Treffer: Online competitive algorithms for maximizing weighted throughput of unit jobs
Department of Computer Science and Information Systems, The University of Hong Kong, Hong-Kong
Department of Computer Science, University of California, Riverside, CA 92521, United States
Mathematical Institute, AS CR, Žitná 25, 11567 Praha, Czech Republic
CC BY 4.0
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We study an online scheduling problem for unit-length jobs, where each job is specified by its release time, deadline, and a nonnegative weight. The goal is to maximize the weighted throughput, that is the total weight of scheduled jobs. We first give a randomized algorithm RMIX with competitive ratio of e/(e - 1) ~ 1.582. Then we consider s-bounded instances where the span of each job is at most s. We give a 1.25-competitive randomized algorithm for 2-bounded instances, and a deterministic algorithm EDFα, whose competitive ratio on s-bounded instances is at most 2 - 2/s + o(1/s). For 3-bounded instances its ratio is Φ ~ 1.618, matching the lower bound. We also consider 2-uniform instances, where the span of each job is 2. We prove a lower bounds for randomized algorithms and deterministic memoryless algorithms. Finally, we consider the multiprocessor case and give an 1/(1 - (M M+1)M)-competitive algorithm for M processors. We also show improved lower bounds for the general and 2-uniform cases.