Euclidean bounded-degree spanning tree ratios

Authors:
Timothy M. Chan
Affiliations:
University of Waterloo, Waterloo, Ontario, Canada
Venue:
Proceedings of the nineteenth annual symposium on Computational geometry
Year:
2003

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Abstract

Let tK be the worst-case (supremum) ratio of the weight of the minimum degree-K spanning tree to the weight of the minimum spanning tree, over all finite point sets in the Euclidean plane. It is known that t2=2 and t5=1. In STOC'94, Khuller, Raghavachari, and Young established the following inequalities: 1.1033= 1.5 and 1.0354= 1.25. We present the first improved upper bounds: t3 and t4 . As a result, we obtain better approximation algorithms for Euclidean minimum bounded-degree spanning trees.Let tK(d) be the analogous ratio in d-dimensional space. Khuller et al. showed that t3(d) for any d. We observe that t3(d).