Multidimensional Binary Vector Assignment Problem: Standard, Structural and Above Guarantee Parameterizations

Marin Bougeret 1 Guillerme Duvillié 2 Rodolphe Giroudeau 2 Rémi Watrigant 2
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 MAORE - Méthodes Algorithmes pour l'Ordonnancement et les Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : In this article we focus on the parameterized complexity of the Multidimensional Binary Vector Assignment problem (called bMVA). An input of this problem is defined by m disjoint sets V1,V2,…,Vm, each composed of n binary vectors of size p. An output is a set of n disjoint m-tuples of vectors, where each m-tuple is obtained by picking one vector from each set Vi. To each m-tuple we associate a p dimensional vector by applying the bit-wise AND operation on the m vectors of the tuple. The objective is to minimize the total number of zeros in these n vectors. bMVA can be seen as a variant of multidimensional matching where hyperedges are implicitly locally encoded via labels attached to vertices, but was originally introduced in the context of integrated circuit manufacturing. We provide for this problem FPT algorithms and negative results (ETH-based results, W[2]-hardness and a kernel lower bound) according to several parameters: the standard parameter k (i.e. the total number of zeros), as well as two parameters above some guaranteed values.
Type de document :
Communication dans un congrès
FCT: Fundamentals of Computation Theory, Aug 2015, Gdańsk, Poland. 20th International Symposium, FCT 2015, Gdańsk, Poland, August 17-19, 2015, Proceedings, LNCS (9210), pp.189-201, 2015, Fundamentals of Computation Theory. 〈10.1007/978-3-319-22177-9_15〉
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01250997
Contributeur : Rodolphe Giroudeau <>
Soumis le : mardi 5 janvier 2016 - 15:00:09
Dernière modification le : jeudi 24 mai 2018 - 15:59:22

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Marin Bougeret, Guillerme Duvillié, Rodolphe Giroudeau, Rémi Watrigant. Multidimensional Binary Vector Assignment Problem: Standard, Structural and Above Guarantee Parameterizations. FCT: Fundamentals of Computation Theory, Aug 2015, Gdańsk, Poland. 20th International Symposium, FCT 2015, Gdańsk, Poland, August 17-19, 2015, Proceedings, LNCS (9210), pp.189-201, 2015, Fundamentals of Computation Theory. 〈10.1007/978-3-319-22177-9_15〉. 〈lirmm-01250997〉

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