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Reducibility and Completeness
, 1998
"... This material was written for Chapter 28 of the CRC Handbook of Algorithms and Theory of Computation, edited by Mikhail Atallah. 1 Introduction There is little doubt that the notion of reducibility is the most useful tool that complexity theory has delivered to the rest of the computer science com ..."
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This material was written for Chapter 28 of the CRC Handbook of Algorithms and Theory of Computation, edited by Mikhail Atallah. 1 Introduction There is little doubt that the notion of reducibility is the most useful tool that complexity theory has delivered to the rest of the computer science community. For most computational problems that arise in realworld applications, such as the Traveling Salesperson Problem, we still know little about their deterministic time or space complexity. We cannot now tell whether classes such as P and NP are distinct. And yet, even without such hard knowledge, it has been useful in practice to take some new problem A whose complexity needs to be analyzed, and announce that A has roughly the same complexity as Traveling Salesperson, by exhibiting efficient ways of reducing each problem to the other. Thus we can say a lot about problems being equivalent in complexity to each other, even if we cannot pinpoint what that complexity is. One reason this ...