A Stochastic Probing Problem with Applications

  • Anupam Gupta
  • Viswanath Nagarajan
Conference paper

DOI: 10.1007/978-3-642-36694-9_18

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7801)
Cite this paper as:
Gupta A., Nagarajan V. (2013) A Stochastic Probing Problem with Applications. In: Goemans M., Correa J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2013. Lecture Notes in Computer Science, vol 7801. Springer, Berlin, Heidelberg

Abstract

We study a general stochastic probing problem defined on a universe V, where each element e ∈ V is “active” independently with probability pe. Elements have weights {we:e ∈ V} and the goal is to maximize the weight of a chosen subset S of active elements. However, we are given only the pe values—to determine whether or not an element e is active, our algorithm must probe e. If element e is probed and happens to be active, then e must irrevocably be added to the chosen set S; if e is not active then it is not included in S. Moreover, the following conditions must hold in every random instantiation:
  • the set Q of probed elements satisfy an “outer” packing constraint,

  • the set S of chosen elements satisfy an “inner” packing constraint.

The kinds of packing constraints we consider are intersections of matroids and knapsacks. Our results provide a simple and unified view of results in stochastic matching [1, 2] and Bayesian mechanism design [3], and can also handle more general constraints. As an application, we obtain the first polynomial-time Ω(1/k)-approximate “Sequential Posted Price Mechanism” under k-matroid intersection feasibility constraints, improving on prior work [3-5].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Anupam Gupta
    • 1
  • Viswanath Nagarajan
    • 2
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityUSA
  2. 2.IBM T.J. Watson Research CenterUSA

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