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Clustering method is one of the most important tools in statistics. In a graph theory model, clustering is the process of finding all dense sub-graphs. In this paper, a new clustering method is introduced. One of the most significant differences between the new method and other existing methods is that this new method constructs a much smaller hierarchical(More)
In this paper, we address the scheduling problem with rejection and non-identical job arrivals, in which we may choose not to process certain jobs and each rejected job incurs a penalty. Our goal is to minimize the sum of the total penalties of the rejected jobs and the maximum completion time of the processed ones. For the off-line variant, we prove its(More)
a r t i c l e i n f o a b s t r a c t Keywords: Analysis of algorithms Parallel-batch scheduling Deteriorating job NP-hard Fully polynomial time approximation scheme (FPTAS) We consider the bounded parallel-batch scheduling problem in which the processing time of a job is a simple linear function of its starting time. The objective is to minimize the(More)
In this paper, we firstly describe a technique named Duplicating, which duplicates machines in batch scheduling environment. Then we discuss several applications of Duplicating in solving batch scheduling problems, for the batch scheduling problem on unrelated parallel machines to minimize makespan, we give an (4 − 2 B)-approximation algorithm and an (2 − 1(More)