Towards Average-Case Complexity Analysis of NP Optimization Problems

For the worst-case complexity measure, if P = NP, then P = OptP, i.e., all NP optimization problems are polynomial-time solvable. On the other hand, it is not clear whether a similar relation holds when considering average-case complexity. We investigate the relationship between the complexity of NP decision problems and that of NP optimization problems under polynomial-time computable distributions, and study what makes them (seemingly) di erent. It is shown that the di erence between PNP tt -samplable and PNP-samplable distributions is crucial.

• Type: Conference
• Year: 1995
• Where: COCO
• Authors: Rainer Schuler, Osamu Watanabe
• Keywords: Algorithms, COCO 1995, NP Decision Problems, NP Optimization Problems, Worst-case Complexity Measure