Computing Minimal Unique Substrings for a Sliding Window

A substring u of a string T is called a minimal unique substring (MUS) of T if u occurs exactly once in T and any proper substring of u occurs at least twice in T. In this paper, we study the problem of computing MUSs for a sliding window over a given string T. We first show how the set of MUSs can change when the window slides over T. We then present an O(nlog σ^′) -time and O(d)-space algorithm to compute MUSs for a sliding window of size d over the input string T of length n, where σ^′≤ d is the maximum number of distinct characters in every window.