The Loading Time Scheduling Problem

In this paper we study precedence constrained scheduling problems, where the tasks can only be executed on a speciied subset of the machines. Each machine has a loading time that is incurred only for the rst task that is scheduled on the machine in a particular run. This basic scheduling problem arises in the context of machining on numerically controlled machines , query optimization in databases, and in other artiicial intelligence applications. We give the rst non-trivial approximation algorithm for this problem. We also prove non-trivial lower bounds on best possible approximation ratios for these problems. These improve on the non-approximability results that are implied by the non-approximability results for the shortest common supersequence problem. We use the same algorithmic technique to obtain approximation algorithms for a problem arising in the context of code generation for parallel machines, and for the weighted shortest common supersequence problem .