Abstract

Smoothed Complexity Theory ¨ MARKUS BLASER, Saarland University BODO MANTHEY, University of Twente Smoothed analysis is a new way of analyzing algorithms introduced by Spielman and Teng. Classical methods like worst-case or average-case analysis have accompanying complexity classes, such as P and Avg-P, respectively. Whereas worst-case or average-case analysis give us a means to talk about the running time of a particular algorithm, complexity classes allow us to talk about the inherent difficulty of problems. Smoothed analysis is a hybrid of worst-case and average-case analysis and compensates some of their drawbacks. Despite its success for the analysis of single algorithms and problems, there is no embedding of smoothed analysis into computational complexity theory, which is necessary to classify problems according to their intrinsic difficulty. We propose a framework for smoothed complexity theory, define the relevant classes, and prove some first hardness results (of bounded halting and tiling) and tractability results (binary optimization problems, graph coloring, satisfiability) within this framework. Categories and Subject Descriptors: F.1.3 [Computation by Abstract Devices]: Complexity Measures and Classes; F.2.0 [Analysis of Algorithms and Problem Complexity]: General General Terms: Theory Additional Key Words and Phrases: Smoothed analysis, computational complexity, average-case complexity ACM Reference Format: ¨