A Simple O (1oglog (rank))-competitive algorithm for the matroid secretary problem

Moran Feldman; Ola Svensson; Rico Zenklusen

A Simple O (1oglog (rank))-competitive algorithm for the matroid secretary problem

Moran Feldman
, Ola Svensson
, Rico Zenklusen

Research output: Contribution to conference › Paper › peer-review

Abstract

Only recently progress has been made in obtaining o (1og (rank))-competitive algorithms for the matroid secretary problem. More precisely, Chakraborty and Lachish (2012) presented a O (√log (rank))-competitive procedure, and Lachish (2014) recently presented a O (1oglog (rank))-competitive algorithm. Both algorithms aie involved with complex analyses. Using different tools, we present a considerably simpler O (1oglog (rank))-competitive algorithm. Our algorithm can be interpreted as a distribution over a simple type of matroid secretary algorithms which are easy to analyze. We are also able to vastly improve on the hidden constant in the competitive ratio.

Original language	English
Pages	1189-1201
Number of pages	13
State	Published - 2015
Externally published	Yes
Event	26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 - San Diego, United States Duration: 4 Jan 2015 → 6 Jan 2015

Conference

Conference	26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015
Country/Territory	United States
City	San Diego
Period	4/01/15 → 6/01/15

Keywords

Matroids
Online algorithms
Secretary problem

ASJC Scopus subject areas

Software
General Mathematics

Cite this

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title = "A Simple O (1oglog (rank))-competitive algorithm for the matroid secretary problem",

abstract = "Only recently progress has been made in obtaining o (1og (rank))-competitive algorithms for the matroid secretary problem. More precisely, Chakraborty and Lachish (2012) presented a O (√log (rank))-competitive procedure, and Lachish (2014) recently presented a O (1oglog (rank))-competitive algorithm. Both algorithms aie involved with complex analyses. Using different tools, we present a considerably simpler O (1oglog (rank))-competitive algorithm. Our algorithm can be interpreted as a distribution over a simple type of matroid secretary algorithms which are easy to analyze. We are also able to vastly improve on the hidden constant in the competitive ratio.",

keywords = "Matroids, Online algorithms, Secretary problem",

author = "Moran Feldman and Ola Svensson and Rico Zenklusen",

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note = "26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 ; Conference date: 04-01-2015 Through 06-01-2015",

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AU - Svensson, Ola

AU - Zenklusen, Rico

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N2 - Only recently progress has been made in obtaining o (1og (rank))-competitive algorithms for the matroid secretary problem. More precisely, Chakraborty and Lachish (2012) presented a O (√log (rank))-competitive procedure, and Lachish (2014) recently presented a O (1oglog (rank))-competitive algorithm. Both algorithms aie involved with complex analyses. Using different tools, we present a considerably simpler O (1oglog (rank))-competitive algorithm. Our algorithm can be interpreted as a distribution over a simple type of matroid secretary algorithms which are easy to analyze. We are also able to vastly improve on the hidden constant in the competitive ratio.

AB - Only recently progress has been made in obtaining o (1og (rank))-competitive algorithms for the matroid secretary problem. More precisely, Chakraborty and Lachish (2012) presented a O (√log (rank))-competitive procedure, and Lachish (2014) recently presented a O (1oglog (rank))-competitive algorithm. Both algorithms aie involved with complex analyses. Using different tools, we present a considerably simpler O (1oglog (rank))-competitive algorithm. Our algorithm can be interpreted as a distribution over a simple type of matroid secretary algorithms which are easy to analyze. We are also able to vastly improve on the hidden constant in the competitive ratio.

KW - Matroids

KW - Online algorithms

KW - Secretary problem

UR - https://www.scopus.com/pages/publications/84938256531

M3 - Paper

AN - SCOPUS:84938256531

SP - 1189

EP - 1201

T2 - 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015

Y2 - 4 January 2015 through 6 January 2015

ER -

A Simple O (1oglog (rank))-competitive algorithm for the matroid secretary problem

Abstract

Conference

Keywords

ASJC Scopus subject areas

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Cite this