Submodular set function: Difference between revisions

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Submodular set function maximization: we do not need a page number within a journal article whose entire topic is this claim, and whose abstract states this claim, and our citation templates do not provide a mechanism for augmenting journal articles with page numbers that are not the whole range of page numbers for the whole article
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# The problem of maximizing a non-negative submodular function admits a 1/2 approximation algorithm.<ref name="FMV" /><ref name="BFNS" /> Computing the [[maximum cut]] of a graph is a special case of this problem.
# The problem of maximizing a monotone submodular function subject to a cardinality constraint admits a <math>1 - 1/e</math> approximation algorithm.<ref name="NVF" />{{page needed|date=October 2020}}<ref>{{Cite web|last=Williamson|first=David P.|title=Bridging Continuous and Discrete Optimization: Lecture 23|url=https://people.orie.cornell.edu/dpw/orie6334/lecture23.pdf}}</ref> The [[maximum coverage problem]] is a special case of this problem.
# The problem of maximizing a monotone submodular function subject to a [[matroid]] constraint (which subsumes the case above) also admits a <math>1 - 1/e</math> approximation algorithm.<ref name="CCPV" /><ref name="FNS" /><ref name="FW" />