License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2016.54
URN: urn:nbn:de:0030-drops-63966
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6396/
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Kesselheim, Thomas ; Tönnis, Andreas

Think Eternally: Improved Algorithms for the Temp Secretary Problem and Extensions

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LIPIcs-ESA-2016-54.pdf (0.5 MB)

Abstract

The Temp Secretary Problem was recently introduced by [Fiat et al., ESA 2015]. It is a generalization of the Secretary Problem, in which commitments are temporary for a fixed duration. We present a simple online algorithm with improved performance guarantees for cases already considered by [Fiat et al., ESA 2015] and give competitive ratios for new generalizations of the problem. In the classical setting, where candidates have identical contract durations gamma << 1 and we are allowed to hire up to B candidates simultaneously, our algorithm is (1/2) - O(sqrt{gamma})-competitive. For large B, the bound improves to 1 - O(1/sqrt{B}) - O(sqrt{gamma}).

Furthermore we generalize the problem from cardinality constraints towards general packing constraints. We achieve a competitive ratio of 1 - O(sqrt{(1+log(d) + log(B))/B}) - O(sqrt{gamma}), where d is the sparsity of the constraint matrix and B is generalized to the capacity ratio of linear constraints. Additionally we extend the problem towards arbitrary hiring durations.

Our algorithmic approach is a relaxation that aggregates all temporal constraints into a non-temporal constraint. Then we apply a linear scaling algorithm that, on every arrival, computes a tentative solution on the input that is known up to this point. This tentative solution uses the non-temporal, relaxed constraints scaled down linearly by the amount of time that has already passed.

BibTeX - Entry

@InProceedings{kesselheim_et_al:LIPIcs:2016:6396,
  author =	{Thomas Kesselheim and Andreas T{\"o}nnis},
  title =	{{Think Eternally: Improved Algorithms for the Temp Secretary Problem and Extensions}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{54:1--54:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Piotr Sankowski and Christos Zaroliagis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6396},
  URN =		{urn:nbn:de:0030-drops-63966},
  doi =		{10.4230/LIPIcs.ESA.2016.54},
  annote =	{Keywords: Secretary Problem, Online Algorithms, Scheduling Problems}
}

Keywords: Secretary Problem, Online Algorithms, Scheduling Problems
Collection: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue Date: 2016
Date of publication: 18.08.2016

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