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 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 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. © 2014 IFIP International Federation for Information Processing.