Incremental complexity of a bi-objective hypergraph transversal problem

Abstract : The hypergraph transversal problem has been intensively studied, from both a theoretical and a practical point of view. In particular , its incremental complexity is known to be quasi-polynomial in general and polynomial for bounded hypergraphs. Recent applications in computational biology however require to solve a generalization of this problem, that we call bi-objective transversal problem. The instance is in this case composed of a pair of hypergraphs (A, B), and the aim is to find minimal sets which hit all the hyperedges of A while intersecting a minimal set of hyperedges of B. In this paper, we formalize this problem, link it to a problem on monotone boolean ∧ − ∨ formulae of depth 3 and study its incremental complexity.
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Ricardo Andrade, Etienne Birmelé, Arnaud Mary, Thomas Picchetti, Marie-France Sagot. Incremental complexity of a bi-objective hypergraph transversal problem. Fundamentals of Computation Theory (FCT2015), Aug 2015, Gdansk, Poland. pp.202-213, ⟨10.1007/978-3-319-22177-9_16 ⟩. ⟨hal-01149392⟩

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