Semidefinite Programming and Approximation Algorithms: A Survey

Computing approximately optimal solutions is an attractive way to cope with NP-hard optimization problems. In the past decade or so, semidefinite programming or SDP (a form of convex optimization that generalizes linear programming) has emerged as a powerful tool for designing such algorithms, and the last few years have seen a profusion of results (worst-case algorithms, average case algorithms, impossibility results, etc).

[1]  Prasad Raghavendra,et al.  Integrality Gaps for Strong SDP Relaxations of UNIQUE GAMES , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[2]  David P. Williamson,et al.  The Design of Approximation Algorithms , 2011 .

[3]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[4]  Subhash Khot On the Unique Games Conjecture (Invited Survey) , 2010, Computational Complexity Conference.

[5]  Luca Trevisan,et al.  Inapproximability of Combinatorial Optimization Problems , 2004, Electron. Colloquium Comput. Complex..

[6]  Sanjeev Arora,et al.  Computational Complexity: A Modern Approach , 2009 .

[7]  Sanjeev Arora,et al.  Euclidean distortion and the sparsest cut , 2005, Symposium on the Theory of Computing.

[8]  M. Goemans Semidefinite programming and combinatorial optimization , 1998 .

[9]  Anupam Gupta,et al.  Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut , 2005, SODA '05.

[10]  David P. Williamson,et al.  Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming , 1995, JACM.

[11]  Carsten Lund,et al.  Hardness of approximations , 1996 .

[12]  Aleksandar Nikolov,et al.  Limits of Approximation Algorithms: PCPs and Unique Games (DIMACS Tutorial Lecture Notes) , 2010, ArXiv.

[13]  F. Rendl Semidefinite programming and combinatorial optimization , 1999 .

[14]  Prasad Raghavendra,et al.  Rounding Semidefinite Programming Hierarchies via Global Correlation , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.