Two approximation algorithms for two-agent scheduling on parallel machines to minimize makespan

Kejun Zhao and Xiwen Lu ()
Additional contact information
Kejun Zhao: School of Science East China University of Science and Technology
Xiwen Lu: School of Science East China University of Science and Technology

Journal of Combinatorial Optimization, 2016, vol. 31, issue 1, No 18, 260-278

Abstract: Abstract A two-agent scheduling problem on parallel machines is considered. Our objective is to minimize the makespan for agent A, subject to an upper bound on the makespan for agent B. When the number of machines, denoted by $$m$$ m , is chosen arbitrarily, we provide an $$O(n)$$ O ( n ) algorithm with performance ratio $$2-\frac{1}{m}$$ 2 - 1 m , i.e., the makespan for agent A given by the algorithm is no more than $$2-\frac{1}{m}$$ 2 - 1 m times the optimal value, while the makespan for agent B is no more than $$2-\frac{1}{m}$$ 2 - 1 m times the threshold value. This ratio is proved to be tight. Moreover, when $$m=2$$ m = 2 , we present an $$O(nlogn)$$ O ( n l o g n ) algorithm with performance ratio $$\frac{1+\sqrt{17}}{4}\approx 1.28$$ 1 + 17 4 ≈ 1.28 which is smaller than $$\frac{3}{2}$$ 3 2 . The ratio is weakly tight.

Keywords: Two-agent scheduling; Parallel machines; Makespan; Approximation algorithm (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-014-9744-y 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:31:y:2016:i:1:d:10.1007_s10878-014-9744-y

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-014-9744-y

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 ().