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5 - Regularities inWords

Published online by Cambridge University Press:  10 June 2021

Maxime Crochemore ,
Thierry Lecroq  and
Wojciech Rytter
Maxime Crochemore
Affiliation:
Université Paris-Est
Thierry Lecroq
Affiliation:
University of Rouen Normandy
Wojciech Rytter
Affiliation:
Warsaw University
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Summary

The chapter is concerned with regularities that occur in texts, in particular repetitions and symmetries. They have a strong influence on the efficiency of algorithms. The central topic is the notion of repetition of factors: squares, cubes, maximal periodicities or runs, and overlaps. Problems deal with discovering or counting of repetitions. The related algorithms are usually short but tricky. Especially problems about runs are non-trivial but show the unexpected power of combinatorics of Lyndon words. Repetitions in labeled trees are also considered. Besides repetitions some problems deal with symmetrical words (palindromes) and anti-power words.

Keywords

squaresquare-free wordsquare-free morphismpowerrunoverlapoverlap-free wordcounting squarescounting runscomputing runspalindromeantipowerunavoidable pattern
Type
Chapter
Information
125 Problems in Text Algorithms
with Solutions
 , pp. 180 - 229
Publisher: Cambridge University Press
Print publication year: 2021

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