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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 26 / No. 1: Twenty-Sixth AAAI Conference on Artificial Intelligence

Don’t Be Strict in Local Search!

March 8, 2023

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Authors

Serge Gaspers

Vienna University of Technology


Eun Jung Kim

LAMSADE-CNRS, Université de Paris-Dauphine


Sebastian Ordyniak

Vienna University of Technology


Saket Saurabh

The Institute of Mathematical Sciences


Stefan Szeider

Vienna University of Technology


DOI:

10.1609/aaai.v26i1.8128


Abstract:

Local Search is one of the fundamental approaches to combinatorial optimization and it is used throughout AI. Several local search algorithms are based on searching the k-exchange neighborhood. This is the set of solutions that can be obtained from the current solution by exchanging at most k elements. As a rule of thumb, the larger k is, the better are the chances of finding an improved solution. However, for inputs of size n, a naive brute-force search of the k-exchange neighborhood requires n(O(k)) time, which is not practical even for very small values of k. Fellows et al. (IJCAI 2009) studied whether this brute-force search is avoidable and gave positive and negative answers for several combinatorial problems. They used the notion of local search in a strict sense. That is, an improved solution needs to be found in the k-exchange neighborhood even if a global optimum can be found efficiently. In this paper we consider a natural relaxation of local search, called permissive local search (Marx and Schlotter, IWPEC 2009) and investigate whether it enhances the domain of tractable inputs. We exemplify this approach on a fundamental combinatorial problem, Vertex Cover. More precisely, we show that for a class of inputs, finding an optimum is hard, strict local search is hard, but permissive local search is tractable. We carry out this investigation in the framework of parameterized complexity.

Topics: AAAI

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HOW TO CITE:

Serge Gaspers|| Eun Jung Kim|| Sebastian Ordyniak|| Saket Saurabh|| Stefan Szeider Don’t Be Strict in Local Search! Proceedings of the AAAI Conference on Artificial Intelligence, 26 (2012) 486.

Serge Gaspers|| Eun Jung Kim|| Sebastian Ordyniak|| Saket Saurabh|| Stefan Szeider Don’t Be Strict in Local Search! AAAI 2012, 486.

Serge Gaspers|| Eun Jung Kim|| Sebastian Ordyniak|| Saket Saurabh|| Stefan Szeider (2012). Don’t Be Strict in Local Search!. Proceedings of the AAAI Conference on Artificial Intelligence, 26, 486.

Serge Gaspers|| Eun Jung Kim|| Sebastian Ordyniak|| Saket Saurabh|| Stefan Szeider. Don’t Be Strict in Local Search!. Proceedings of the AAAI Conference on Artificial Intelligence, 26 2012 p.486.

Serge Gaspers|| Eun Jung Kim|| Sebastian Ordyniak|| Saket Saurabh|| Stefan Szeider. 2012. Don’t Be Strict in Local Search!. "Proceedings of the AAAI Conference on Artificial Intelligence, 26". 486.

Serge Gaspers|| Eun Jung Kim|| Sebastian Ordyniak|| Saket Saurabh|| Stefan Szeider. (2012) "Don’t Be Strict in Local Search!", Proceedings of the AAAI Conference on Artificial Intelligence, 26, p.486

Serge Gaspers|| Eun Jung Kim|| Sebastian Ordyniak|| Saket Saurabh|| Stefan Szeider, "Don’t Be Strict in Local Search!", AAAI, p.486, 2012.

Serge Gaspers|| Eun Jung Kim|| Sebastian Ordyniak|| Saket Saurabh|| Stefan Szeider. "Don’t Be Strict in Local Search!". Proceedings of the AAAI Conference on Artificial Intelligence, 26, 2012, p.486.

Serge Gaspers|| Eun Jung Kim|| Sebastian Ordyniak|| Saket Saurabh|| Stefan Szeider. "Don’t Be Strict in Local Search!". Proceedings of the AAAI Conference on Artificial Intelligence, 26, (2012): 486.

Serge Gaspers|| Eun Jung Kim|| Sebastian Ordyniak|| Saket Saurabh|| Stefan Szeider. Don’t Be Strict in Local Search!. AAAI[Internet]. 2012[cited 2023]; 486.


ISSN: 2374-3468


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