An optimal online algorithm for the parallel-batch scheduling with job processing time compatibilities

被引：8
|
作者：
Fu, Ruyan [1 ]
Tian, Ji [1 ]
Li, Shisheng [2 ]
Yuan, Jinjiang [3 ]
机构：
[1] China Univ Min & Technol, Sch Math, Xuzhou 221116, Jiangsu, Peoples R China
[2] Zhongyuan Univ Technol, Dept Informat & Computat Sci, Zhengzhou 450007, Henan, Peoples R China
[3] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China
来源：
JOURNAL OF COMBINATORIAL OPTIMIZATION | 2017年 / 34卷 / 04期
关键词：
Online scheduling; Batch machine; Compatibility; Competitive ratio; MINIMIZE MAKESPAN; FAMILY JOBS; MACHINE; SEMICONDUCTOR;
D O I：
10.1007/s10878-017-0139-8
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
We consider the online (over time) scheduling on a single unbounded parallel-batch machine with job processing time compatibilities to minimize makespan. In the problem, a constant alpha > 0 is given in advance. Each job J(j) has a normal processing time p(j). Two jobs J(i) and J(j) are compatible if max{p(i), p(j)} <= (1 + alpha) . min{p(i), p(j)}. In the problem, mutually compatible jobs can form a batch being processed on the machine. The processing time of a batch is equal to the maximum normal processing time of the jobs in this batch. For this problem, we provide an optimal online algorithm with a competitive ratio of 1 + beta(alpha), where beta(alpha) is the positive root of the equation (1 + alpha)x(2) + alpha x = 1 + alpha .
引用
收藏
页码：1187 / 1197
页数：11
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