List scheduling in order of α-points on a single machine

Authors:
Martin Skutella
Affiliations:
Fachbereich Mathematik, Universität Dortmund, Dortmund, Germany
Venue:
Efficient Approximation and Online Algorithms
Year:
2006

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Abstract

Many approximation results for single machine scheduling problems rely on the conversion of preemptive schedules into (preemptive or non-preemptive) solutions. The initial preemptive schedule is usually an optimal solution to a combinatorial relaxation or a linear programming relaxation of the scheduling problem under consideration. It therefore provides a lower bound on the optimal objective function value. However, it also contains structural information which is useful for the construction of provably good feasible schedules. In this context, list scheduling in order of so-called α-points has evolved as an important and successful tool. We give a survey and a uniform presentation of several approximation results for single machine scheduling with total weighted completion time objective from the last years which rely on the concept of α-points.