Abstract
In this paper we consider bi-criteria geometric optimization problems, in particular, the minimum diameter minimum cost spanning tree problem and the minimum radius minimum cost spanning tree problem for a set of points in the plane. The former problem is to construct a minimum diameter spanning tree among all possible minimum cost spanning trees, while the latter is to construct a minimum radius spanning tree among all possible minimum cost spanning trees. The graph-theoretic minimum diameter minimum cost spanning tree (MDMCST) problem and the minimum radius minimum cost spanning tree (MRMCST) problem have been shown to be NP-hard. We will show that the geometric version of these two problems, GMDMCST problem and GMRMCST problem are also NP-hard. We also give two heuristic algorithms, one MCST-based and the other MDST-based for the GMDMCST problem and present some experimental results.
Research supported in part by the National Science Council under the Grants No. NSC-94-2213-E-001-004, NSC-95-2221-E-001-016-MY3, and NSC 94-2752-E-002-005-PAE, and by the Taiwan Information Security Center (TWISC), National Science Council under the Grant No. NSC94-3114-P-001-001-Y.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Garey, M.R., Johnson, D.S.: Computers and Intractability: a guide to the theory of NP-completeness. Freeman, San Francisco (1979)
Hakimi, S.L.: Optimal locations of switching centers and medians of a graph. Operations Research 12, 405–459 (1964)
Hassin, R., Tamir, A.: On the minimum diameter spanning tree problem. Information Processing Letters 53, 109–111 (1995)
Ho, J.M.: Optimal Trees in Network Design, Ph.D Dissertation, Northwestern University (May 1989)
Ho, J.M., Lee, D.T., Chang, C.H., Wong, C.K.: Minimum Diameter Spanning Trees and Related Problems. SICOMP 20(5), 987–997 (1991)
Kariv, O., Hakimi, S.L.: An algorithmic approach to network location problems. I: The p-Centers. SIAM Journal on Applied Math. 37, 513–537 (1979)
Kruskal, J.B.: On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem. Problem. Amer. Math. Soc. 7 (1956)
Prim, R.C.: Shortest Connection Networks and Some Generalizations. Bell System Tech. J. (1957)
Seo, D.Y.: On the Complexity of Bicriteria Spanning Tree Problems for a Set of Points in the Plane, Ph. D Dissertation, Northwestern University (1999)
Chan, T.M.: Semi-online maintenance of geometric optima and measures. SIAM Journal on Computing 32, 700–716 (2003)
Algorithm Benchmark System (ABS), http://www.opencps.org
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Seo, D.Y., Lee, D.T., Lin, TC. (2009). Geometric Minimum Diameter Minimum Cost Spanning Tree Problem. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-10631-6_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10630-9
Online ISBN: 978-3-642-10631-6
eBook Packages: Computer ScienceComputer Science (R0)