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We propose a general dual-fitting technique for analyzing on-line scheduling algorithms in the unrelated machines setting where the objective function involves weighted flow-time, and we allow the machines of the on-line algorithm to have (1 + ε)-extra speed than the offline optimum (the so-called speed augmentation model). Typically, such algorithms are(More)
In this paper we initiate the study of job scheduling on related and unrelated machines so as to minimize the maximum flow time or the maximum weighted flow time (when each job has an associated weight). Previous work for these metrics considered only the setting of parallel machines, while previous work for scheduling on unrelated machines only considered(More)
Factor Analysis is a very useful linear algebra technique used for dimensionality reduction. It is also used for data compression and visualization of high dimensional datasets. This technique tries to identify from among a large set of variables, a reduced set of components which summarizes the original data. This is done by identifying groups of variables(More)
Lecture 7: The critical probability for bond percolation in 2 dimensions is 1 2 7th, 14th and 21th October 2008 7.1 Introduction From percolation theory we know that there exists a probability p c such that ∀p > p c , there exists an infinite component in an infinite mesh and a θ(n 2) component in a n × n mesh with high probability. We saw the Kaklamanis(More)
We study two variants of the classical strip packing problem, or packing rectangles into a rectangle of fixed width and minimum height, a classical NP-hard cutting stock problem. The first result presented in this paper is an OP T + O(1// 2) approximation scheme for resource augmented strip packing in which we are allowed to increase the width of strip by.(More)
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