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Journal of Combinatorial Optimization

, Volume 28, Issue 1, pp 25–37 | Cite as

Recognition of overlap graphs

  • Theodoros P. Gevezes
  • Leonidas S. Pitsoulis
Article

Abstract

Overlap graphs occur in computational biology and computer science, and have applications in genome sequencing, string compression, and machine scheduling. Given two strings \(s_{i}\) and \(s_{j}\), their overlap string is defined as the longest string \(v\) such that \(s_{i} = uv\) and \(s_{j} = vw\), for some non empty strings \(u,w\), and its length is called the overlap between these two strings. A weighted directed graph is an overlap graph if there exists a set of strings with one-to-one correspondence to the vertices of the graph, such that each arc weight in the graph equals the overlap between the corresponding strings. In this paper, we characterize the class of overlap graphs, and we present a polynomial time recognition algorithm as a direct consequence. Given a weighted directed graph \(G\), the algorithm constructs a set of strings that has \(G\) as its overlap graph, or decides that this is not possible.

Keywords

Strings Shortest superstring problem Overlap graphs Recognition algorithm 

Notes

Acknowledgments

This research has been co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: Heracleitus II. Investing in knowledge society through the European Social Fund.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematical, Physical and Computational SciencesAristotle University of ThessalonikiThessalonikiGreece

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