Computational bounds on randomized algorithms for online bin stretching (2405.19071v1)
Abstract: A frequently studied performance measure in online optimization is competitive analysis. It corresponds to the worst-case ratio, over all possible inputs of an algorithm, between the performance of the algorithm and the optimal offline performance. However, this analysis may be too pessimistic to give valuable insight on a problem. Several workarounds exist, such as randomized algorithms. This paper aims to propose computational methods to construct randomized algorithms and to bound their performance on the classical online bin stretching problem. A game theory method is adapted to construct lower bounds on the performance of randomized online algorithms via linear programming. Another computational method is then proposed to construct randomized algorithms which perform better than the best deterministic algorithms known. Finally, another lower bound method for a restricted class of randomized algorithm for this problem is proposed.
- Online computation and competitive analysis / Allan Borodin, Ran El-Yaniv. Cambridge University Press, Cambridge, 1998.
- Robert J . Aumann. 28. Mixed and Behavior Strategies in Infinite Extensive Games, pages 627–650. Princeton University Press, Princeton, 1964.
- On-line bin-stretching. Theoretical Computer Science, 268(1):17–41, 2001.
- On the power of randomization in on-line algorithms. Algorithmica, 11(1):2–14, Jan 1994.
- Discovering and certifying lower bounds for the online bin stretching problem. Theoretical Computer Science, 938:1–15, 2022.
- Michael Gabay. High-multiplicity Scheduling and Packing Problems : Theory and Applications. Theses, Université de Grenoble, October 2014.
- Improved lower bounds for the online bin stretching problem. 4OR, 15(2):183–199, Jun 2017.
- H. W. Kuhn. Extensive games and the problem of information. In Contributions to the theory of games. Volume II, Annals of Mathematics Studies, pages 245–266. Princeton University Press, Princeton, N. J, 1953.
- Online bin stretching lower bounds: Improved search of computational proofs, 2022. https://arxiv.org/abs/2207.04931v2.
- Matej Lieskovský. Better algorithms for online bin stretching via computer search, 2022. https://arxiv.org/abs/2201.12393.
- M.P. Renault and A. Rosén. Lower and Upper Bounds for Online Algorithms with Advice. Lille thèses. 2014.
- Bernhard von Stengel. Equilibrium computation for two-player games in strategic and extensive form. In Algorithmic Game Theory, chapter 3, pages 73–78. Cambridge University Press, 2007.