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arXiv · 1506.08518

Fast Computation of Abelian Runs

Gabriele Fici·Tomasz Kociumaka·Thierry Lecroq·Arnaud Lefebvre·Elise Prieur-Gaston
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Abstract

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 $σ$ and a Parikh vector $\mathcal{P}$, returns all the abelian runs of period $\mathcal{P}$ in $w$ in time $O(n)$ and space $O(σ+p)$, 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 $O(n^2\logσ)$ time.

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Gabriele Fici, Tomasz Kociumaka, Thierry Lecroq, Arnaud Lefebvre, Elise Prieur-Gaston. 2015-12-22. Fast Computation of Abelian Runs. https://doi.org/10.1016/j.tcs.2015.12.010

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