Online computation and competitive analysis
Online computation and competitive analysis
An optimal online algorithm for single machine scheduling to minimize total general completion time
Journal of Combinatorial Optimization
A class of on-line scheduling algorithms to minimize total completion time
Operations Research Letters
| Hi-index | 0.89 |
In this paper we study the problem of online scheduling of jobs with release times on a single machine to minimize the total general completion time @?C"j^@a, where C"j is the completion time of job J"j and @a=1 is a constant. It has been shown in the paper by Liu et al., namely, ''An optimal online algorithm for single machine scheduling to minimize total general completion time'' (Liu et al., 2010) [2] that the lower bound on the competitive ratio of any online algorithm is 2^@a. The authors also attempted to prove that the online algorithm DSPT (Delayed Shortest Processing Time) is 2^@a-competitive. Unfortunately, Lemma 2 in the paper, which is crucial in the proof, is indeed incorrect. This leaves the performance of DSPT as an open question. The contribution of this paper is two-fold. First, we give a counterexample to this lemma and an explanation of the flaw in the argument. Second, we give a proof that DSPT is 2^@a-competitive. Together with the lower bound by Liu et al., this implies that DSPT is an optimal online algorithm for minimizing the total general completion time.