The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where elements arrive one-by-one in random order, revealing a weight upon arrival. The decision whether to select an element has to be taken immediately after its arrival. The different applications that map to the secretary problem ask for different constraint families to be handled. The most prominent ones are matroid constraints, which both capture many relevant settings and admit strongly competitive secretary algorithms. However, dealing with more involved constraints proved to be much more difficult, and strong algorithms are known only for a few specific settings. In this paper, we present a general framework for dealing with the secretary problem over the intersection of several matroids. This framework allows us to combine and exploit the large set of matroid secretary algorithms known in the literature. As one consequence, we get constant-competitive secretary algorithms over the intersection of any constant number of matroids whose corresponding (single-)matroid secretary problems are currently known to have a constant-competitive algorithm. Moreover, we show that our results extend to submodular objectives.
|Title of host publication||29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018|
|Publisher||Association for Computing Machinery|
|Number of pages||18|
|State||Published - 2018|
|Event||29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States|
Duration: 7 Jan 2018 → 10 Jan 2018
|Name||Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms|
|Conference||29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018|
|Period||7/01/18 → 10/01/18|
Bibliographical noteFunding Information:
∗SupportedbyIsraelScienceFoundation grant1357/16,ERC Starting Grant 335288-OptAppro x, and Swiss National Science Foundation grant200021 165866. †Dept. ofMathematicsandComputerScience, OpenUniversity of Israel. Email: email@example.com. ‡SchoolofComputerandCommunication Sciences, EPFL. Email:firstname.lastname@example.org. §DepartmentofMathematics, ETHZurich, Zurich, Switzerland. Email: email@example.com.
© Copyright 2018 by SIAM.
- Matroid intersection
- Matroid secretary problem
- Online algorithms