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Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone.
Optimal choice of the stopping moment of a Markov process
E. B. Dynkin · 1963
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The efficacy of the “greedy” algorithm
Thomas A. Jenkyns · 1976
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An analysis of the greedy heuristic for independence systems
Bernhard Korte and Dirk Hausmann · 1976
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An analysis of approximations for maximizing submodular set functions. II
M. L. Fisher, G. L. Nemhauser, and L. A. Wolsey · 1978
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An analysis of approximations for maximizing submodular set functions. I
G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher · 1978
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Worst case analysis of greedy type algorithms for independence systems
D. Hausmann, B. Korte, and T. A. Jenkyns · 1980
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Maximising real-valued submodular functions: primal and dual heuristics for location problems
Laurence A. Wolsey · 1982
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The secretary problem and its extensions: a review
P. R. Freeman · 1983
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Who solved the secretary problem?
T.S. Ferguson · 1989
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The budgeted maximum coverage problem
Samir Khuller, Anna Moss, and Joseph Naor · 1999
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Maximizing the spread of influence through a social network
D. Kempe, J. Kleinberg, and É. Tardos · 2003
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Adaptive limited-supply online auctions
Mohammad Taghi Hajiaghayi, Robert Kleinberg, and David C. Parkes · 2004
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A note on maximizing a submodular set function subject to a knapsack constraint
Maxim Sviridenko · 2004
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A polynomial time approximation scheme for the multiple knapsack problem
Chandra Chekuri and Sanjeev Khanna · 2005
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A multiple-choice secretary algorithm with applications to online auctions
Robert Kleinberg · 2005
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Matroids, secretary problems, and online mechanisms
Moshe Babaioff, Nicole Immorlica, and Robert Kleinberg · 2007
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A knapsack secretary problem with applications
M. Babaioff, N. Immorlica, D. Kempe, and R. Kleinberg · 2007
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Maximizing a submodular set function subject to a matroid constraint (extended abstract)
Gruia Calinescu, Chandra Chekuri, Martin Pál, and Jan Vondrák · 2007
Secretary problems: weights and discounts
Moshe Babaioff, Michael Dinitz, Anupam Gupta, Nicole Immorlica, and Kunal Talwar · 2009
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Maximizing a monotone submodular function subject to a matroid constraint
Gruia Calinescu, Chandra Chekuri, Martin Pál, and Jan Vondrák · 2009
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A secretary problem with submodular payoff function
Robert D. Kleinberg · 2009
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Algorithms for secretary problems on graphs and hypergraphs
Nitish Korula and Martin Pál · 2009
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Maximizing submodular set functions subject to multiple linear constraints
Ariel Kulik, Hadas Shachnai, and Tami Tamir · 2009
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Maximizing nonmonotone submodular functions under matroid or knapsack constraints
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Jon Lee, Maxim Sviridenko, and Jan Vondrák · 2009
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Jan Vondrák · 2009
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