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 Σ of at least two symbols, we propose an algorithm to obtain a set of strings C, written over Σ, 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, |Σ|, 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.
CITATION STYLE
Braga, M. D. V., & Meidanis, J. (2002). An algorithm that builds a set of strings given its overlap graph. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2286, pp. 52–63). Springer Verlag. https://doi.org/10.1007/3-540-45995-2_10
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