Inferring Strings from Graphs and Arrays

This paper introduces a new problem of inferring strings from graphs, and inferring strings from arrays. Given a graph G or an array A, we infer a string that suits the graph, or the array, under some condition. Firstly, we solve the problem of finding a string w such that the directed acyclic subsequence graph (DASG) of w is isomorphic to a given graph G. Secondly, we consider directed acyclic word graphs (DAWGs) in terms of string inference. Finally, we consider the problem of finding a string w of a minimal size alphabet, such that the suffix array (SA) of w is identical to a given permutation p = p1, . . . , pn of integers 1, . . . , n. Each of our three algorithms solving the above problems runs in linear time with respect to the input size.