Competitive-ratio approximation schemes for makespan scheduling problems

Abstract

The concept of competitive-ratio approximation scheme was recently proposed in [7]. Such a scheme algorithmically constructs an online algorithm with a competitive ratio arbitrarily close to the best possible competitive ratio for a given online problem. In this paper we continue this line of research by addressing several makespan scheduling problems and introducing new ideas: we combine the classical technique of structuring and simplifying the input instance for approximation schemes, with the new technique of guessing the end of the schedule (time after which no job is processed and released), which allows us to reduce the infinite-size set of on-line algorithms to a relevant set of finite size. This is the key idea for eventually allowing an enumeration scheme that finds a near optimal on-line algorithm.We demonstrate how this technique can be successfully applied to three basicmakespan online over time scheduling problems: scheduling on unrelated parallel machines, job shop scheduling and single machine scheduling with delivery times. © Springer-Verlag 2013.