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| 基于原始对偶方法求解网络流量监测集算法 |
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刘湘辉1,2, 殷建平1, 卢锡城1, 蔡志平1, 赵建民3
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1.国防科学技术大学,计算机学院,湖南,长沙,410073;2.国防科学技术大学,电子科学与工程学院,湖南,长沙,410073;3.浙江师范大学,计算机学院,浙江,金华,321004
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| 摘要: |
| 考虑网络节点的流守恒特性,网络流量的有效监测问题可抽象为求给定图G(V,E)的最小弱顶点覆盖集的问题和基于流划分的最小弱顶点覆盖集的问题,这是NP难的问题.首先分析了弱顶点覆盖集的约束关系,并给出了问题的整数规划形式.然后利用原始对偶方法构造了求解最小弱顶点覆盖集的近似算法,并分析了算法的比界为2.进一步分析了求解基于最大流划分的最小弱顶点覆盖集的近似算法. |
| 关键词: 弱顶点覆盖 NP难的 近似算法 流守恒 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant No.60373023 (国家自然科学基金) |
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| Algorithm for the Network Flow Monitoring Set Based on Primal-Dual Method |
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LIU Xiang-Hui,YIN Jian-Ping,LU Xi-Cheng,CAI Zhi-Ping,ZHAO Jian-Min
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| Abstract: |
| Efficiently monitoring the network flow is important to a variety of network applications. Considering the equation of flow conservation, the problem of efficient monitoring is regarded as the problem of finding out the minimum weak vertex cover set and the minimum weak vertex cover set based on flow partition for a given graph G(V,E) which are all proved NP-Complete. Firstly the constraints of weak vertex cover set are analyzed and the integer programming formulation for it is given. Next an approximation algorithm for the minimum weak vertex cover set problem is constructed and the approximation ratio of 2 by primal-dual method is analyzed. Finally the approximation algorithm for the minimum weak vertex cover set is analyzed based on the maximal flow partition. |
| Key words: weak vertex cover NP-hard approximation algorithm flow conservation |
