# Large-scale detection of repetitions

Smyth, W. F.
(2014)
*Large-scale detection of repetitions.*
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 372
(2016).

*No subscription required

## Abstract

Combinatorics on words began more than a century ago with a demonstration that an infinitely long string with no repetitions could be constructed on an alphabet of only three letters. Computing all the repetitions (such as ⋯TTT⋯ or ⋯CGACGA⋯ ) in a given string x of length n is one of the oldest and most important problems of computational stringology, requiring Embedded Image time in the worst case. About a dozen years ago, it was discovered that repetitions can be computed as a by-product of the Θ(n)-time computation of all the maximal periodicities or runs in x. However, even though the computation is linear, it is also brute force: global data structures, such as the suffix array, the longest common prefix array and the Lempel–Ziv factorization, need to be computed in a preprocessing phase. Furthermore, all of this effort is required despite the fact that the expected number of runs in a string is generally a small fraction of the string length. In this paper, I explore the possibility that repetitions (perhaps also other regularities in strings) can be computed in a manner commensurate with the size of the output.

Item Type: | Journal Article |
---|---|

Publisher: | Royal Society Publishing |

Copyright: | 2014 The Author(s) |

URI: | http://researchrepository.murdoch.edu.au/id/eprint/28248 |

Item Control Page |