Efficient Enumeration of Distinct Factors Using Package Representations.

We investigate properties and applications of a new compact representation of string factors: families of packages . In a string T , each package represents the factors of T of length that start in the interval . A family of packages represents the set defined as the union of the sets of factors represented by individual packages in . We show how to efficiently enumerate and showcase that this is a generic tool for enumerating important classes of factors of T , such as powers and antipowers. Our approach is conceptually simpler than problem-specific methods and provides a unifying framework for such problems, which we hope can be further exploited. We also consider a special case of the problem in which every occurrence of every factor represented by is captured by some package in . For both applications mentioned above, we construct an efficient package representation that satisfies this property. We develop efficient algorithms that, given a family of m packages in a string of length n , report all distinct factors represented by these packages in time for the general case and in the optimal time for the special case. We can also compute in time in the general case and in time in the special case. In particular, we improve over the state-of-the-art -time algorithm for computing the number of distinct k -antipower factors, by providing an algorithm that runs in time, and we obtain an alternative linear-time algorithm to enumerate distinct squares.