Abstract
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.
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References
de Bruijn, N.G.: A combinatorial problem. In: Proceedings of Koninklijke Nederlandse Academie van Wetenschappen, vol. 49, pp. 758–764 (1946)
Kautz, W.: Bounds on directed (d,k)-graphs. In: Theory of Cellular Logic Networks and Machines (1968)
Du, D.Z., Gao, F., Hsu, D.F.: De Bruiin digraphs, Kautz digraphs, and their generalizations. In: Combinatorial Network Theory, vol. 1, pp. 65–105 (1996)
Boucher, C., Bowe, A., Gagie, T., Puglisi, S.J., Sadakane, K.: Variable-order de Bruijn graphs. In: Proceedings of IEEE Data Compression Conference, 7–9 April 2015
Bermond, J.-C., Peyrat, C.: De Bruijn and Kautz networks: a competitor for the hypercube? In: Hypercube and Distributed Computers, pp. 279–293 (1989)
Imase, M., Itoh, M.: A design for directed graphs with minimum diameter. IEEE Trans. Comput. C–32(8), 782–784 (1983)
Du, D.Z., Hsu, D.F., Peck, G.W.: Connectivity of consecutive-d digraph. Discret. Appl. Math. 37/38, 169–177 (1992)
Plesnik, J.: The complexity of designing a network with minimum diameter. Networks 11(1), 77–85 (1981)
Miwa, H., Ito, H.: Sparse spanning subgraph preserving connectivity and distance between vertices and vertex subsets. IEICE Trans. Fundam. E81–A(5), 832–841 (1998)
Garey, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness (1978)
CAIDA. http://www.caida.org/
Acknowledgements
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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Miyanagi, K., Miwa, H. (2020). Problem of Determining Weights of Edges for Reducing Diameter. In: Barolli, L., Nishino, H., Miwa, H. (eds) Advances in Intelligent Networking and Collaborative Systems. INCoS 2019. Advances in Intelligent Systems and Computing, vol 1035. Springer, Cham. https://doi.org/10.1007/978-3-030-29035-1_34
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DOI: https://doi.org/10.1007/978-3-030-29035-1_34
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