Fast algorithms for parametric scheduling come from extensions to parametric maximum flow
Fast algorithms for parametric scheduling come from extensions to parametric maximum flow
复制标题
参数化调度的快速算法来自于参数化最大流的扩展
DOI：
--
复制
发表时间：
1996
期刊：
影响因子：
--
通讯作者：
S. McCormick
中科院分区：
文献类型：
--
作者：
J. Yates;W. Orlikowski;Kazuo Okamura;S. McCormick
Chen（1994）开发了一个有吸引力的变体，即通过释放日期和临时日期进行独立的工作，这在实践中通常可以付费减少工作的两个参数最大流量问题。 . Serafini (1996) considers scheduling independent jobs with due dates on multiple machines, where jobs can be split among machines so that pieces of a single job can execute in parallel. Minimizing the maximum tardiness again gives a parametric max flow problem. A third problem这种类型的棒球队在一个赛季中可能会输掉多少场比赛，而不会首先被淘汰（假设其他团队最佳地分配了胜利和损失）。 Brumelle等。 - Gallo等人（GGT）的最大流量方法（1989年）。应用程序。
Chen (1994) develops an attractive variant of the classical problem of preemptively scheduling independent jobs with release dates and due dates. Chen suggests that in practice one can often pay to reduce the processing requirement of a job. This leads to two parametric max flow problems. Serafini (1996) considers scheduling independent jobs with due dates on multiple machines, where jobs can be split among machines so that pieces of a single job can execute in parallel. Minimizing the maximum tardiness again gives a parametric max flow problem. A third problem of this type is deciding how many more games a baseball team can lose part way through a season without being eliminated from finishing first (assuming a best possible distribution of wins and losses by other teams). A fourth such problem is an extended selection problem of Brumelle et al. (1995a), where we want to discount the costs of “tree-structured” tools as little as possible to be able to process all jobs at a profit. It is tempting to try to solve these problems with the parametric push-relabel max flow methods of Gallo et al. (GGT) (1989). However, all these applications appear to violate the conditions necessary to apply GGT. We extend GGT in three ways that allow it to be applied to all four of the above applications. We also consider some other applications where these ideas apply. Our extensions to GGT yield faster algorithms for all these applications.