Abstract
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 Edf α , 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 \(1/(1-(\frac{M}{M+1})^M)\)-competitive algorithm for M processors. We also show improved lower bounds for the general and 2-uniform cases.
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Bartal, Y. et al. (2004). Online Competitive Algorithms for Maximizing Weighted Throughput of Unit Jobs. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_17
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DOI: https://doi.org/10.1007/978-3-540-24749-4_17
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