On the Advice Complexity of the Set Cover Problem [chapter]

Dennis Komm, Richard Královič, Tobias Mömke
2012 Lecture Notes in Computer Science  
Recently, a new approach to get a deeper understanding of online computation has been introduced: the study of the advice complexity of online problems. The idea is to measure the information that online algorithms need to be supplied with to compute high-quality solutions and to overcome the drawback of not knowing future input requests. In this paper, we study the advice complexity of an online version of the well-known set cover problem introduced by Alon et al.: for a ground set of size n
more » ... d a set family of m subsets of the ground set, we obtain bounds in both n and m. We prove that a linear number of advice bits is both sufficient and necessary to perform optimally. Furthermore, for any constant c, we prove that n − c bits are enough to construct a ccompetitive online algorithm and this bound is tight up to a constant factor (only depending on c). Moreover, we show that a linear number of advice bits is both necessary and sufficient to be optimal with respect to m, as well. We further show lower and upper bounds for achieving c-competitiveness also in m.
doi:10.1007/978-3-642-30642-6_23 fatcat:qluinziykvbmfinqboqp3k5xpi