Semi-online scheduling on two uniform processors

Authors:
Enrico Angelelli;Maria Grazia Speranza;Zsolt Tuza
Affiliations:
Department of Quantitative Methods, University of Brescia, Brescia, Italy;Department of Quantitative Methods, University of Brescia, Brescia, Italy;Computer and Automation Institute, Hungar. Acad. Sci., Budapest, Hungary and Department of Computer Science, University of Pannonia, Veszprém, Hungary
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

In this paper we consider the problem of semi-online scheduling on two uniform processors, in the case where the total sum of the tasks is known in advance. Tasks arrive one at a time and have to be assigned to one of the two processors before the next one arrives. The assignment cannot be changed later. The objective is the minimization of the makespan. Assume that the speed of the fast processor is s, while the speed of the slow one is normalized to 1. As a function of s, we derive general lower bounds on the competitive ratio achievable with respect to offline optimum, and design on-line algorithms with guaranteed upper bound on their competitive ratio. The algorithms presented for s=3 are optimal, as well as for s=1 and for 1+174@?s@?1+32.