Abstract
AbstractMakespan minimization on identical parallel machines, or machine scheduling for short, is a fundamental problem in combinatorial optimization. In this problem, a set of jobs with processing times has to be assigned to a set of machines with the goal of minimizing the latest finishing time of the jobs, i.e., the makespan. While machine scheduling in NP-hard and therefore does not admit a polynomial time algorithm guaranteed to find an optimal solution (unless P=NP), there is a well-known polynomial time approximation scheme (PTAS) for this problem, i.e., a family of \((1+\varepsilon )\)-approximations for each \(\varepsilon >0\). The question of whether there is a PTAS for a given problem is considered fundamental in approximation theory. The author’s dissertation considers this question for several variants of machine scheduling, and the present work summarizes the dissertation.KeywordsSchedulingParallel machinesMakespanApproximationPTAS
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