Geometric Minimum Diameter Minimum Cost Spanning Tree Problem

Authors:
Dae Young Seo;D. T. Lee;Tien-Ching Lin
Affiliations:
Department of Computer Engineering, Korea Polytechnic University, Korea;Institute of Information Science, Academia Sinica, Taipei, Taiwan and Dept. of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan;Institute of Information Science, Academia Sinica, Taipei, Taiwan
Venue:
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Year:
2009

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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.