An efficient polynomial time approximation scheme for load balancing on uniformly related machines

• 成果类型: Article
• 署名作者: Epstein, Leah; Levin, Asaf
• 署名单位: University of Haifa; Technion Israel Institute of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0706-4
• 发表日期: 2014
• 页码: 1-23
• 关键词: algorithms; bounds; processors; number

摘要

We consider basic problems of non-preemptive scheduling on uniformly related machines. For a given schedule, defined by a partition of the jobs into m subsets corresponding to the m machines, denotes the completion time of machine i. Our goal is to find a schedule that minimizes or maximizes for a fixed value of p such that . For the minimization problem is equivalent to the well-known problem of minimizing the norm of the vector of the completion times of the machines, and for , the maximization problem is of interest. Our main result is an efficient polynomial time approximation scheme (EPTAS) for each one of these problems. Our schemes use a non-standard application of the so-called shifting technique. We focus on the work (total size of jobs) assigned to each machine and introduce intervals of work that are forbidden. These intervals are defined so that the resulting effect on the goal function is sufficiently small. This allows the partition of the problem into sub-problems (with subsets of machines and jobs) whose solutions are combined into the final solution using dynamic programming. Our results are the first EPTAS's for this natural class of load balancing problems.