We consider the following non-preemptive semi-online scheduling problem. Jobs with non-increasing sizes arrive one by one to be scheduled on two uniformly related machines, with the goal of minimizing the makespan. We analyze both the optimal overall competitive ratio, and the optimal competitive ratio as a function of the speed ratio (q≥1) between the two machines. We show that the greedy algorithm LPT has optimal competitive ratio 14(1+17)≈1.28 overall, but does not have optimal competitive ratio for every value of q. We determine the intervals of q where LPT is an algorithm of optimal competitive ratio, and design different algorithms of optimal competitive ratio for the intervals where it fails to be the best algorithm. As a result, we give a tight analysis of the competitive ratio for every speed ratio.
Bibliographical noteFunding Information:
– The research of Lene M. Favrholdt was supported in part by the Danish Natural Sci-ence Research Council (SNF) and in part by the Future and Emerging Technologies program of the EU under contract number IST-1999-14186 (ALCOM-FT).
– The research of Leah Epstein was supported in part by the Israel Science Foundation, (grant no. 250/01).
- Competitive ratio
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics