Free Bits, PCPs and Non-Approximability - Towards Tight Results

This paper continues the investigation of the connection between probabilistically checkable proofs PCPs the approximability of NP-optimization problems. The emphasis is on proving tight non-approximability results via consideration of measures like the free bit complexity" and the amortized free bit complexity" of proof systems. The rst 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 which has amortized free bit complexity of 2+ , implying that approximating Max Clique within N 1 3 , , and approximating the Chromatic Number within N 1 5 , , are hard assuming NP 6= coRP, for any 0. We also derive the rst explicit and reasonable constant hardness factors for Min Vertex Cover, Max2SAT, and Max Cut, and improve the hardness factor for Max3SAT. We note that our non-approximability factors for MaxSNP problems are appreciably close to the values known to be achievable by polynomial t...

• Type: Conference
• Year: 1995
• Where: FOCS
• Authors: Mihir Bellare, Oded Goldreich, Madhu Sudan
• Keywords: Amortized Free Bit, FOCS 1995, Free Bit Complexity, Max Clique, Theoretical Computer Science