Abstract
In this study, a lifting procedure is applied to some existing formulations of the Diameter Constrained Minimum Spanning Tree Problem. This problem typically models network design applications where all vertices must communicate with each other at minimum cost, while meeting or surpassing a given quality requirement. An alternative formulation is also proposed for instances of the problem where the diameter of feasible spanning trees can not exceed given odd numbers. This formulation dominated their counterparts in this study, in terms of the computation time required to obtain proven optimal solutions. First ever computational results are presented here for complete graph instances of the problem. Sparse graph instances as large as those found in the literature were solved to proven optimality for the case where diameters can not exceed given odd numbers. For these applications, the corresponding computation times are competitive with those found in the literature.
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Achuthan, N.R., Caccetta, L., Caccetta, P.A., Geelen, J.F.: Algorithms for the minimum weight spanning tree with bounded diameter problem. In: Phua, K.H., Wand, C.M., Yeong, W.Y., Leong, T.Y., Loh, H.T., Tan, K.C., Chou, F.S. (eds.) Optimisation Techniques and Applications, vol. 1, pp. 297–304. World Scientific, Singapore (1992)
Achuthan, N.R., Caccetta, L., Caccetta, P.A., Geelen, J.F.: Computational methods for the diameter restricted minimum weight spanning tree problem. Australasian Journal of Combinatorics 10, 51–71 (1994)
Bookstein, A., Klein, S.T.: Compression of correlated bitvectors. Information Systems 16, 110–118 (2001)
Deo, N., Abdalla, A.: Computing a diameter-constrained minimum spanning tree in parallel. In: Bongiovanni, G., Petreschi, R., Gambosi, G. (eds.) CIAC 2000. LNCS, vol. 1767, pp. 17–31. Springer, Heidelberg (2000)
Desrochers, M., Laporte, G.: Improvements and extensions to the Miller-Tucker- Zemlin subtour elimination constraints. Operations Research Letters 10, 27–36 (1991)
Garey, M.R., Johnson, D.S.: Computers and intractability: A guide to the theory of NP-Completeness. W.H. Freeman, New York (1979)
Gouveia, L., Magnanti, T.L.: Modelling and solving the diameter-constrained minimum spanning tree problem. Technical report, DEIO-CIO, Faculdade de Ciências (2000)
Handler, G.Y.: Minimax location of a facility in an undirected graph. Transportation Science 7, 287–293 (1978)
Miller, C.E., Tucker, A.W., Zemlin, R.A.: Integer programming formulations and traveling salesman problems. Journal of the ACM 7, 326–329 (1960)
Padberg, M.: The boolean quadric polytope: Some characteristics and facets. Mathematical Programming 45, 139–172 (1988)
Raymond, K.: A tree-based algorithm for distributed mutual exclusion. ACM Transactions on Computers 7, 61–77 (1989)
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dos Santos, A.C., Lucena, A., Ribeiro, C.C. (2004). Solving Diameter Constrained Minimum Spanning Tree Problems in Dense Graphs. In: Ribeiro, C.C., Martins, S.L. (eds) Experimental and Efficient Algorithms. WEA 2004. Lecture Notes in Computer Science, vol 3059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24838-5_34
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DOI: https://doi.org/10.1007/978-3-540-24838-5_34
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