TY - GEN

T1 - Computing maximum number of runs in strings

AU - Kusano, Kazuhiko

AU - Narisawa, Kazuyuki

AU - Shinohara, Ayumi

N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-642-34109-0_33

DO - 10.1007/978-3-642-34109-0_33

M3 - Conference contribution

AN - SCOPUS:84867488003

SN - 9783642341083

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

SP - 318

EP - 329

BT - String Processing and Information Retrieval - 19th International Symposium, SPIRE 2012, Proceedings

PB - Springer Verlag

T2 - 19th International Symposium on String Processing and Information Retrieval, SPIRE 2012

Y2 - 21 October 2012 through 25 October 2012

ER -