Combinatorics of minimal absent words for a sliding window

Tooru Akagi,Yuki Kuhara,Takuya Mieno,Yuto Nakashima,Shunsuke Inenaga,Hideo Bannai,Masayuki Takeda

doi:10.1016/j.tcs.2022.06.002

Combinatorics of minimal absent words for a sliding window

Tooru Akagi, Yuki Kuhara + Show 5 more

Open Access

https://doi.org/10.1016/j.tcs.2022.06.002

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Journal: Theoretical Computer Science	Publication Date: Jun 3, 2022
Citations: 1	License type: cc-by

Affiliation: Kyushu University, Japan Society for the Promotion of Science, Tokyo Medical and Dental University

#Minimal Absent Words #Sliding Window Model + Show 7 more

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Abstract

A string w is called a minimal absent word (MAW) for another string T if w does not occur in T but the proper substrings of w occur in T. For example, let Σ={a,b,c} be the alphabet. Then, the set of MAWs for string w=abaab is {aaa,aaba,bab,bb,c}. In this paper, we study combinatorial properties of MAWs in the sliding window model, namely, how the set of MAWs changes when a sliding window of fixed length d is shifted over the input string T of length n, where 1≤d<n. We present tight upper and lower bounds on the maximum number of changes in the set of MAWs for a sliding window over T, both in the cases of general alphabets and binary alphabets. Our bounds improve on the previously known best bounds [Crochemore et al., 2020].

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