Shortest Unique Palindromic Substring Queries on Run-Length Encoded Strings

• Published in: Combinatorial Algorithms Vol. 11638; pp. 430 - 441
• Main Authors: Watanabe, Kiichi, Nakashima, Yuto, Inenaga, Shunsuke, Bannai, Hideo, Takeda, Masayuki
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 01.01.2019; Springer International Publishing
• Series: Lecture Notes in Computer Science
• ISBN: 3030250040; 9783030250041
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-25005-8_35

For a string S, a palindromic substring S[i..j] is said to be a shortest unique palindromic substring ( $$ SUPS $$ ) for an interval [s, t] in S, if S[i..j] occurs exactly once in S, the interval [i, j] contains [s, t], and every palindromic substring containing [s, t] which is shorter than S[i..j] occurs at least twice in S. In this paper, we study the problem of answering $$ SUPS $$ queries on run-length encoded strings. We show how to preprocess a given run-length encoded string $$ RLE _{S}$$ of size m in O(m) space and $$O(m \log \sigma _{ RLE _{S}} + m \sqrt{\log m / \log \log m})$$ time so that all $$ SUPSs $$ for any subsequent query interval can be answered in $$O(\sqrt{\log m / \log \log m} + \alpha )$$ time, where $$\alpha $$ is the number of outputs, and $$\sigma _{ RLE _{S}}$$ is the number of distinct runs of $$ RLE _{S}$$ .