Semi-online early work maximization problems on two hierarchical uniform machines with partial information of processing time
Man Xiao,
Xiaoqiao Liu and
Weidong Li ()
Additional contact information
Man Xiao: Yunnan University
Xiaoqiao Liu: Yunnan University
Weidong Li: Yunnan University
Journal of Combinatorial Optimization, 2023, vol. 46, issue 3, No 4, 19 pages
Abstract:
Abstract In this paper, we consider four semi-online early work maximization problems on two hierarchical uniform machines $$M_1$$ M 1 and $$M_2$$ M 2 , where machine $$M_1$$ M 1 with speed $$s>0$$ s > 0 is available for all jobs and machine $$M_2$$ M 2 with speed 1 is only available for high-hierarchy jobs. When the total size of all jobs is known, we design an optimal online algorithm with a competitive ratio of $$\min \{1+s,\frac{2+2s}{1+2s}\}$$ min { 1 + s , 2 + 2 s 1 + 2 s } . When the total size of low-hierarchy jobs is known, we design an optimal online algorithm with a competitive ratio of $$\min {\{1+s, \frac{\sqrt{9\,s^2+10\,s+1}-s-1}{2\,s}}\}$$ min { 1 + s , 9 s 2 + 10 s + 1 - s - 1 2 s } . When the total size of high-hierarchy jobs is known, we design an optimal online algorithm with a competitive ratio of $$\min \{\sqrt{s+1}, \sqrt{s^2+2\,s+2}-s\}$$ min { s + 1 , s 2 + 2 s + 2 - s } . When both the total sizes of low-hierarchy and high-hierarchy jobs are known, we give a lower bound $$\frac{2s+2}{s+2}$$ 2 s + 2 s + 2 for the case $$s\le \frac{2}{3}$$ s ≤ 2 3 , and an optimal online algorithm with a competitive ratio of $$\frac{3s+3}{3s+2}$$ 3 s + 3 3 s + 2 for the case $$s>\frac{2}{3}$$ s > 2 3 .
Keywords: Semi-online; Early work; Competitive ratio; Uniform machines; Hierarchy (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:
Downloads: (external link)
http://link.springer.com/10.1007/s10878-023-01086-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:46:y:2023:i:3:d:10.1007_s10878-023-01086-7
Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878
DOI: 10.1007/s10878-023-01086-7
Access Statistics for this article
Journal of Combinatorial Optimization is currently edited by Thai, My T.
More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().