A Simple $O(\log\log(\mathrm{rank}))$-Competitive Algorithm for the Matroid Secretary Problem
نویسندگان
چکیده
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))-competitive procedure, and Lachish (2014) later presented a O(log log(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(log log(rank))-competitive algorithm for the matroid secretary problem. Our algorithm can be interpreted as a distribution over a simple type of matroid secretary algorithms which are easy to analyze. Due to the simplicity of our procedure, we are also able to vastly improve on the hidden constant in the competitive ratio.
منابع مشابه
Improved competitive ratio for the matroid secretary problem
The Matroid Secretary Problem, introduced by Babaioff et al. (2007), is a generalization of the Classical Secretary Problem. In this problem, elements from a matroid are presented to an on-line algorithm in a random order. Each element has a weight associated with it, which is revealed to the algorithm along with the element. After each element is revealed the algorithm must make an irrevocable...
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