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Smoothed Complexity Theory

Published:11 May 2015Publication History
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Abstract

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.

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      • Published in

        cover image ACM Transactions on Computation Theory
        ACM Transactions on Computation Theory  Volume 7, Issue 2
        May 2015
        101 pages
        ISSN:1942-3454
        EISSN:1942-3462
        DOI:10.1145/2775140
        Issue’s Table of Contents

        Copyright © 2015 ACM

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 11 May 2015
        • Accepted: 1 November 2014
        • Revised: 1 March 2014
        • Received: 1 March 2013
        Published in toct Volume 7, Issue 2

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