1. Bounds for the Convergence Time of Local Search in Scheduling Problems
- Author
-
Michael Etscheid, Tobias Brunsch, and Heiko Röglin
- Subjects
Machine scheduling ,Mathematical optimization ,021103 operations research ,Job shop scheduling ,Computer science ,0211 other engineering and technologies ,Smoothed analysis ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Scheduling (computing) ,Computer Science::Performance ,010201 computation theory & mathematics ,Best response ,Price of anarchy ,Computer Science::Operating Systems ,Computer Science::Distributed, Parallel, and Cluster Computing - Abstract
We study the convergence time of local search for a standard machine scheduling problem in which jobs are assigned to identical or related machines. Local search corresponds to the best response dynamics that arises when jobs selfishly try to minimize their costs. We assume that each machine runs a coordination mechanism that determines the order of execution of jobs assigned to it. We obtain various new polynomial and pseudo-polynomial bounds for the well-studied coordination mechanisms Makespan and Shortest-Job-First, using worst-case and smoothed analysis. We also introduce a natural coordination mechanism FIFO, which takes into account the order in which jobs arrive at a machine, and study both its impact on the convergence time and its price of anarchy.
- Published
- 2016