Giannakopoulos, Yiannis and Grosz, Alexander and Melissourgos, Themistoklis (2024) On the Smoothed Complexity of Combinatorial Local Search. In: The 51st EATCS International Colloquium on Automata, Languages, and Programming (ICALP), 2024-07-08 - 2024-07-12, Tallinn, Estonia.
Giannakopoulos, Yiannis and Grosz, Alexander and Melissourgos, Themistoklis (2024) On the Smoothed Complexity of Combinatorial Local Search. In: The 51st EATCS International Colloquium on Automata, Languages, and Programming (ICALP), 2024-07-08 - 2024-07-12, Tallinn, Estonia.
Giannakopoulos, Yiannis and Grosz, Alexander and Melissourgos, Themistoklis (2024) On the Smoothed Complexity of Combinatorial Local Search. In: The 51st EATCS International Colloquium on Automata, Languages, and Programming (ICALP), 2024-07-08 - 2024-07-12, Tallinn, Estonia.
Abstract
We propose a unifying framework for smoothed analysis of combinatorial local optimization problems, and show how a diverse selection of problems within the complexity class PLS can be cast within this model. This abstraction allows us to identify key structural properties, and corresponding parameters, that determine the smoothed running time of local search dynamics. We formalize this via a black-box tool that provides concrete bounds on the expected maximum number of steps needed until local search reaches an exact local optimum. This bound is particularly strong, in the sense that it holds for any starting feasible solution, any choice of pivoting rule, and does not rely on the choice of specific noise distributions that are applied on the input, but it is parameterized by just a global upper bound ϕ on the probability density. The power of this tool can be demonstrated by instantiating it for various PLS-hard problems of interest to derive efficient smoothed running times (as a function of ϕ and the input size). Most notably, we focus on the important local optimization problem of finding pure Nash equilibria in Congestion Games, that has not been studied before from a smoothed analysis perspective. Specifically, we propose novel smoothed analysis models for general and Network Congestion Games, under various representations, including explicit, step-function, and polynomial resource latencies. We study PLS-hard instances of these problems and show that their standard local search algorithms run in polynomial smoothed time. Further applications of our framework to a wide range of additional combinatorial problems can be found in the full version of our paper.
Item Type: | Conference or Workshop Item (Paper) |
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Additional Information: | Published proceedings: _not provided_ |
Uncontrolled Keywords: | Smoothed Analysis; local search; better-response dynamics; PLS-hardness; combinatorial local optimization; congestion games; pure Nash equilibria |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Computer Science and Electronic Engineering, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 10 Jul 2024 09:15 |
Last Modified: | 19 Jul 2024 03:23 |
URI: | http://repository.essex.ac.uk/id/eprint/38402 |
Available files
Filename: LIPIcs.ICALP.2024.72.pdf
Licence: Creative Commons: Attribution 4.0