Free Bits, PCPs, and Nonapproximability-Towards Tight Results

This paper continues the investigation of the connection between probabilistically checkable proofs (PCPs) and the approximability of NP-optimization problems. The emphasis is on proving tight nonapproximability results via consideration of measures such as the “free-bit complexity” and the “amortized free-bit complexity” of proof systems. The first part of the paper presents a collection of new proof systems based on a new errorcorrecting code called the long code. We provide a proof system that has amortized free-bit complexity of 2 + , implying that approximating MaxClique within N 1 3 − , and approximating the Chromatic Number within N 1 5 − , are hard, assuming NP = coRP, for any > 0. We also derive the first explicit and reasonable constant hardness factors for Min Vertex Cover, Max2SAT, and Max Cut, and we improve the hardness factor for Max3SAT. We note that our nonapproximability factors for MaxSNP problems are appreciably close to the values known to be achie...

• Type: Journal
• Year: 1998
• Where: SIAMCOMP
• Authors: Mihir Bellare, Oded Goldreich, Madhu Sudan
• Keywords: Free-bit Complexity, Probabilistically Checkable Proofs, Proof Systems, SIAMCOMP 1998