Abstract
The k-overlap graph for a set of strings is a graph such that each vertex corresponds to a string and there is a directed edge between two vertices if there is an overlap of at least k characters between their corresponding strings. Given a directed graph G, an integer k ≥ 1, and a finite alphabet ∑ of at least two symbols, we propose an algorithm to obtain a set of strings C, written over ∑, such that G is its k-overlap graph. The algorithm runs in exponential time on the maximum degree of G, due to the size of the returned strings, but in polynomial time on k, ∑, and the size of the graph. A practical application of this algorithm is its use to prove the NP-hardness of Minimum Contig Problems family (MCP) and its variation MCPr, which are based on the DNA Fragment Assembly problem.
Research supported by Brazilian agencies FAPESP (Grant 97/11629-2), and CNPq (Grant Pronex 664107/1997-4).
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References
M. D. V. Braga. Grafos de Seqüências de DNA. Master’s thesis, Instituto de Computação, UNICAMP, Campinas, SP, November 2000. In Portuguese at http://www.ic.unicamp.br/~meidanis/research/fa.html.
R. Diestel. Graph Theory. Springer-Verlag New York, Inc, 1997.
C. E. Ferreira, C. C. de Souza, and Y. Wakabayashi. Rearrangement of DNA fragments: a branch-and-cut algorithm. Discrete Applied Mathematics, 2001. To appear.
D. Gusfield, G. M. Landau, and B. Schieber. An efficient algorithm for the all pairs suffix-prefix problem. Information Processing Letters, 41(4):181–185, March 1992.
A. Schrijver. Bipartite edge coloring in O(Δm) time. SIAM Journal on Computing, 28(3):841–846, 1998.
J. C. Setubal and J. Meidanis. Introduction to Computational Molecular Biology. PWS Publishing Company, 1997.
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Braga, M.D.V., Meidanis, J. (2002). An Algorithm That Builds a Set of Strings Given Its Overlap Graph. In: Rajsbaum, S. (eds) LATIN 2002: Theoretical Informatics. LATIN 2002. Lecture Notes in Computer Science, vol 2286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45995-2_10
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DOI: https://doi.org/10.1007/3-540-45995-2_10
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