Semidefinite Programming and Approximation Algorithms: A Survey

• Published in: Algorithms and Computation pp. 6 - 9
• Main Author: Arora, Sanjeev
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• ISBN: 3642255906; 9783642255908
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-25591-5_2

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.