The 50th Annual Symposium on Foundations of Computer Science (FOCS) was held a couple of weeks ago in Atlanta. This conference (along with STOC and SODA) is one of the the major venues for recent advances in algorithm design and computational complexity. Computation is now a major ingredient of almost any field of science, without which many of the recent achievements would not have happened (e.g., Human Genome decoding). As the 50th anniversary of FOCS, this event was a landmark in the history of foundations of computer science. Below, we give a quick report of some highlights from this event and our research contribution:

- In a special one-day workshop before the conference, four pioneer researchers of theoretical computer science talked about historical, contemporary, and future research directions. Richard Karp gave an interesting survey on "Great Algorithms," where he discussed algorithms such as the simplex method for linear programming and fast matrix multiplication; he gave examples of algorithms with high impact on our daily lives, as well as algorithms that changed our way of thinking about computation. As an example of an algorithm with great impact on our lives, he gave the PageRank algorithm designed by Larry and Sergey at Google. Mihalis Yannakakis discussed the recent impact of studying game theory and equilibria from a computational perspective and discussed the relationships between the complexity classes PLS, FIXP, and PPAD. In particular he discussed completeness of computing pure and mixed Nash equilibria for PLS, and for FIXP and PPAD respectively. Noga Alon gave a technical talk about efficient routing on expander graphs, and presented a clever combinatorial algorithm to route demand between multiple pairs of nodes in an online fashion. Finally, Manuel Blum gave an entertaining and mind-stimulating talk about the potential contribution of computer science to the study of human consciousness, educating the community on the notion of "Global Workspace Theory."
- The conference program included papers in areas related to algorithm and data structure design, approximation and optimization, computational complexity, learning theory, cryptography, quantum computing, and computational economics. The best student paper awards went to Alexander Shrstov and Jonah Sherman for their papers "The intersection of two halfspaces has high threshold degree" and "Breaking the multicommodity flow barrier for O(sqrt(log n))-approximations to sparsest cut." The program included many interesting results like the polynomial-time smoothed analysis of the k-means clustering algorithm (by David Arthur, Bodo Manthey and Heiko Roeglin), and a stronger version of Azuma's concentration inequality used to show optimal bin-packing bounds (by Ravi Kannan). The former paper studies a variant of the well-known k-means algorithm that works well in practice, but whose worst-case running time can be exponential. By analyzing this algorithm in the smoothed analysis framework, the paper gives a new explanation for the success of the k-means algorithm in practice.
- We presented our recent result about online stochastic matching in which we improve the approximation factor of computing the maximum cardinality matching in an online stochastic setting. The original motivation for this work is online ad allocation which was discussed in a previous blog post. In this algorithm, using our prior on the input (or our historical stochastic information), we compute two disjoint solutions to an instance that we expect to happen; then online, we try one solution first, and if it fails, we try the the other solution. The algorithm is inspired by the idea of "power of two choices," which has proved useful in online load balancing and congestion control. Using this method, we improve the worst-case guarantee of the online algorithm past the notorious barrier of 1-1/e. We hope that employing this idea and our technique for online stochastic optimization will find other applications in related stochastic resource allocation problems.