On the advice complexity of the set cover problem
2012 (English)In: Computer Science - Theory and Applications, Springer Berlin/Heidelberg, 2012, Vol. 7353 LNCS, 241-252 p.Conference paper (Refereed)
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 and 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 c-competitive 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.
Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2012. Vol. 7353 LNCS, 241-252 p.
, Lecture Notes in Computer Science, ISSN 0302-9743 ; 7353
Advice complexity, Constant factors, High-quality solutions, Lower and upper bounds, On-line algorithms, Online computations, Online problems, Online versions, Set cover problem, Algorithms, Competition, Computation theory
IdentifiersURN: urn:nbn:se:kth:diva-103660DOI: 10.1007/978-3-642-30642-6_23ScopusID: 2-s2.0-84865559124ISBN: 978-364230641-9OAI: oai:DiVA.org:kth-103660DiVA: diva2:561291
7th International Computer Science Symposium in Russia on Computer Science - Theory and Applications, CSR 2012; Nizhny Novgorod;3 July 2012 through 7 July 2012
QC 201210182012-10-182012-10-172012-10-18Bibliographically approved