Coffman and Sethi proposed a heuristic algorithm, called LD (Longest Decreasing), for multi-processor scheduling, to minimize makespan over flowtime-optimal schedules. The LD algorithm is an extension of a very well-known list scheduling algorithm, Longest Processing Time (LPT) list scheduling, to this bicriteria scheduling problem. Coffman and Sethi conjectured (in 1976) that the LD algorithm has the following precise 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 (2016), 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 some other fundamental problems (such as the assembly line-balancing problem) and algorithms.

Coffman和Sethi提出了一种启发式算法，称为LD（最长递减），用于多处理器调度，以最大程度地缩短了整个运行时间最优调度的制造时间。LD算法是对此双标准调度问题的一种非常著名的列表调度算法（最长处理时间（LPT）列表调度）的扩展。Coffman和Sethi（在1976年）推测LD算法具有以下精确的最坏情况下的性能界限：$\frac{5}{4}-\frac{3}{4（4米-\mathrm{1个}）}$，其中m是机器数。在本文中，利用作者和Huang（2016）的一些最新工作，这些工作向猜想暴露了各种假定的最小反例的非常强的组合特性，我们提供了这一猜想的证明。该问题和LD算法与其他一些基本问题（例如装配线平衡问题）和算法有关。