Problem of Determining Weights of Edges for Reducing Diameter

  • Kaito Miyanagi
  • Hiroyoshi MiwaEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1035)


It is necessary to reduce delay in an information network. The total delay time between two nodes is the sum of the delay times in all links and nodes contained in the path between the nodes; therefore, we can reduce the total delay time by reducing the delay times in some links and nodes in the path. Since the additional cost such as the increase of the link speed is necessary, the links whose speed is increased must be determined by considering the trade-off between performance and cost. In this paper, we formulate this network design problem as an optimization problem of determining the weight of each edge so that the diameter of a network is less than or equal to a given threshold. The objective of this optimization problem is to minimize the sum of the costs under the condition that the number of edges whose weight is changed is restricted. We prove that this problem is NP-complete, and we propose a polynomial-time algorithm to the problem that the number of edges whose weights are changed is restricted to one.



This work was partially supported by the Japan Society for the Promotion of Science through Grants-in-Aid for Scientific Research (B) (17H01742) and JST CREST JPMJCR1402.


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Authors and Affiliations

  1. 1.Graduate School of Science and TechnologyKwansei Gakuin UniversitySanda-shiJapan

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