Local Search: Complexity and Approximation

Abstract : This chapter sets up a formal framework for local search and provides a certain number of useful definitions for the rest of this work. It gives a few examples of combinatorial optimization problems with the neighborhoods classically used. The chapter devotes the complexity class polynomial-time local search (PLS). It examines in more detail the complexity of the standard local search algorithm. On the subject of the quality of the solutions, the chapter looks at a restrictive theorem regarding the quality of the solutions provided by a local search algorithm for NP-hard and strongly NP-hard problems. It describes several classical combinatorial optimization problems for which local search algorithms provide solutions that are (1 + ε{lunate})-approximate with regard to a global optimum. Furthermore, despite its use in solving NP-hard problems, local search is also used in other domains such as game theory. © ISTE Ltd 2014. All rights reserved.
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Submitted on : Tuesday, December 17, 2013 - 9:34:29 AM
Last modification on : Tuesday, January 14, 2020 - 1:36:09 PM

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Eric Angel, Petros Christopoulos, Vassilis Zissimopoulos. Local Search: Complexity and Approximation. Vangelis Th. Paschos. Paradigms of Combinatorial Optimization: Problems and New Approaches: 2nd Edition, John Wiley & Sons, Inc., pp.435--471, 2014, 978-184821148-3. ⟨10.1002/9781118600207.ch14⟩. ⟨hal-00919596⟩

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