Lachish, Oded (2014) O(log log Rank) competitive ratio for the Matroid Secretary Problem. In: UNSPECIFIED (ed.) 2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS) (2014). Piscataway, U.S.: IEEE, pp. 326-225. ISBN 9781479965175.
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Abstract
In the Matroid Secretary Problem (MSP), the elements of the ground set of a Matroid are revealed on-line one by one, each together with its value. An algorithm for the MSP is called Matroid-Unknown if, at every stage of its execution, it only knows (i) the elements that have been revealed so far and their values and (ii) an oracle for testing whether or not a subset the elements that have been revealed so far forms an independent set. An algorithm is called Known-Cardinality if it knows (i), (ii) and also knows from the start the cardinality n of the ground set of the Matroid. We present here a Known-Cardinality algorithm with a competitive-ratio of order log log the rank of the Matroid. The prior known results for a OC algorithm are a competitive-ratio of log the rank of the Matroid, by Babaioff et al. (2007), and a competitive-ratio of square root of log the rank of the Matroid, by Chakraborty and Lachish (2012).
Metadata
| Item Type: | Book Section |
|---|---|
| Additional Information: | Philadelphia, PA, USA. 18-21 Oct 2014 |
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Dr Oded Lachish |
| Date Deposited: | 02 Nov 2015 14:57 |
| Last Modified: | 09 Aug 2023 12:37 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/13239 |
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