Smoothed Performance Guarantees for Local Search
We study popular local search and greedy algorithms for scheduling. The performance guarantee of these algorithms is well understood, but the worst-case lower bounds seem somewhat contrived and it is questionable if they arise in practical applications. To find out how robust these bounds are, we study the algorithms in the framework of smoothed analysis, in which instances are subject to some degree of random noise.
While the lower bounds for all scheduling variants with restricted machines are rather robust, we find out that the bounds are fragile for unrestricted machines. In particular, we show that the smoothed performance guarantee of the jump and the lex-jump algorithm are (in contrast to the worst case) independent of the number of machines. They are Θ(φ) and Θ(logφ), respectively, where 1/φ is a parameter measuring the magnitude of the perturbation. The latter immediately implies that also the smoothed price of anarchy is Θ(logφ) for routing games on parallel links. Additionally we show that for unrestricted machines also the greedy list scheduling algorithm has an approximation guarantee of Θ(logφ).
Unable to display preview. Download preview PDF.
- 6.Brunsch, T., Röglin, H., Rutten, C., Vredeveld, T.: Smoothed Performance Guarantees for Local Search. ArXiv e-prints (May 2011), http://arxiv.org/abs/1105.2686
- 8.Czumaj, A., Vöcking, B.: Tight bounds for worst-case equilibria. Transactions on Algorithms ACM 3(1) (2007)Google Scholar
- 9.Englert, M., Röglin, H., Vöcking, B.: Worst case and probabilistic analysis of the 2-opt algorithm for the TSP. In: Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1295–1304 (2007)Google Scholar
- 14.Hoefer, M., Souza, A.: Tradeoffs and average-case equilibria in selfish routing. ACM Transactions on Computation Theory 2(1), article 2 (2010)Google Scholar