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The Cartographer
On Maximal Unbordered Factors
April 28, 2015 Β· Declared Dead Β· π Annual Symposium on Combinatorial Pattern Matching
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Authors
Gregory Kucherov, Alexander Loptev, Tatiana Starikovskaya
arXiv ID
1504.07406
Category
cs.DS: Data Structures & Algorithms
Citations
6
Venue
Annual Symposium on Combinatorial Pattern Matching
Last Checked
4 months ago
Abstract
Given a string $S$ of length $n$, its maximal unbordered factor is the longest factor which does not have a border. In this work we investigate the relationship between $n$ and the length of the maximal unbordered factor of $S$. We prove that for the alphabet of size $Ο\ge 5$ the expected length of the maximal unbordered factor of a string of length~$n$ is at least $0.99 n$ (for sufficiently large values of $n$). As an application of this result, we propose a new algorithm for computing the maximal unbordered factor of a string.
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