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arXiv · 1507.00990

Using the Johnson-Lindenstrauss lemma in linear and integer programming

Ky Vu·Pierre-Louis Poirion·Leo Liberti
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Abstract

The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors with low distortion on their pairwise Euclidean distances. This result is often used in algorithms such as $k$-means or $k$ nearest neighbours since they only use Euclidean distances, and has sometimes been used in optimization algorithms involving the minimization of Euclidean distances. In this paper we introduce a first attempt at using this lemma in the context of feasibility problems in linear and integer programming, which cannot be expressed only in function of Euclidean distances.

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Ky Vu, Pierre-Louis Poirion, Leo Liberti. 2015-07-03. Using the Johnson-Lindenstrauss lemma in linear and integer programming. https://arxiv.org/abs/1507.00990

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