Two semi-online scheduling problems on two uniform machines

Authors:
C. T. Ng;Zhiyi Tan;Yong He;T. C. E. Cheng
Affiliations:
Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China;Department of Mathematics, State Key Lab of CAD & CG, Zhejiang University, Hangzhou 310027, PR China;Department of Mathematics, State Key Lab of CAD & CG, Zhejiang University, Hangzhou 310027, PR China;Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

This paper considers two semi-online scheduling problems, one withknown optimal value and the other with known total sum, on twouniform machines with a machine speed ratio of s≥1. For thefirst problem, we provide an optimal algorithm fors∈[1+√3/2, 1+√21/4], and improvedalgorithms or/and lower bounds for s∈[1+√21/4,√3], over which the optimal algorithm is unknown. As aresult, the largest gap between the competitive ratio and the lowerbound decreases to 0.02192. For the second problem, we also presentalgorithms and lower bounds for s≥1. The largest gap between thecompetitive ratio and the lower bound is 0.01762, and the length ofthe interval over which the optimal algorithm is unknown is0.47382. Our algorithms and lower bounds for these two problemsprovide insights into their differences, which are unusual from theviewpoint of the known results on these two semi-online schedulingproblems in the literature.