On-line Algorithms for a Single Machine Scheduling Problem

An increasingly significant branch of computer science is the study of online algorithms. In this paper, we apply the theory of on-line algorithms to job scheduling. In particular, we study the nonpreemptive single machine scheduling of independent jobs with arbitrary release dates to minimize the total completion time. We design and analyze two on-line algorithms which make scheduling decisions without knowing about jobs that will arrive in future. Keywords: job scheduling, on-line algorithm, c-competitiveness 1 Introduction Given a sequence of requests, an on-line algorithm is one that responds to each request in the order it appears in the sequence without the knowledge of any request following it in the sequence. For instance, in the bin packing problem, a list L = (a 1 ; a 2 ; : : : ; a n ) of reals in (0; 1] needs to be packed into the minimum number of unit-capacity bins. An on-line bin packing algorithm packs a i , where i starts from 1, without knowing about a i+1 ; : : : ; ..