Approximation algorithms for NP-hard problems
Approximation algorithms
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
Integrality Gaps for Strong SDP Relaxations of UNIQUE GAMES
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
On the Unique Games Conjecture (Invited Survey)
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
The Design of Approximation Algorithms
The Design of Approximation Algorithms
Rounding Semidefinite Programming Hierarchies via Global Correlation
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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Computing approximate solutions for NP-hard problems is an important research endeavor. Since the work of Goemans-Williamson in 1993, semidefinite programming (a form of convex programming in which the variables are vector inner products) has been used to design the current best approximation algorithms for problems such as MAX-CUT, MAX-3SAT, SPARSEST CUT, GRAPH COLORING, etc. The talk will survey this area, as well as its fascinating connections with topics such as geometric embeddings of metric spaces, and Khot's unique games conjecture. The talk will be self-contained.