Approximate Local Search in Combinatorial Optimization
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Author(s)
Orlin, James B.
Punnen, Abraham P.
Schulz, Andreas S.
Date Issued
August 15, 2003
Series/Report no.
MIT Sloan School of Management Working Paper;4325-03
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
Subjects
Local Search
Neighborhood Search
Approximation Algorithms
Computational Complexity
Combinatorial Optimization
0/1-Integer Programming
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