Solving Tall Dense Linear Programs in Nearly Linear Time
STOC '20: 52nd Annual ACM SIGACT Symposium on Theory of Computing Chicago IL USA June, 2020(2020)
摘要
In this paper we provide an O(nd+d3) time randomized algorithm for solving linear programs with d variables and n constraints with high probability. To obtain this result we provide a robust, primal-dual O(√d)-iteration interior point method inspired by the methods of Lee and Sidford (2014, 2019) and show how to efficiently implement this method using new data-structures based on heavy-hitters, the Johnson–Lindenstrauss lemma, and inverse maintenance. Interestingly, we obtain this running time without using fast matrix multiplication and consequently, barring a major advance in linear system solving, our running time is near optimal for solving dense linear programs among algorithms that do not use fast matrix multiplication.
更多查看译文
关键词
linear program, interior point method, nearly linear time
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络