Combinatorics of minimal absent words for a sliding window - Akagi, Tooru; Kuhara, Yuki; Mieno, Takuya; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki (Theoretical computer science, 2022)
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].