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What and Who
Title:Combinatorial Secretary Problems with Ordinal Information
Speaker:Bojana Kodric
coming from:Max-Planck-Institut für Informatik - D1
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
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Level:AG Audience
Date, Time and Location
Date:Thursday, 8 December 2016
Duration:30 Minutes
Building:E1 4
The secretary problem is a classic model for online decision making. Recently, combinatorial extensions such as matroid or matching secretary problems have become an important tool to study algorithmic problems in dynamic markets. Here the decision maker must know the numerical value of each arriving element, which can be a demanding informational assumption. In this paper, we initiate the study of combinatorial secretary problems with ordinal information, in which the decision maker only needs to be aware of a preference order consistent with the values of arrived elements. The goal is to design online algorithms with small competitive ratios.

For a number of existing algorithms, we observe that the restriction to ordinal information does not represent any additional obstacle. They maintain their competitive ratios even in the ordinal model. For bipartite matching and independent set in graphs with bounded independence, we give new algorithms that obtain constant competitive ratios in the ordinal model. Moreover, we show that ordinal variants of the submodular matroid secretary problems can be solved using algorithms for the linear versions by extending a result from (Feldman and Zenklusen 2015).

Finally, in the matroid secretary problem we provide a lower bound of Ω( n/(log n)) for algorithms that are oblivious to the matroid structure, where n is the total number of elements. This contrasts an upper bound of O(log n) in the cardinal model, and it shows that the technique of thresholding is not sufficient for good algorithms in the ordinal model.

Name(s):Bojana Kodric
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Created by:Bojana Kodric, 11/24/2016 11:10 AMLast modified by:Uwe Brahm/MPII/DE, 12/08/2016 04:01 AM
  • Bojana Kodric, 11/24/2016 11:14 AM
  • Bojana Kodric, 11/24/2016 11:10 AM -- Created document.