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=p 1,...,p n of integers 1,...,n. Each of our three algorithms solving the above problems runs in linear time with respect to the input size.
KeywordsLinear Time Directed Acyclic Graph Sink Node Longe Path Lexicographic Order
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