## Abstract

We present a simple construction and analysis of an Ω(log logN) integrality gap for the well-known Sparsest Cut semi-definite program (SDP). This holds for the uniform demands version (i.e. edge expansion). The same quantitative gap was proved earlier by Devanur, Khot, Saket, and Vishnoi [STOC 2006], following an integrality gap for non-uniform demands due to Khot and Vishnoi [FOCS 2005]. These previous constructions involve a complicated SDP solution and analysis, while our gap instance, vector solution, and analysis are somewhat simpler and more intuitive. Furthermore, our approach is rather general, and provides a variety of different gap examples derived from quotients of the hypercube. It also illustrates why the lower bound is stuck at Ω(log logN), and why new ideas are needed in order to derive stronger examples.

Original language | English (US) |
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Title of host publication | Theory of Computing 2011 - Proceedings of the 17th Computing |

Subtitle of host publication | The Australasian Theory Symposium, CATS 2011 |

Pages | 11-21 |

Number of pages | 11 |

Volume | 119 |

State | Published - 2011 |

Externally published | Yes |

Event | Theory of Computing 2011 - 17th Computing: The Australasian Theory Symposium, CATS 2011 - Perth, WA, Australia Duration: Jan 17 2011 → Jan 20 2011 |

### Other

Other | Theory of Computing 2011 - 17th Computing: The Australasian Theory Symposium, CATS 2011 |
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Country/Territory | Australia |

City | Perth, WA |

Period | 1/17/11 → 1/20/11 |

## Keywords

- Integrality gap
- Semidefinite programming
- Sparsest Cut

## ASJC Scopus subject areas

- Computer Networks and Communications
- Computer Science Applications
- Hardware and Architecture
- Information Systems
- Software