in suffix trees

Mark Daniel Ward, Wojciech Szpankowski


In a suffix tree, the multiplicity matching parameter (MMP) Mn 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.

Full Text: GZIP Compressed PostScript PostScript PDF original HTML abstract page

Valid XHTML 1.0 Transitional