# The Lazy Matroid Problem

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.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [18 references]

https://hal.inria.fr/hal-01402029
Contributor : Hal Ifip <>
Submitted on : Thursday, November 24, 2016 - 10:48:25 AM
Last modification on : Wednesday, October 14, 2020 - 4:01:16 AM
Long-term archiving on: : Monday, March 20, 2017 - 8:59:46 PM

### File

978-3-662-44602-7_6_Chapter.pd...
Files produced by the author(s)

### Citation

Laurent Gourvès, Jérôme Monnot, Aris Pagourtzis. The Lazy Matroid Problem. 8th IFIP International Conference on Theoretical Computer Science (TCS), Sep 2014, Rome, Italy. pp.66-77, ⟨10.1007/978-3-662-44602-7_6⟩. ⟨hal-01402029⟩

Record views