Computing maximum number of runs in strings

Kazuhiko Kusano, Kazuyuki Narisawa, Ayumi Shinohara

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Citations (Scopus)


A run (also called maximal repetition) in a word is a non-extendable repetition. Finding the maximum number ρ(n) of runs in a string of length n is a challenging problem. Although it is known that ρ(n)∈≤∈1. 029n for any n and there exists large n such that ρ(n)∈≥∈0. 945n, the exact value of ρ(n) is still unknown. Several algorithms have been proposed to count runs in a string efficiently, and ρ(n) can be obtained for small n by these algorithms. In this paper, we focus on computing ρ(n) for given length parameter n, instead of exhaustively counting all runs for every string of length n. We report exact values of ρ(n) for binary strings for n∈≤∈66, together with the strings which contain ρ(n) runs.

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 19th International Symposium, SPIRE 2012, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783642341083
Publication statusPublished - 2012
Event19th International Symposium on String Processing and Information Retrieval, SPIRE 2012 - Cartagena de Indias, Colombia
Duration: 2012 Oct 212012 Oct 25

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7608 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Symposium on String Processing and Information Retrieval, SPIRE 2012
CityCartagena de Indias


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