Only recently, progress has been made in obtaining o(log(rank))-competitive algorithms for the matroid secretary problem. More precisely, Chakraborty and Lachish (2012) presented a O((log(rank))1/2)-competitive procedure, and Lachish (2014) later presented a O(loglog(rank))-competitive algorithm. Both these algorithms and their analyses are very involved, which is also reflected in the extremely high constants in their competitive ratios. Using different tools, we present a considerably simpler O(loglog(rank))-competitive algorithm for the matroid secretary problem. Our algorithm can be interpreted as a distribution over a simple type of matroid secretary algorithms that are easy to analyze. Because of the simplicity of our procedure, we are also able to vastly improve on the hidden constant in the competitive ratio.
Bibliographical noteFunding Information:
Funding: The research of M. Feldman and O. Svensson has been supported by ERC [Starting Grant 335288-OptApprox]. The research of the third author has been supported by the Swiss National Science Foundation [Grant 200021_165866].
- Online algorithms
- Secretary problem