## Ruling out PTAS for graph min-bisection, dense k-subgraph, and bipartite clique

Venue: | SIAM J. Comput |

Citations: | 28 - 0 self |

### BibTeX

@ARTICLE{Khot_rulingout,

author = {Subhash Khot},

title = {Ruling out PTAS for graph min-bisection, dense k-subgraph, and bipartite clique},

journal = {SIAM J. Comput},

year = {},

volume = {36},

pages = {1025--1071}

}

### OpenURL

### Abstract

Abstract Assuming that NP 6 ` "ffl?0 BPTIME(2nffl), we show that Graph Min-Bisection, Dense kSubgraph and Bipartite Clique have no Polynomial Time Approximation Scheme (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 certain precise sense. Among the several new techniques we introduce, the most interesting one gives a way of certifying that a given polynomial belongs to a given linear subspace of polynomials. As is important for our purpose, the certificate itself happens to be another polynomial and it can be checked probabilistically by reading a constant number of its values.