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The limitations of linear and semidefinite programming
The fact that Linear Programming (LP) can be solved in polynomial time (and, also, efficiently in practice) and that it has such a rich geometric theory and such remarkable expressive power makes LP a...
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The Limitations of the Spectral Partitioning Algorithm
We continue to talk about the problem of estimating the expansion of a graph , focusing on the closely related sparsest cut, defined as The spectral paritioning algorithm first finds a vector...
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How Good is the Leighton-Rao Relaxation?
Continuing our seemingly never-ending series on approximations to edge expansion, we come to the question of how good is the Leighton-Rao relaxation. Given a graph , we are trying to approximate the...
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Survey on Hardness of Approximation
In 2004 I wrote a survey on hardness of approximation as a book chapter for a book on approximation algorithm. I have just prepared a revised version for a new edition of the book. While it would have...
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On the Unique Games Conjecture (part 2)
[I am preparing a survey talk on Unique Games for a mathematics conference, and writing a survey paper for a booklet that will be distributed at the conference. My first instinct was to write a...
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Two recent papers by Cui Peng
Cui Peng of Renmin University in Beijing has recently released two preprints, one claiming a proof of P=NP and one claiming a refutation of the Unique Games Conjecture; I will call them the “NP paper”...
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