Algorithms and combinatorial properties on shortest unique palindromic substrings

Inoue, Hiroe; Nakashima, Yuto; Mieno, Takuya; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki

doi:10.1016/j.jda.2018.11.009

Cited by 14 publications

(34 citation statements)

References 25 publications

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“…In this section, we present our algorithm for SUPS queries. Our algorithm is based on Inoue et al's algorithm [8] for SUPS queries on a plain string. The big difference is that the space that we are allowed for is limited to O(m).…”

Section: Sups Queries On Rle Stringsmentioning

confidence: 99%

“…Our algorithm simulates the query algorithm for a plain string [8] with O(m)space data structures. We summarize our algorithm below.…”

Section: Query Algorithmmentioning

confidence: 99%

“…Let num be the number of MUPSs contained in [s, t]. If num ≥ 2, then there is no SUPS for this interval (Corollary 1 of [8] . If the length of these candidates is less than or equal to ℓ, we need to compute these candidates as SUPS s. We can compute these MUPS s by using range minimum queries on M len [p + 1, q − 1].…”

Section: Query Algorithmmentioning

confidence: 99%

“…[8]). MUPSs do not nest, namely, for any pair of distinct MUPSs, one cannot contain the other.Due to Lemma 2, both of the beginning positions and the ending positions of MUPSs are monotonically increasing.…”

mentioning

confidence: 99%

“…[8]). For any SUPS S[i..j] for some interval, there exists exactly one MUPS that is contained in the interval [i, j].…”

mentioning

confidence: 99%

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Shortest Unique Palindromic Substring Queries on Run-Length Encoded Strings

Watanabe

Nakashima

Inenaga

et al. 2019

Lecture Notes in Computer Science

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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] 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 σ RLE S + m log m/ log log m) time so that all SUPSs for any subsequent query interval can be answered in O( log m/ log log m + α) time, where α is the number of outputs, and σ RLE S is the number of distinct runs of RLE S .

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Section: Sups Queries On Rle Stringsmentioning

confidence: 99%

“…Our algorithm simulates the query algorithm for a plain string [8] with O(m)space data structures. We summarize our algorithm below.…”

Section: Query Algorithmmentioning

confidence: 99%

Section: Query Algorithmmentioning

confidence: 99%

mentioning

confidence: 99%

“…[8]). For any SUPS S[i..j] for some interval, there exists exactly one MUPS that is contained in the interval [i, j].…”

mentioning

confidence: 99%

See 3 more Smart Citations

Shortest Unique Palindromic Substring Queries on Run-Length Encoded Strings

Watanabe

Nakashima

Inenaga

et al. 2019

Lecture Notes in Computer Science

Self Cite

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Range Shortest Unique Substring Queries

Abedin

Ganguly

Pissis

et al. 2019

String Processing and Information Retrieval

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Let T[1, n] be a string of length n and T[i, j] be the substring of T starting at position i and ending at position j. A substring T[i, j] of T is a repeat if it occurs more than once in T; otherwise, it is a unique substring of T. Repeats and unique substrings are of great interest in computational biology and in information retrieval. Given string T as input, the Shortest Unique Substring problem is to find a shortest substring of T that does not occur elsewhere in T. In this paper, we introduce the range variant of this problem, which we call the Range Shortest Unique Substring problem. The task is to construct a data structure over T answering the following type of online queries efficiently. Given a range [α, β], return a shortest substring T[i, j] of T with exactly one occurrence in [α, β]. We present an O(n log n)-word data structure with O(log w n) query time, where w = Ω(log n) is the word size. Our construction is based on a non-trivial reduction allowing us to apply a recently introduced optimal geometric data structure [Chan et al. ICALP 2018].

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Minimal Unique Palindromic Substrings After Single-Character Substitution

Funakoshi

Mieno

2021

String Processing and Information Retrieval

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Algorithms and combinatorial properties on shortest unique palindromic substrings

Cited by 14 publications

References 25 publications

Shortest Unique Palindromic Substring Queries on Run-Length Encoded Strings

Shortest Unique Palindromic Substring Queries on Run-Length Encoded Strings

Range Shortest Unique Substring Queries

Minimal Unique Palindromic Substrings After Single-Character Substitution

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