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Exploring the constrained maximum edge-weight connected graph problem

  • Zhen-ping Li
  • Shi-hua Zhang
  • Xiang-Sun ZhangEmail author
  • Luo-nan Chen
Article

Abstract

Given an edge weighted graph, the maximum edge-weight connected graph (MECG) is a connected subgraph with a given number of edges and the maximal weight sum. Here we study a special case, i.e. the Constrained Maximum Edge-Weight Connected Graph problem (CMECG), which is an MECG whose candidate subgraphs must include a given set of k edges, then also called the k-CMECG. We formulate the k-CMECG into an integer linear programming model based on the network flow problem. The k-CMECG is proved to be NP-hard. For the special case 1-CMECG, we propose an exact algorithm and a heuristic algorithm respectively. We also propose a heuristic algorithm for the k-CMECG problem. Some simulations have been done to analyze the quality of these algorithms. Moreover, we show that the algorithm for 1-CMECG problem can lead to the solution of the general MECG problem.

Keywords

connected subgraph integer linear programming model network flow constraint Steiner network maximum edge weight heuristic algorithm 

2000 MR Subject Classification

90-08 90B10 94C15 

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Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer Berlin Heidelberg 2009

Authors and Affiliations

  • Zhen-ping Li
    • 1
  • Shi-hua Zhang
    • 2
  • Xiang-Sun Zhang
    • 2
    Email author
  • Luo-nan Chen
    • 3
    • 4
  1. 1.School of InformationBeijing Wuzi UniversityBeijingChina
  2. 2.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  3. 3.Institute of Systems BiologyShanghai UniversityShanghaiChina
  4. 4.Department of Electrical Engineering and ElectronicsOsaka Sangyo UniversityOsakaJapan

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