An On-Line Algorithm for Some Uniform Processor Scheduling

Abstract

This paper considers the problem of on-line scheduling a set of independent jobs on m uniform machines (M1, M2,⋯, Mm) in which machine M′is processing speed is si=1(i=1,⋯, m−1) and sm=s>1. List Scheduling [Yookum Cho and Sartaj Sahni. Bounds for list schedules on uniform processors. SIAM J. Compute. 9(1980), pp91–103.] guarantees a worst case performance of 3m−1/m+1(m≥3) and 1+√5/2(m=2) for this problem.We prove that this worst case bound cannot be imporved for m=2 and m=3 and for every m≥4, an algorithm with worst case performance at most 3m−1/m+1−e is presented when sm=2, where e is a fixed positive number, and then we improve the bound for general sm=s>1.