Approximation Schemes for Machine Scheduling

Abstract

Makespan 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.