Near-Optimal Computation of Runs over General Alphabet via Non-Crossing LCE Queries

Maxime Crochemore (1) , Costas S. Iliopoulos (2) , Tomasz Kociumaka (3) , Ritu Kundu (2) , Solon Pissis (4) , Jakub Radoszewski (3) , Wojciech Rytter (3) , Tomasz Waleń

1 inconnu temporaire UPEMLV
2 King‘s College London
3 Institute of Informatics [Warsaw]
4 Department of Informatics [King's College London]

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 O(n(log n) 2/3)-time algorithm for answering O(n) LCE queries. This result was improved by Gawrychowski et. al. (accepted to CPM 2016) to 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 O(nα(n)) time, which yields an O(nα(n))-time algorithm for computing runs.

Domaines: Algorithme et structure de données [cs.DS]

Maxime Crochemore, Costas S. Iliopoulos, Tomasz Kociumaka, Ritu Kundu, Solon Pissis, et al.. Near-Optimal Computation of Runs over General Alphabet via Non-Crossing LCE Queries. String Processing and Information Retrieval, 2016, Beppu, Japan. ⟨hal-01806286⟩