Chapter

Mathematical Foundations of Computer Science 2003

Volume 2747 of the series Lecture Notes in Computer Science pp 208-217

Inferring Strings from Graphs and Arrays

  • Hideo BannaiAffiliated withHuman Genome Center, Institute of Medical Science, University of Tokyo
  • , Shunsuke InenagaAffiliated withDepartment of Informatics
  • , Ayumi ShinoharaAffiliated withDepartment of InformaticsPRESTO, Japan Science and Technology Corporation (JST)
  • , Masayuki TakedaAffiliated withDepartment of InformaticsPRESTO, Japan Science and Technology Corporation (JST)

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Abstract

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.