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An average-case analysis of bin packing with uniformly distributed item sizes
We analyze the one-dimensional bin-packing problem under the assumption that bins have unit capacity, and that items to be packed are drawn from a uniform distribution on [0,1]. Building on some recent work by Frederickson, we give an algorithm which uses n/2+0(n^½) bins on the average to pack n items. (Knodel has achieved a similar result.) The analysis involves the use of a certain 1-dimensional random walk. We then show that even an optimum packing under this distribution uses n/2+0(n^1/2) bins on the average, so our algorithm is asymptotically optimal, up to constant factors on the amount of wasted space. Finally, following Frederickson, we show that two well-known greedy bin-packing algorithms use no more bins than our algorithm; thus their behavior is also in asymptotically optimal in this sense
A new role for science - I
Science and technology are in desperate need of change,
just because they have been extraordinarily successful
George Baillie on peptide array, a technique that transformed research on phosphodiesterases
George Baillie speaks to Francesca Lake (Managing Editor, Future Science OA). George Baillie is a Professor and PI within the Institute of Cardiovascular and Medical Sciences at the University of Glasgow (Glasgow, UK). His research over the last 15 years has examined many aspects of the cAMP signaling pathway in disease and he has published over 140 papers on the subject. His major discovery was that phosphodiesterases are ‘compartmentalized’, and it is their location within cells that direct their function. The Baillie/Houslay laboratory was the first to discover a specific function for a single isoform of PDE4 (namely PDE4D5 with β-arrestin desensitizes the β2-adrenergic receptor). His laboratory has since gone on to ascribe functions to several other PDE4 isoforms. He is a founder and director of Sannox Therapeutics, a spin-out venture within University of Glasgow. He is also a member of the Editorial Board of Future Science OA and Co-Editor of Cellular Signalling
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