Facility location and the geometric minimum-diameter spanning tree
نویسندگان
چکیده
منابع مشابه
Facility Location and the Geometric Minimum-Diameter Spanning Tree
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 with one or two nodes of degree greater 1, respectively. The more difficult dipolar case can so far only be solved in slightly subcubic time. This pap...
متن کاملApproximating the geometric minimum-diameter spanning tree
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...
متن کاملApproximating the Geometric Minimum-Diameter Spanning Tree
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...
متن کاملGeometric Minimum Diameter Spanning Tree Problem
Given a set P of n points in a plane, the Geometric Minimum Diameter Spanning Tree (GMDST) of P is a tree that spans P and minimizes the Euclidian length of the longest path. The best known algorithm for this problem runs in slightly sub-cubic time. In this report, I have surveyed some algorithms and approximation schemes developed for this problem and investigated the relation between this pro...
متن کاملGeometric Minimum Diameter Minimum Cost Spanning Tree Problem
In this paper we consider bi-criteria geometric optimization problems, in particular, the minimum diameter minimum cost spanning tree problem and the minimum radius minimum cost spanning tree problem for a set of points in the plane. The former problem is to construct a minimum diameter spanning tree among all possible minimum cost spanning trees, while the latter is to construct a minimum radi...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2004
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2003.07.007