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A complexity and approximation framework for the maximization scaffolding problem. (English) Zbl 1328.68085

Summary: We explore in this paper some complexity issues inspired by the contig scaffolding problem in bioinformatics. We focus on the following problem: given an undirected graph with no loop, and a perfect matching on this graph, find a set of cycles and paths covering every vertex of the graph, with edges alternatively in the matching and outside the matching, and satisfying a given constraint on the numbers of cycles and paths. We show that this problem is \(\mathcal{NP}\)-complete, even in planar bipartite graphs. Moreover, we show that there is no subexponential-time algorithm for several related problems unless the exponential-time hypothesis fails. Lastly, we also design two polynomial-time approximation algorithms for complete graphs.

MSC:

68Q25 Analysis of algorithms and problem complexity
05C85 Graph algorithms (graph-theoretic aspects)
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
68W25 Approximation algorithms

Software:

Ragout; SOPRA; GRASS; SCARPA
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References:

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