Approximate Local Search in Combinatorial Optimization

James B. Orlin, Abraham P. Punnen and Andreas S. Schulz

No 4325-03, Working papers from Massachusetts Institute of Technology (MIT), Sloan School of Management

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

Keywords: Local Search; Neighborhood Search; Approximation Algorithms; Computational Complexity; Combinatorial Optimization; 0/1-Integer Programming (search for similar items in EconPapers)
Date: 2003-08-15
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