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Decomposition algorithms for the maximum‐weight connected graph problem

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  • Heungsoon Felix Lee
  • Daniel R. Dooly

Abstract

Given a positive integer R and a weight for each vertex in a graph, the maximum‐weight connected graph problem (MCG) is to find a connected subgraph with R vertices that maximizes the sum of their weights. MCG has applications to communication network design and facility expansion. The constrained MCG (CMCG) is MCG with a constraint that one predetermined vertex must be included in the solution. In this paper, we introduce a class of decomposition algorithms for MCG. These algorithms decompose MCG into a number of small CMCGs by adding vertices one at a time and building a partial graph. They differ in the ordering of adding vertices. Proving that finding an ordering that gives the minimum number of CMCGs is NP‐complete, we present three heuristic algorithms. Experimental results show that these heuristics are very effective in reducing computation and that different orderings can significantly affect the number of CMCGs to be solved. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 817–837, 1998

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  • Heungsoon Felix Lee & Daniel R. Dooly, 1998. "Decomposition algorithms for the maximum‐weight connected graph problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(8), pages 817-837, December.
    • Handle: RePEc:wly:navres:v:45:y:1998:i:8:p:817-837
    DOI: 10.1002/(SICI)1520-6750(199812)45:83.0.CO;2-1
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    1. Heungsoon Felix Lee & Daniel R. Dooly, 1996. "Algorithms for the constrained maximum‐weight connected graph problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(7), pages 985-1008, October.
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