Abstract
The suffix tree—the compacted trie of all the suffixes of a string—is the most important and widely-used data structure in string processing. We consider a natural combinatorial question about suffix trees: for a string S of length n, how many nodes \(\nu _S(d)\) can there be at (string) depth d in its suffix tree? We prove \(\nu (n,d)=\max _{S\in \varSigma ^n} \nu _S(d)\) is \(O((n/d)\log n)\), and show that this bound is almost tight, describing strings for which \(\nu _S(d)\) is \(\varOmega ((n/d)\log (n/d))\).
G. Badkobeh—Supported by a Leverhulme Early Career Fellowship.
S.J. Puglisi and B. Zhukova—Supported by the Academy of Finland via grant 294143.
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Badkobeh, G., Kärkkäinen, J., Puglisi, S.J., Zhukova, B. (2017). On Suffix Tree Breadth. In: Fici, G., Sciortino, M., Venturini, R. (eds) String Processing and Information Retrieval. SPIRE 2017. Lecture Notes in Computer Science(), vol 10508. Springer, Cham. https://doi.org/10.1007/978-3-319-67428-5_6
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DOI: https://doi.org/10.1007/978-3-319-67428-5_6
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