A better semi-online algorithm for Q3/s1 = s2≤ s3/Cmin with the known largest size

Abstract

This paper investigates the semi-online machine covering problem on three special uniform machines with the known largest size. Denote by s j the speed of each machine, j = 1, 2, 3. Assume 0 < s 1 = s 2 = r ≤ t = s 3 , and let s = t/r be the speed ratio. An algorithm with competitive ratio max{2, 3s+6 s+6 } is presented. We also show the lower bound is at least max{2, 3s s+6 }. For s ≤ 6, the algorithm is an optimal algorithm with the competitive ratio 2. Besides, its overall competitive ratio is 3 which matches the overall lower bound. The algorithm and the lower bound in this paper improve the results of Luo and Sun.