Instructor : Nikhil Bansal Scribe : Seeun

Instructor : Nikhil Bansal Scribe : Yiqun Chen 1 The general MWU setting

We can view the prediction problem considered previously as the following: We have m experts and we maintain a vector pt (probability distribution) over the experts and at each round nature reveals loss `t ∈ {0, 1}n. We incur expected loss pt · `t and therefore cumulative loss ∑T t=1 pt· `t. Moreover, in randomized weighted majority we set wi(t+1) = wi(t)(1− ) if i makes an mistake and we choos...

Instructor : Nikhil Bansal Scribe : Tim Oosterwijk 1 Independent set problem for bipartite graphs

Last lecture, we started a discussion about the independent set (“stable set”) problem. For a given graph G = (V,E), an independent set is a subset of vertices that are mutually non-adjacent. The independent set problem asks to find the maximum cardinality of such a vertex set. We saw this problem is notoriously NP-hard: it is NP-hard to approximate within a factor n1−ε for any ε > 0. However, ...

Instructor : Nikhil Bansal Scribe :

In this lecture we will be looking into the secretary problem, and an interesting variation of the problem called the incentive comparable secretary problem. For both of these problems we will show how they can be solved though a correspondence between all possible strategies and the feasible solution space to a linear program. In both cases this will allow us to derive an algorithm and prove t...

LP-Based Robust Algorithms for Noisy Minor-Free and Bounded Treewidth Graphs

We give a general approach to solve various optimization problems on noisy minor-free and bounded treewidth graphs, where some fraction of the edges have been corrupted adversarially. Our results are motivated by a previous work of Magen and Moharrami, who gave a (1 + )approximate estimation algorithm for the independent set problem on noisy planar graphs, but left open the question of how to a...

Instructor : Chandra Chekuri Scribe : Rachit Agarwal