有向多路切割问题的2-逼近算法

IF 1.6 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

SIAM Journal on Computing Pub Date : 2002-02-01 DOI:10.1137/S009753979732147X

Siam Staff

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引用次数: 19

摘要

有向多路切割将一组端子T={s1，…， sk}在有向容化图G=(V,E)中。寻找最小定向多路切割是一个np困难问题。我们给出了一个多项式时间算法，该算法对该问题的逼近系数为2。这改进了Garg, Vazirani和Yannakakis的结果[第21届国际自动机，语言和编程研讨会论论集，耶路撒冷，以色列，1994，第487—498页]，他们给出了一个算法，该算法实现了2 log k的近似因子。我们的近似算法使用了一种新的技术来放松多路流函数，以找到一个有向的多路切。这也暗示了有向多路切割问题的线性规划的完整性间隙不超过2。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A 2-Approximation Algorithm for the Directed Multiway Cut Problem

A directed multiway cut separates a set of terminals T={s1, . . . , sk} in a directed capacitated graph G=(V,E). Finding a minimum directed multiway cut is an NP-hard problem. We give a polynomial-time algorithm that achieves an approximation factor of 2 for this problem. This improves the result of Garg, Vazirani, and Yannakakis [Proceedings of the 21st International Colloquium on Automata, Languages, and Programming, Jerusalem, Israel, 1994, pp. 487--498], who gave an algorithm that achieves an approximation factor of 2 log k. Our approximation algorithm uses a novel technique for relaxing a multiway flow function in order to find a directed multiway cut. It also implies that the integrality gap of the linear program for the directed multiway cut problem is at most 2.

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来源期刊

SIAM Journal on Computing 工程技术-计算机：理论方法

CiteScore

4.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.