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 ε-local optimality and show that an ε-local optimum can be identified in time polynomial in the problem size and 1/ε whenever the corresponding neighborhood can be searched in polynomial time, for ε > 0. If the neighborhood can be searched in polynomial time for a δ-local optimum, a variation of our main algorithm produces a (δ + ε)-local optimum in time polynomial in the problem size and 1/ε. As a consequence, a combinatorial optimization problem has a fully polynomial-time approximation scheme if and only if the problem of determining a better solution - the so-called augmentation problem - has a fully polynomial-time approximation scheme.
Originalsprache | Englisch |
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Seiten | 580-589 |
Seitenumfang | 10 |
Publikationsstatus | Veröffentlicht - 2004 |
Extern publiziert | Ja |
Veranstaltung | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA., USA/Vereinigte Staaten Dauer: 11 Jan. 2004 → 13 Jan. 2004 |
Konferenz
Konferenz | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms |
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Land/Gebiet | USA/Vereinigte Staaten |
Ort | New Orleans, LA. |
Zeitraum | 11/01/04 → 13/01/04 |