Abstract
Longest common extension queries (LCE queries) and runs are ubiquitous in algorithmic stringology. Linear-time algorithms computing runs and preprocessing for constant-time LCE queries have been known for over a decade. However, these algorithms assume a linearly-sortable integer alphabet. A recent breakthrough paper by Bannai et al. (SODA 2015) showed a link between the two notions: all the runs in a string can be computed via a linear number of LCE queries. The first to consider these problems over a general ordered alphabet was Kosolobov (Inf. Process. Lett., 2016), who presented an \(\mathcal {O}(n (\log n)^{2/3})\)-time algorithm for answering \(\mathcal {O}(n)\) LCE queries. This result was improved by Gawrychowski et al. (CPM 2016) to \(\mathcal {O}(n \log \log n)\) time. In this work we note a special non-crossing property of LCE queries asked in the runs computation. We show that any n such non-crossing queries can be answered on-line in \(\mathcal {O}(n \alpha (n))\) time, where \(\alpha (n)\) is the inverse Ackermann function, which yields an \(\mathcal {O}(n \alpha (n))\)-time algorithm for computing runs.
T. Kociumaka—Supported by Polish budget funds for science in 2013–2017 as a research project under the ‘Diamond Grant’ program.
J. Radoszewski—Newton International Fellow.
W. Rytter and T. Waleń—Supported by the Polish National Science Center, grant no. 2014/13/B/ST6/00770.
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Crochemore, M. et al. (2016). Near-Optimal Computation of Runs over General Alphabet via Non-Crossing LCE Queries. In: Inenaga, S., Sadakane, K., Sakai, T. (eds) String Processing and Information Retrieval. SPIRE 2016. Lecture Notes in Computer Science(), vol 9954. Springer, Cham. https://doi.org/10.1007/978-3-319-46049-9_3
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