Minimal Unique Palindromic Substrings After Single-Character Substitution

Funakoshi, Mitsuru; Mieno, Takuya

doi:10.1007/978-3-030-86692-1_4

Cited by 6 publications

(14 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Afterward, Abedin et al [1] improved the complexities. Also, the problems of computing the longest Lyndon substring [29], the longest palindrome [15], and the set of MUPSs [14] were considered in the after-edit model.…”

Section: Related Workmentioning

confidence: 99%

“…3). It is known that the number of MUPSs covering any interval is O(log n) [14], hence the width of a query range of RmQ is also O(log n). We call the range minimum query such that the width of any query is constrained in O(polylog(n)) LogRmQ.…”

Section: Sliding-window Data Structuresmentioning

confidence: 99%

“…As related work, the set of minimal unique palindromic substrings (MUPSs) can be maintained efficiently in the sliding-window model [25]. Also, the set of MUPSs can be updated efficiently in the after-edit model [14]. Since MUPSs are strongly related to SUPSs, we utilize the above known results for MUPSs as black boxes.…”

Section: Introductionmentioning

confidence: 99%

“…Also, given a string T , the data structure can be constructed in O(n) time.Proof. Given a substitution operation, we can detect all the changes of MUPSs in O(log σ + (log log n) 2 + d) time[14]. Then, the set of MUPSs can be updated in O(d) time, the predecessor/successor data structures can be updated in O(d log log n) time, and the LogRmQ data structure can be updated in amortized O(d) time by Lemma 2.…”

mentioning

confidence: 99%

“…Further, the LogRmQ data structure can be computed in O(n) time by Lemma 2. Note that the total query time can be written as Õ(1) time if k is in polylog(n) since d ∈ O(log n) always holds[14].…”

mentioning

confidence: 99%

See 4 more Smart Citations

Shortest Unique Palindromic Substring Queries in Semi-dynamic Settings

Mieno¹,

Funakoshi²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

A palindromic substring T [i..j] of a string T is said to be a shortest unique palindromic substring (SUPS) in T for an interval [p, q] if T [i..j] is a shortest one such that T [i..j] occurs only once in T , and [i, j] contains [p, q]. The SUPS problem is, given a string T of length n, to construct a data structure that can compute all the SUPSs for any given query interval. It is known that any SUPS query can be answered in O(α) time after O(n)-time preprocessing, where α is the number of SUPSs to output [Inoue et al., 2018]. In this paper, we first show that α is at most 4, and the upper bound is tight. Also, we present an algorithm to solve the SUPS problem for a sliding window that can answer any query in O(log log W ) time and update data structures in amortized O(log σ) time, where W is the size of the window, and σ is the alphabet size. Furthermore, we consider the SUPS problem in the after-edit model and present an efficient algorithm. Namely, we present an algorithm that uses O(n) time for preprocessing and answers any k SUPS queries in O(log n log log n + k log log n) time after single character substitution. As a by-product, we propose a fully-dynamic data structure for range minimum queries (RmQs) with a constraint where the width of each query range is limited to polylogarithmic. The constrained RmQ data structure can answer such a query in constant time and support a single-element edit operation in amortized constant time.

show abstract