### Abstract

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.

Original language | English (US) |
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Title of host publication | Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings |

Pages | 6-9 |

Number of pages | 4 |

DOIs | |

State | Published - Dec 26 2011 |

Event | 22nd International Symposium on Algorithms and Computation, ISAAC 2011 - Yokohama, Japan Duration: Dec 5 2011 → Dec 8 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7074 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 22nd International Symposium on Algorithms and Computation, ISAAC 2011 |
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Country | Japan |

City | Yokohama |

Period | 12/5/11 → 12/8/11 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Arora, S. (2011). Semidefinite programming and approximation algorithms: A survey. In

*Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings*(pp. 6-9). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS). https://doi.org/10.1007/978-3-642-25591-5_2