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Approximate Local Search in Combinatorial Optimization

Author

Listed:
  • Orlin, James B.
  • Punnen, Abraham P.
  • Schulz, Andreas S.

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

Suggested Citation

  • Orlin, James B. & Punnen, Abraham P. & Schulz, Andreas S., 2003. "Approximate Local Search in Combinatorial Optimization," Working papers 4325-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    • Handle: RePEc:mit:sloanp:3539
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    File URL: http://hdl.handle.net/1721.1/3539
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