Semi-online Hierarchical Load Balancing Problem with Bounded Processing Times
In this paper, we consider the online hierarchical scheduling problem on two parallel machines, with the objective of maximizing the minimum machine load. Since no competitive algorithm exists for this problem, we consider the semi-online version with bounded processing times, in which the processing times are bounded by an interval [1,α] where α ≥ 1. We prove that no algorithm can have a competitive ratio less than 1 + α and give an optimal algorithm with the competitive ratio of 1 + α. Moreover, if we further know the sum of jobs’ processing time in advance, we prove that no algorithm can have a competitive ratio less than α where 1 ≤ α < 2, and we also propose an algorithm which is shown to be optimal for the case 1 ≤ α < 2.
KeywordsScheduling Semi-online Load balancing Competitive ratio Hierarchy
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