Robust Monotone Submodular Function Maximization

We consider a robust formulation, introduced by Krause et al. (2008), of the classic cardinality constrained monotone submodular function maximization problem, and give the first constant factor approximation results. The robustness considered is w.r.t. adversarial removal of a given number of eleme...

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Bibliographic Details
Published inInteger Programming and Combinatorial Optimization Vol. 9682; pp. 312 - 324
Main Authors Orlin, James B., Schulz, Andreas S., Udwani, Rajan
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 01.01.2016
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Approximation Algorithm
Approximation Ratio
Full Version
Greedy Algorithm
Mathematical theory of computation
Sensor Placement
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Summary:We consider a robust formulation, introduced by Krause et al. (2008), of the classic cardinality constrained monotone submodular function maximization problem, and give the first constant factor approximation results. The robustness considered is w.r.t. adversarial removal of a given number of elements from the chosen set. In particular, for the fundamental case of single element removal, we show that one can approximate the problem up to a factor $$(1-1/e)-\epsilon $$ by making $$O(n^{\frac{1}{\epsilon }})$$ queries, for arbitrary $$\epsilon >0$$ . The ideas are also extended to more general settings.
Bibliography:Original Abstract: We consider a robust formulation, introduced by Krause et al. (2008), of the classic cardinality constrained monotone submodular function maximization problem, and give the first constant factor approximation results. The robustness considered is w.r.t. adversarial removal of a given number of elements from the chosen set. In particular, for the fundamental case of single element removal, we show that one can approximate the problem up to a factor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1-1/e)-\epsilon $$\end{document} by making \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n^{\frac{1}{\epsilon }})$$\end{document} queries, for arbitrary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon >0$$\end{document}. The ideas are also extended to more general settings.
ISBN:9783319334608
3319334603
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-33461-5_26