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Divergence-proving Techniques for Best Fit Bin Packing and Random Fit (2001)
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@MISC{Maymounkov01divergence-provingtechniques,
author = {Petar Maymounkov},
title = {Divergence-proving Techniques for Best Fit Bin Packing and Random Fit},
year = {2001}
}
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Abstract
This work discusses my attempts to extend Kenyon and Mitzenmacher’s technique for proving diveregnce of the online approximation algorithm Best Fit to Random Fit – another approximation algorithm for the well-known NP-hard problem of bin packing. In specific, the paper goes over Kenyon and Mitzenmacher’s recent advances on divergence of the waste of Best Fit bin packing for the skewed distributions U{αk, k} with α ∈ [0.66, 2/3) in detail, and describes the modifications I made to their methods in attempt to prove diveregence for Random Fit under the same input conditions. Acknowledgements I would like to thank my thesis adviser Professor Michael Mitzenmacher for waking my appreciation for the problems of Computer Science, and my interest in stochastic processes and their applications to algorithms. I am very glad that he had the enthusiasm to share his views of Computer Science in his great research classes, because they have made me decide to continue my career in that field. Thanks to Professor Leslie Valiant and to Professor Michael Rabin for the excellent lectures and advice that they have given throughout my years at Harvard. Thanks to Christian Crudder for proof-reading my thesis and providing valuable suggestions. PETAR MAYMOUNKOV SENIOR THESIS 1
Keyphrases
random fit best fit bin packing computer science great research class mitzenmacher technique thesis adviser professor michael mitzenmacher bin packing professor michael rabin christian crudder excellent lecture valuable suggestion stochastic process best fit bin recent advance approximation algorithm well-known np-hard problem petar maymounkov senior thesis professor leslie valiant input condition online approximation algorithm best fit skewed distribution
