- Conference Paper
Rights / licenseCreative Commons Attribution 3.0 Unported
Weak submodularity is a natural relaxation of the diminishing return property, which is equivalent to submodularity. Weak submodularity has been used to show that many (monotone) functions that arise in practice can be efficiently maximized with provable guarantees. In this work we introduce two natural generalizations of weak submodularity for non-monotone functions. We show that an efficient randomized greedy algorithm has provable approximation guarantees for maximizing these functions subject to a cardinality constraint. We then provide a more refined analysis that takes into account that the weak submodularity parameter may change (sometimes improving) throughout the execution of the algorithm. This leads to improved approximation guarantees in some settings. We provide applications of our results for monotone and non-monotone maximization problems. Show more
Book title31st International Symposium on Algorithms and Computation (ISAAC 2020)
Journal / seriesLeibniz International Proceedings in Informatics (LIPIcs)
Pages / Article No.
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Subjectweakly submodular; non-monotone; local submodularity ratio
Organisational unit09487 - Zenklusen, Rico / Zenklusen, Rico
NotesDue to the Coronavirus (COVID-19) the conference was conducted virtually.
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