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 (M ₁, M₂,⋯, M_m) in which machine M′ _is processing speed is s _i=1(i=1,⋯, m−1) and s _m=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−ε is presented when s _m=2, where ε is a fixed positive number, and then we improve the bound for general s _m=s>1.