Abstract
We consider the problems of computing r-approximate traveling salesman tours and r-approximate minimum spanning trees for a set of n points in ℝd, where d≥ 1 is a constant. In the algebraic computation tree model, the complexities of both these problems are shown to be θ(nlog(n/r)), for all n and r such that r<n and r is larger than some constant. In the more powerful model of computation that additionally uses the floor function and random access, both problems can be solved in O(n) time if r=θ(n 1−1/d).
Part of this work was done while the authors were at the Max-Planck-Institut für Informatik, Saarbrücken.
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© 1996 Springer-Verlag Berlin Heidelberg
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Das, G., Kapoor, S., Smid, M. (1996). On the complexity of approximating Euclidean traveling salesman tours and minimum spanning trees. In: Chandru, V., Vinay, V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1996. Lecture Notes in Computer Science, vol 1180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62034-6_38
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DOI: https://doi.org/10.1007/3-540-62034-6_38
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