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Constrained Non-monotone Submodular Maximization: Offline and Secretary Algorithms

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Internet and Network Economics (WINE 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6484))

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Abstract

Constrained submodular maximization problems have long been studied, most recently in the context of auctions and computational advertising, with near-optimal results known under a variety of constraints when the submodular function is monotone. In this paper, we give constant approximation algorithms for the non-monotone case that work for p-independence systems (which generalize constraints given by the intersection of p matroids that had been studied previously), where the running time is \(\text{poly}(n,p)\). Our algorithms and analyses are simple, and essentially reduce non-monotone maximization to multiple runs of the greedy algorithm previously used in the monotone case.

We extend these ideas to give a simple greedy-based constant factor algorithms for non-monotone submodular maximization subject to a knapsack constraint, and for (online) secretary setting (where elements arrive one at a time in random order and the algorithm must make irrevocable decisions) subject to uniform matroid or a partition matroid constraint. Finally, we give an O(logk) approximation in the secretary setting subject to a general matroid constraint of rank k.

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Author information

Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA

    Anupam Gupta

  2. Microsoft Research New England, Cambridge, MA

    Aaron Roth

  3. Princeton University, Princeton, NJ

    Grant Schoenebeck

  4. Microsoft Research, Mountain View, CA

    Kunal Talwar

Authors
  1. Anupam Gupta
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  2. Aaron Roth
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  3. Grant Schoenebeck
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  4. Kunal Talwar
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Editor information

Editors and Affiliations

  1. Department of Management Science and Engineering, Stanford University, 94305, Stanford, CA, USA

    Amin Saberi

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Gupta, A., Roth, A., Schoenebeck, G., Talwar, K. (2010). Constrained Non-monotone Submodular Maximization: Offline and Secretary Algorithms. In: Saberi, A. (eds) Internet and Network Economics. WINE 2010. Lecture Notes in Computer Science, vol 6484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17572-5_20

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  • DOI: https://doi.org/10.1007/978-3-642-17572-5_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17571-8

  • Online ISBN: 978-3-642-17572-5

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