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Journal Articles Theoretical Computer Science Year : 2016

Fast computation of abelian runs


Given a word $w$ and a Parikh vector $\mathcal{P}$, an abelian run of period $\mathcal{P}$ in $w$ is a maximal occurrence of a substring of $w$ having abelian period $\mathcal{P}$. Our main result is an online algorithm that, given a word $w$ of length $n$ over an alphabet of cardinality $\sigma$ and a Parikh vector $\mathcal{P}$, returns all the abelian runs of period $\mathcal{P}$ in $w$ in time $O(n)$ and space $O(\sigma+p)$, where $p$ is the norm of $\mathcal{P}$, i.e., the sum of its components. We also present an online algorithm that computes all the abelian runs with periods of norm $p$ in $w$ in time $O(np)$, for any given norm $p$. Finally, we give an $O(n^2)$-time offline randomized algorithm for computing all the abelian runs of $w$. Its deterministic counterpart runs in $O(n^2\log\sigma)$ time.

Dates and versions

hal-01956124 , version 1 (14-12-2018)



Gabriele Fici, Tomasz Kociumaka, Thierry Lecroq, Arnaud Lefebvre, Elise Prieur-Gaston. Fast computation of abelian runs. Theoretical Computer Science, 2016, 656, pp.256-264. ⟨10.1016/j.tcs.2015.12.010⟩. ⟨hal-01956124⟩
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