@inproceedings{62fc1074ca5941419d8544298e893306,

title = "An O(log n)-competitive algorithm for online machine minimization",

abstract = "We consider the online machine minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on a minimum number of machines. Our main result is a general O(log m)-competitive algorithm for the online problem, where m is the optimal number of machines used in an offline solution. This is the first improvement on an intriguing problem in nearly two decades. To date, the best known result is a O(log(pmax/pmin))-competitive algorithm by Phillips et al. (STOC 1997) that depends on the ratio of maximum and minimum job sizes, pmax and pmin. Even for m = 2 no better algorithm was known. Our algorithm is in this case constant-competitive. When applied to laminar or agreeable instances, our algorithm achieves a competitive ratio of O(1) even independently of m. The following two key components lead to our new result. Firstly, we derive a new lower bound on the optimum value that relates the laxity and the number of jobs with intersecting time windows. Then, we design a new algorithm that is tailored to this lower bound and balances the delay of jobs by taking the number of currently running jobs into account.",

author = "Lin Chen and Nicole Megow and Kevin Schewior",

year = "2016",

language = "English",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery",

pages = "155--163",

editor = "Robert Krauthgamer",

booktitle = "27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016",

note = "null ; Conference date: 10-01-2016 Through 12-01-2016",

}