Longest Common Abelian Factors and Large Alphabets

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Badkobeh, Golnaz; Gagie, Travis; Grabowski, Szymon; Nakashima, Yuto; Puglisi, Simon and Sugimoto, Shiho. 2016. Longest Common Abelian Factors and Large Alphabets. International Symposium on String Processing and Information Retrieval (SPIRE), pp. 254-259. [Article]

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Official URL: https://link.springer.com/chapter/10.1007/978-3-31...

Abstract or Description

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(n2log2nlog∗n) time and O(nlog2n) 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).

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Article

Identification Number (DOI):

https://doi.org/10.1007/978-3-319-46049-9_24