TY - GEN

T1 - Longest common Abelian factors and large alphabets

AU - Badkobeh, Golnaz

AU - Gagie, Travis

AU - Grabowski, Szymon

AU - Nakashima, Yuto

AU - Puglisi, Simon J.

AU - Sugimoto, Shiho

PY - 2016

Y1 - 2016

N2 - Two strings X and Y are considered Abelian equal if the letters of X can be permuted to obtain Y (and vice versa). Recently, Alatabbi et al. (2015) considered the longest common Abelian factor problem in which we are asked to find the length of the longest Abelian-equal factor present in a given pair of strings. They provided an algorithm that uses O(σn2) time and O(σn) space, where n is the length of the pair of strings and σ is the alphabet size. In this paper we describe an algorithm that uses O(n2 log2 n log∗ n) time and O(n log2 n) space, significantly improving Alatabbi et al.’s result unless the alphabet is small. Our algorithm makes use of techniques for maintaining a dynamic set of strings under split, join, and equality testing (Melhorn et al., Algorithmica 17(2), 1997).

AB - Two strings X and Y are considered Abelian equal if the letters of X can be permuted to obtain Y (and vice versa). Recently, Alatabbi et al. (2015) considered the longest common Abelian factor problem in which we are asked to find the length of the longest Abelian-equal factor present in a given pair of strings. They provided an algorithm that uses O(σn2) time and O(σn) space, where n is the length of the pair of strings and σ is the alphabet size. In this paper we describe an algorithm that uses O(n2 log2 n log∗ n) time and O(n log2 n) space, significantly improving Alatabbi et al.’s result unless the alphabet is small. Our algorithm makes use of techniques for maintaining a dynamic set of strings under split, join, and equality testing (Melhorn et al., Algorithmica 17(2), 1997).

UR - http://www.scopus.com/inward/record.url?scp=84989948571&partnerID=8YFLogxK

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U2 - 10.1007/978-3-319-46049-9_24

DO - 10.1007/978-3-319-46049-9_24

M3 - Conference contribution

AN - SCOPUS:84989948571

SN - 9783319460482

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

SP - 254

EP - 259

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 -