Abstract
The rectilinear Steiner tree problem asks for a shortest tree connecting given points in the plane with rectilinear distance. The best theoretically analyzed algorithm for this problem with a fairly practical behaviour bases on dynamic programming and has a running time of O(n 2·.2.62n) (Ganley/Cohoon). The best implementation can solve random problems of size 35 (Salowe/Warme) within a day. In this paper we improve the theoretical worst-case time bound to O(n · 2.38n), for random problem instances we prove a running time of less than O(2n). In practice, our ideas lead to even more drastic improvements. Extensive experiments show that the range for the size of random problems solvable within a day on a workstation is almost doubled. For exponential time algorithms, this is an enormous step.
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© 1997 Springer-Verlag Berlin Heidelberg
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Fößmeier, U., Kaufmann, M. (1997). Solving rectilinear Steiner tree problems exactly in theory and practice. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_14
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DOI: https://doi.org/10.1007/3-540-63397-9_14
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