On the maximum degree of minimum spanning trees
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Minimum Networks in Uniform Orientation Metrics
SIAM Journal on Computing
Optimal Steiner hull algorithm
Computational Geometry: Theory and Applications
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Given a set Z of n=2, we consider the problem of finding a @l-Steiner hull of Z, i.e., a region containing every Steiner minimal tree for Z in the @l-metric. We define a @l-Steiner hull @l-SH(Z) of Z as a set obtained by a maximal sequence of removals of certain open wedge-shaped regions from an initial hull followed by a simplification of its boundary. A perhaps surprising result is presented, namely that a Euclidean MST for Z can be used to decompose the problem of finding @l-SH(Z) into subproblems. Each of these can then be solved recursively using linear searches combined with a sweep line approach. Using this result, we present an algorithm computing @l-SH(Z). This algorithm has O(@lnlogn) running time and O(@ln) space requirement which is optimal for constant @l. We prove that @l-SH(Z) is independent of the order of removals of the open wedge-shaped regions.