Bin packing problem

Abstract: The following abstract problem models several practical problems in computer science and operations research: given a list L of real numbers between 0 and l, place the elements of L into a minimum number $L^ * $ of “bins” so that no bin contains numbers whose sum exceeds l. Motivated by the likelihood that an excessive amount of computation will be required by any algorithm which actually determines an optimal placement, we examine the performance of a number of simple algorithms which obtain “good” placements. The first-fit algorithm places each number, in succession, into the first bin in which it fits. The best-fit algorithm places each number, in succession, into the most nearly full bin in which it fits. We show that neither the first-fit nor the best-fit algorithm will ever use more than $\frac{17}{10}L^ * + 2$ bins. Furthermore, we outline a proof that, if L is in decreasing order, then neither algorithm will use more than $\frac{11}{9} L^ * + 4$ bins. Examples are given to show that both upper bou...

Abstract: There has been a great deal of interest recently in the relative power of on-line and off-line algorithms. An on-line algorithm receives a sequence of requests and must respond to each request as soon as it is receiveD. An off-line algorithm may wait until all requests have been received before determining its responses. One approach to evaluating an on-line algorithm is to compare its performance with that of the best possible off-line algorithm for the same problem. Thus, given a measure of "profit", the performance of an on-line algorithm can be measured by the worst-case ratio of its profit to that of the optimal off-line algorithm. This general approach has been applied in a number of contexts, including data structures [SITa], bin packing [CoGaJo], graph coloring [GyLe] and the k-server problem [MaMcSI]. Here we apply it to bipartite matching and show that a simple randomized on-line algorithm achieves the best possible performance.

Abstract: Consolidation of applications in cloud computing environments presents a significant opportunity for energy optimization. As a first step toward enabling energy efficient consolidation, we study the inter-relationships between energy consumption, resource utilization, and performance of consolidated workloads. The study reveals the energy performance trade-offs for consolidation and shows that optimal operating points exist. We model the consolidation problem as a modified bin packing problem and illustrate it with an example. Finally, we outline the challenges in finding effective solutions to the consolidation problem.