## Abstract

Assuming that NP ⊄ ∩ _{ε>0} BPTIME(2 ^{nε}), we show that Graph Min-Bisection, Densest Subgraph and Bipartite Clique have no PTAS. We give a reduction from the Minimum Distance of Code Problem (MDC). Starting with an instance of MDC, we build a Quasi-random PCP that suffices to prove the desired inapproximability results. In a Quasi-random PCP, the query pattern of the verifier looks random in some precise sense. Among the several new techniques introduced, we give a way of certifying that a given polynomial belongs to a given subspace of polynomials. As is important for our purpose, the certificate itself happens to be another polynomial and it can be checked by reading a constant number of its values.

Original language | English (US) |
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Pages (from-to) | 136-145 |

Number of pages | 10 |

Journal | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |

State | Published - 2004 |

Event | Proceedings - 45th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2004 - Rome, Italy Duration: Oct 17 2004 → Oct 19 2004 |

## ASJC Scopus subject areas

- General Engineering