On Variants of the Matroid Secretary Problem

  • Shayan Oveis Gharan
  • Jan Vondrák
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)


We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constant-factor competitive algorithm for the “random assignment” model where the weights are assigned randomly to the elements of a matroid, and then the elements arrive on-line in an adversarial order (extending a result of Soto [20]). This is under the assumption that the matroid is known in advance. If the matroid is unknown in advance, we present an O(logr logn)-approximation, and prove that a better than O(logn / loglogn) approximation is impossible. This resolves an open question posed by Babaioff et al. [3].

As a natural special case, we also consider the classical secretary problem where the number of candidates n is unknown in advance. If n is chosen by an adversary from {1,…,N}, we provide a nearly tight answer, by providing an algorithm that chooses the best candidate with probability at least 1/(H N − 1 + 1) and prove that a probability better than 1/H N cannot be achieved (where H N is the N-th harmonic number).


Approximation Algorithm Online Auction Secretary Problem Transversal Matroids Natural Special Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Shayan Oveis Gharan
    • 1
  • Jan Vondrák
    • 2
  1. 1.Stanford UniversityStanfordUSA
  2. 2.IBM Almaden Research CenterSan JoseUSA

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