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The Approximability of NPhard Problems Sanjeev Arora #

Summary: The Approximability of NP­hard Problems
Sanjeev Arora #
Princeton University
1 Introduction
Many problems in combinatorial optimization are
NP­hard (see [60]). This has forced researchers to
explore techniques for dealing with NP­completeness.
Some have considered algorithms that solve ``typi­
cal'' or ``average'' instances instead of worst­case in­
stances [86, 100]. In practice, however, identifying
``typical'' instances is not easy. Other researchers
have tried to design approximation algorithms. An
algorithm achieves an approximation ratio # for a
maximization problem if, for every instance, it pro­
duces a solution of value at least OPT/#, where
OPT is the value of the optimal solution. (For a
minimization problem, achieving a ratio # involves
finding a solution of cost at most #OPT .) Note
that the approximation ratio is # 1 by definition.
After twenty­five years of research, approxima­


Source: Arora, Sanjeev - Department of Computer Science, Princeton University


Collections: Computer Technologies and Information Sciences