多处理机调度LD算法的逼近比及Coffman-Sethi猜想
Approximation Ratio of LD Algorithm for Multi-Processor Scheduling and the Coffman-Sethi Conjecture
摘要：
Coffman和Sethi提出了一种启发式算法，称为LD，多处理器调度，以最小化最大完工时间超过流量时间最优的计划。LD算法是一个非常著名的列表调度算法，最长处理时间（LPT）列表调度，我们的双标准调度问题的自然扩展。1976年，Coffman和Sethi证明了LD算法的最坏性能界是：$\frac{5}{4} - \frac{3}{4(4m-1)}$，其中m是机器数。本文利用作者和Huang在2013年的一些工作，揭示了该猜想的各种假定极小反例的一些非常强的组合性质，给出了该猜想的一个证明.该问题和LD算法与其他基本问题（如装配线平衡问题）和其他算法有联系。
英文摘要：
Coffman and Sethi proposed a heuristic algorithm, called LD, for multi-processor scheduling, to minimize makespan over flowtime-optimal schedules. LD algorithm is a natural extension of a very well-known list scheduling algorithm, Longest Processing Time (LPT) list scheduling, to our bicriteria scheduling problem. Moreover, in 1976, Coffman and Sethi conjectured that LD algorithm has precisely the following worst-case performance bound: $\frac{5}{4} - \frac{3}{4(4m-1)}$, where m is the number of machines. In this paper, utilizing some recent work by the authors and Huang, from 2013, which exposed some very strong combinatorial properties of various presumed minimal counterexamples to the conjecture, we provide a proof of this conjecture. The problem and the LD algorithm have connections to other fundamental problems (such as the assembly line-balancing problem) and to other algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
