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Approximate Local Search in Combinatorial Optimization

Author(s)
Orlin, James B.; Punnen, Abraham P.; Schulz, Andreas S.
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Abstract
Local search algorithms for combinatorial optimization problems are in general of pseudopolynomial running time and polynomial-time algorithms are often not known for finding locally optimal solutions for NP-hard optimization problems. We introduce the concept of epsilon-local optimality and show that an epsilon-local optimum can be identified in time polynomial in the problem size and 1/epsilon whenever the corresponding neighborhood can be searched in polynomial time, for epsilon > 0. If the neighborhood can be searched in polynomial time for a delta-local optimum, we present an algorithm that produces a (delta+epsilon)-local optimum in time polynomial in the problem size and 1/epsilon. As a consequence, a combinatorial optimization problem has a fully polynomial-time approximation scheme if and only if it has a fully polynomial-time augmentation schem
Date issued
2003-08-15
URI
http://hdl.handle.net/1721.1/3539
Series/Report no.
MIT Sloan School of Management Working Paper;4325-03
Keywords
Local Search, Neighborhood Search, Approximation Algorithms, Computational Complexity, Combinatorial Optimization, 0/1-Integer Programming

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