Minimizing the continuous diameter when augmenting a geometric tree with a shortcut
نویسندگان
چکیده
منابع مشابه
Minimizing the Continuous Diameter When Augmenting a Tree with a Shortcut
We augment a tree T with a shortcut pq to minimize the largest distance between any two points along the resulting augmented tree T + pq. We study this problem in a continuous and geometric setting where T is a geometric tree in the Euclidean plane, where a shortcut is a line segment connecting any two points along the edges of T , and we consider all points on T + pq (i.e., vertices and points...
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We seek to augment a geometric network in the Euclidean plane with shortcuts to minimize its continuous diameter, i.e., the largest network distance between any two points on the augmented network. Unlike in the discrete setting where a shortcut connects two vertices and the diameter is measured between vertices, we take all points along the edges of the network into account when placing a shor...
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Given a set P of points in the plane, a geometric minimum-diameter spanning tree (GMDST) of P is a spanning tree of P such that the longest path through the tree is minimized. In this paper, we present an approximation algorithm that generates a tree whose diameter is no more than (1+ ) times that of a GMDST, for any > 0. Our algorithm reduces the problem to several grid-aligned versions of the...
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Let P be a set of n points in the plane. The geometric minimum-diameter spanning tree (MDST) of P is a tree that spans P and minimizes the Euclidian length of the longest path. It is known that there is always a monoor a dipolar MDST, i.e. a MDST whose longest path consists of two or three edges, respectively. The more difficult dipolar case can so far only be solved in O(n) time. This paper ha...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2020
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2020.101631