In this paper, we propose a novel approach to combine compact directed acyclic word graphs (CDAWGs) and grammar-based compression. This leads us to an efficient self-index, called Linear-size CDAWGs (L-CDAWGs), which can be represented with O(ẽT log n) bits of space allowing for O(log n)-time random and O(1)-time sequential accesses to edge labels, and O(m log σ + occ)-time pattern matching. Here,ẽT is the number of all extensions of maximal repeats in T , n and m are respectively the lengths of the text T and a given pattern, σ is the alphabet size, and occ is the number of occurrences of the pattern in T . The repetitiveness measurẽ eT is known to be much smaller than the text length n for highly repetitive text. For constant alphabets, our L-CDAWGs achieve O(m + occ) pattern matching time with O(e r T log n) bits of space, which improves the pattern matching time of Belazzougui et al.'s run-length BWT-CDAWGs by a factor of log log n, with the same space complexity. Here, e r T is the number of right extensions of maximal repeats in T . As a byproduct, our result gives a way of constructing a straight-line program (SLP) of size O(ẽT ) for a given text T in O(n +ẽT log σ) time.

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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 . A string w is called a minimal absent word (MAW) of T if w does not occur in T and any proper substring of w occurs in T . In this paper, we study the problems of computing MUSs and MAWs in a sliding window over a given string T . We first show how the set of MUSs can change in a sliding window over T , and present an O(n log σ)-time and O(d)-space algorithm to compute MUSs in a sliding window of width d over T , where σ is the maximum number of distinct characters in every window. We then give tight upper and lower bounds on the maximum number of changes in the set of MAWs in a sliding window over T . Our bounds improve on the previous results in [Crochemore et al., 2017].

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