Abstract : This article introduces the lazy matroid problem, which captures the goal of saving time or money in certain task selection scenarios. We are given a budget B and a matroid ${\cal M}$ with weights on its elements. The problem consists in finding an independent set F of minimum weight. In addition, F is feasible if its augmentation with any new element x implies that either F + x exceeds B or F + x is dependent. Our first result is a polynomial time approximation scheme for this NP-hard problem which generalizes a recently studied version of the lazy bureaucrat problem. We next study the approximability of a more general setting called lazy staff matroid. In this generalization, every element of ${\cal M}$ has a multidimensional weight. We show that approximating this generalization is much harder than for the lazy matroid problem since it includes the independent dominating set problem.
https://hal.inria.fr/hal-01402029
Contributeur : Hal Ifip
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Soumis le : jeudi 24 novembre 2016 - 10:48:25
Dernière modification le : jeudi 11 janvier 2018 - 06:17:30
Document(s) archivé(s) le : lundi 20 mars 2017 - 20:59:46
