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)|
|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