Exploring the constrained maximum edge-weight connected graph problem
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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.
Keywordsconnected subgraph integer linear programming model network flow constraint Steiner network maximum edge weight heuristic algorithm
2000 MR Subject Classification90-08 90B10 94C15
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