Space-Efficient Interior Point Method, with applications to Linear Programming and Maximum Weight Bipartite Matching
| Autor: | Liu, S. Cliff, Song, Zhao, Zhang, Hengjie, Zhang, Lichen, Zhou, Tianyi |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the problem of solving linear program in the streaming model. Given a constraint matrix $A\in \mathbb{R}^{m\times n}$ and vectors $b\in \mathbb{R}^m, c\in \mathbb{R}^n$, we develop a space-efficient interior point method that optimizes solely on the dual program. To this end, we obtain efficient algorithms for various different problems: * For general linear programs, we can solve them in $\widetilde O(\sqrt n\log(1/\epsilon))$ passes and $\widetilde O(n^2)$ space for an $\epsilon$-approximate solution. To the best of our knowledge, this is the most efficient LP solver in streaming with no polynomial dependence on $m$ for both space and passes. * For bipartite graphs, we can solve the minimum vertex cover and maximum weight matching problem in $\widetilde O(\sqrt{m})$ passes and $\widetilde O(n)$ space. In addition to our space-efficient IPM, we also give algorithms for solving SDD systems and isolation lemma in $\widetilde O(n)$ spaces, which are the cornerstones for our graph results. Comment: 72 pages, full version |
| Databáze: | arXiv |
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