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

Authors Thomas Kesselheim, Andreas Tönnis

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Thomas Kesselheim
Andreas Tönnis

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Thomas Kesselheim and Andreas Tönnis. Think Eternally: Improved Algorithms for the Temp Secretary Problem and Extensions. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 54:1-54:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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.
  • Secretary Problem
  • Online Algorithms
  • Scheduling Problems


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  1. Shipra Agrawal and Nikhil R. Devanur. Fast algorithms for online stochastic convex programming. In Proc. 26th Symp. Discr. Algorithms (SODA), pages 1405-1424, 2015. URL:
  2. Shipra Agrawal, Zizhuo Wang, and Yinyu Ye. A dynamic near-optimal algorithm for online linear programming. Operations Research, 62(4):876-890, 2014. URL:
  3. Moshe Babaioff, Nicole Immorlica, David Kempe, and Robert Kleinberg. A knapsack secretary problem with applications. In Proc. 10thIntl. Workshop Approximation Algorithms for Combinatorial Optimization Problems (APPROX), pages 16-28, 2007. URL:
  4. Moshe Babaioff, Nicole Immorlica, and Robert Kleinberg. Matroids, secretary problems, and online mechanisms. In Proc. 18th Symp. Discr. Algorithms (SODA), pages 434-443, 2007. URL:
  5. MohammadHossein Bateni, Mohammad Taghi Hajiaghayi, and Morteza Zadimoghaddam. Submodular secretary problem and extensions. ACM Trans. Algorithms, 9(4):32, 2013. URL:
  6. Nikhil R. Devanur, Kamal Jain, Balasubramanian Sivan, and Christopher A. Wilkens. Near optimal online algorithms and fast approximation algorithms for resource allocation problems. In Proc. 12thConf. Econom. Comput. (EC), pages 29-38, 2011. URL:
  7. Eugene B. Dynkin. The optimum choice of the instant for stopping a markov process. In Sov. Math. Dokl, volume 4, pages 627-629, 1963. Google Scholar
  8. Hossein Esfandiari, Nitish Korula, and Vahab S. Mirrokni. Online allocation with traffic spikes: Mixing adversarial and stochastic models. In Proceedings of the Sixteenth ACM Conference on Economics and Computation, EC'15, Portland, OR, USA, June 15-19, 2015, pages 169-186, 2015. URL:
  9. Moran Feldman, Joseph Naor, and Roy Schwartz. Improved competitive ratios for submodular secretary problems (extended abstract). In Proc. 14thIntl. Workshop Approximation Algorithms for Combinatorial Optimization Problems (APPROX), pages 218-229, 2011. URL:
  10. Moran Feldman, Ola Svensson, and Rico Zenklusen. A simple O(log log(rank))-competitive algorithm for the matroid secretary problem. In Proc. 26th Symp. Discr. Algorithms (SODA), pages 1189-1201, 2015. URL:
  11. Amos Fiat, Ilia Gorelik, Haim Kaplan, and Slava Novgorodov. The temp secretary problem. In Proc. 23rdEuropean Symp. Algorithms (ESA), pages 631-642, 2015. URL:
  12. M. Gardner. Scientific american, 1960. Google Scholar
  13. Anupam Gupta and Marco Molinaro. How experts can solve LPs online. In Proc. 22ndEuropean Symp. Algorithms (ESA), pages 517-529, 2014. URL:
  14. Edward G. Coffman Jr., Philippe Flajolet, Leopold Flatto, and Micha Hofri. The maximum of a random walk and its application to rectangle packing. Probability in the Engineering and Informational Sciences, 12(3):373-386, 1998. URL:
  15. Thomas Kesselheim, Robert D. Kleinberg, and Rad Niazadeh. Secretary problems with non-uniform arrival order. In Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC 2015, Portland, OR, USA, June 14-17, 2015, pages 879-888, 2015. URL:
  16. Thomas Kesselheim, Klaus Radke, Andreas Tönnis, and Berthold Vöcking. An optimal online algorithm for weighted bipartite matching and extensions to combinatorial auctions. In Proc. 21st European Symp. Algorithms (ESA), pages 589-600, 2013. URL:
  17. Thomas Kesselheim, Klaus Radke, Andreas Tönnis, and Berthold Vöcking. Primal beats dual on online packing lps in the random-order model. In Proc. 46th Symp. Theory of Computing (STOC), pages 303-312, 2014. URL:
  18. Robert D. Kleinberg. A multiple-choice secretary algorithm with applications to online auctions. In Proc. 16th Symp. Discr. Algorithms (SODA), pages 630-631, 2005. URL:
  19. Nitish Korula and Martin Pál. Algorithms for secretary problems on graphs and hypergraphs. In Proc. 36th Intl. Coll. Autom. Lang. Program. (ICALP), pages 508-520, 2009. URL:
  20. Oded Lachish. O(log log rank) competitive ratio for the matroid secretary problem. In Proc. 55th Symp. Foundations of Computer Science (FOCS), pages 326-335, 2014. URL:
  21. Denis V Lindley. Dynamic programming and decision theory. Applied Statistics, pages 39-51, 1961. Google Scholar
  22. Richard J. Lipton and Andrew Tomkins. Online interval scheduling. In Proc. 5thSymp. Discr. Algorithms (SODA), pages 302-311, 1994. URL:
  23. Tengyu Ma, Bo Tang, and Yajun Wang. The simulated greedy algorithm for several submodular matroid secretary problems. In Proc. 30th Symp. Theoret. Aspects of Computer Science (STACS), pages 478-489, 2013. URL:
  24. Alessandro Panconesi and Aravind Srinivasan. Randomized distributed edge coloring via an extension of the chernoff-hoeffding bounds. SIAM J. Comput., 26(2):350-368, 1997. URL:
  25. Gerhard J. Woeginger. On-line scheduling of jobs with fixed start and end times. Theoret. Comput. Sci., 130(1):5-16, 1994. URL:
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