Oded Lachish
Birkbeck
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 decision on whether
or not to select it. The goal is to pick an independent set with the
sum of the weights of the selected elements as large as possible.
Babaioff et al gave an algorithm for the Matroid Secretary Problem
with a competitive ratio of O(log(rho)), where rho is the rank of the
matroid. It has been conjectured that a constant competitive-ratio is
achievable for this problem. This will be about an algorithm that has
a competitive ratio of O(sqrt(log(rho))).
This is joint work with Sourav Chakraborty