Random Projections for Linear Programming
证明了随机投影矩阵能保持到锥的距离，并利用该结果设计概率算法近似求解线性规划，适用于大规模随机生成的LP实例和纠错编码问题。
Random projections are random linear maps, sampled from appropriate distributions, which approximately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well known Johnson-Lindenstrauss lemma states that there are random matrices with surprisingly few rows which approximately preserve pairwise Euclidean distances among a set of points. This is commonly used to speed up algorithms based on Euclidean distances. We prove that these matrices also preserve other quantities, such as the distance to a cone. We exploit this result to devise a probabilistic algorithm to approximately solve linear programs. We show that this algorithm can approximately solve very large randomly generated LP instances. We also showcase its application to an error correction coding problem.