Showing papers by "J. B. G. Frenk published in 1987"
TL;DR: Under mild conditions on the probability distribution, strong asymptotic optimality results are obtained for the LPT Longest Processing Time rule, in which the jobs are assigned to the machines in order of nonincreasing processing requirements.
Abstract: For the problem of minimizing makespan on parallel machines of different speed, the behaviour of list scheduling rules is subjected to a probabilistic analysis under the assumption that the processing requirements of the jobs are independent, identically distributed nonnegative random variables. Under mild conditions on the probability distribution, we obtain strong asymptotic optimality results for the LPT Longest Processing Time rule, in which the jobs are assigned to the machines in order of nonincreasing processing requirements.
55 citations
TL;DR: In this paper, the authors present a new approximation algorithm for the two-dimensional bin-packing problem based on two one-dimensional bag-packing algorithms, which can also be used for those cases where the output is required to be on-line.
Abstract: We present a new approximation algorithm for the two-dimensional bin-packing problem. The algorithm is based on two one-dimensional bin-packing algorithms. Since the algorithm is of next-fit type it can also be used for those cases where the output is required to be on-line (e. g. if we open an new bin we have no possibility to pack elements into the earlier opened bins). We give a tight bound for its worst-case and show that this bound is a parameter of the maximal sizes of the items to be packed. Moreover, we also present a probabilistic analysis of this algorithm.
44 citations