Title: Algorithms for submodular matroid secretary problems

Speaker: Yajun Wang, MSRA

Time/Date:  Friday, Oct 12, 11-12
Location: Room 3408

Abstract:

We study the matroid secretary problems with submodular valuation functions. In these problems,
the elements arrive in random order. When one element arrives, we have to make an
immediate and irrevocable decision on whether to accept it or not. The set of accepted elements
must form an independent set in a predefined matroid. Our objective is to maximize the value
of the accepted elements. In this paper, we focus on the case that the valuation function is a
non-negative and monotonically non-decreasing submodular function.
We introduce a general algorithm for such submodular matroid secretary problems. In particular,
we obtain constant competitive algorithms for the cases of laminar matroids and transversal
matroids. Our algorithms can be further applied to any independent set system defined by the
intersection of a constant number of laminar matroids, while still achieving constant competitive
ratios. Notice that laminar matroids generalize uniform matroids and partition matroids.
On the other hand, when the underlying valuation function is linear, our algorithm achieves
a competitive ratio of 9.6 for laminar matroids, which significantly improves the previous result.