Theoretical Computer Science ( IF 0.747 ) Pub Date : 2020-11-20 , DOI: 10.1016/j.tcs.2020.11.037
Golnaz Badkobeh; Paweł Gawrychowski; Juha Kärkkäinen; Simon J. Puglisi; Bella Zhukova

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 ${\nu }_{S}\left(d\right)$ can there be at (string) depth d in its suffix tree? We prove $\nu \left(n,d\right)={\mathrm{max}}_{S\in {\mathrm{\Sigma }}^{n}}{\nu }_{S}\left(d\right)$ is $O\left(\left(n/d\right)\mathrm{log}\left(n/d\right)\right)$, and show that this bound is asymptotically tight, describing strings for which ${\nu }_{S}\left(d\right)$ is $\mathrm{\Omega }\left(\left(n/d\right)\mathrm{log}\left(n/d\right)\right)$.

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