On-line scheduling with extendable working time on a small number of machines

Authors:
Deshi Ye;Guochuan Zhang
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China;Department of Mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China and Institut für Informatik und Praktische Mathematik, Universität Kiel, Olshausenstrasse 40, ...
Venue:
Information Processing Letters
Year:
2003

Citing 4
Cited 0

A 13/12 approximation algorithm for bin packing with extendable bins

Information Processing Letters
When does a dynamic programming formulation guarantee the existence of an FPTAS?

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for extensible bin packing

SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness

Quantified Score

Hi-index	0.89

Visualization

Abstract

Speranza and Tuza [Ann. Oper. Res. 86 (1999) 494-506] studied the on-line problem of scheduling jobs on m identical machines with extendable working time. In this problem, each machine is assumed to have an identical regular working time, which can be extended if necessary. The working time of a machine is the larger one between its regular working time and the total processing time of jobs assigned to it. The objective is to minimize the total working time of machines. They presented an on-line algorithm Hx, with a competitive ratio at most 1.228 for any number of machines by choosing an appropriate parameter x. In this paper we consider a small number of machines. The best choices of x are given for m = 2, 3, 4 and the tight bounds, 7/6, 11/9 and 19/16, respectively, are proved. Among them, the algorithm for m = 2 is best possible. We then derive a new algorithm for m = 3 with a competitive ratio 7/6.