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
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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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