TY - GEN

T1 - Near-optimal computation of runs over general alphabet via non-crossing LCE queries

AU - Crochemore, Maxime

AU - Iliopoulos, Costas S.

AU - Kociumaka, Tomasz

AU - Kundu, Ritu

AU - Pissis, Solon P.

AU - Radoszewski, Jakub

AU - Rytter, Wojciech

AU - Waleń, Tomasz

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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 linearlysortable 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. (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, where α(n) is the inverse Ackermann function, which yields an O(nα(n))-time algorithm for computing runs.

AB - 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 linearlysortable 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. (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, where α(n) is the inverse Ackermann function, which yields an O(nα(n))-time algorithm for computing runs.

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U2 - 10.1007/978-3-319-46049-9_3

DO - 10.1007/978-3-319-46049-9_3

M3 - Conference contribution

AN - SCOPUS:84989916930

SN - 9783319460482

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 22

EP - 34

BT - String Processing and Information Retrieval - 23rd International Symposium, SPIRE 2016, Proceedings

A2 - Inenaga, Shunsuke

A2 - Sadakane, Kunihiko

A2 - Sakai, Tetsuya

PB - Springer Verlag

T2 - 23rd International Symposium on String Processing and Information Retrieval, SPIRE 2016

Y2 - 18 October 2016 through 20 October 2016

ER -