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A new framework for analyzing online bin packing algorithms is presented. This framework presents a unified way of explaining the performance of algorithms based on the Harmonic approach. Within this framework, it is shown that a new algorithm, Harmonic++, has asymptotic performance ratio at most 1.58889. It is also shown that the analysis of Harmonic+1(More)
The problem of online multiprocessor scheduling with rejection was introduced by Bartal, Leonardi, Marchetti-Spaccamela, Sgall and Stougie 4]. They show that for this problem the competitive ratio is 1 + 2:61803, where is the golden ratio. A modiied model of multipro-cessor scheduling with rejection is presented where preemption is allowed. For this model,(More)
New upper and lower bounds are presented for a multi-dimensional generalization of bin packing called box packing.Several variants of this problem, including bounded space box packing, square packing, variable sized box packing and resource augmented box packing are also studied. The main results, stated for <i>d</i> = 2, are as follows: A new upper bound(More)
We investigate the problem of semi-online scheduling jobs on m identical parallel machines where the jobs arrive in order of decreasing sizes. We present a complete solution for the preemptive variant of semi-online scheduling with decreasing job sizes. We give matching lower and upper bounds on the competitive ratio for any xed number m of machines; these(More)
We present the first general framework for proving lower bounds for randomized online algorithms using the von Neu-mann/Yao principle. This framework encompasses and explains many existent lower bound results, and allows us to prove several new ones. The foremost of the new results is a lower bound of 1.58197 for the online TCP acknowledgment problem of(More)