Computing a minimum-dilation spanning tree is NP-hard
نویسندگان
چکیده
منابع مشابه
Computing a Minimum-Dilation Spanning Tree is NP-hard
Given a set S of n points in the plane, a minimumdilation spanning tree of S is a tree with vertex set S of smallest possible dilation. We show that given a set S of n points and a dilation δ > 1, it is NP-hard to determine whether a spanning tree of S with dilation at most δ exists.
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We prove that computing a geometric minimum-dilation graph on a given set of points in the plane, using not more than a given number of edges, is an NP-hard problem, no matter if edge crossings are allowed or forbidden. We also show that the problem remains NP-hard even when a minimum-dilation tour or path is sought; not even an FPTAS exists in this case.
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We prove that computing a minimum-dilation (Euclidean) Hamilton circuit or path on a given set of points in the plane is NP-hard.
متن کاملar X iv : c s . C G / 0 70 30 23 v 1 6 M ar 2 00 7 Computing a Minimum - Dilation Spanning Tree is NP - hard ∗
In a geometric network G = (S,E), the graph distance between two vertices u, v ∈ S is the length of the shortest path in G connecting u to v. The dilation of G is the maximum factor by which the graph distance of a pair of vertices differs from their Euclidean distance. We show that given a set S of n points with integer coordinates in the plane and a rational dilation δ > 1, it is NP-hard to d...
متن کاملMinimum Dilation Geometric Spanning Trees
The Minimum Dilation Geometric Spanning Tree Problem (MDGSTP) is N P-hard, which justifies the development of heuristics to it. This paper presents heuristics based on the GRASP metaheuristic paradigm for MDGSTP. The input of this problem is a set of points P = {p1, p2, . . . , pn} in the plane. Let the geometric graph G(P) associated with P be the undirected weighted complete graph of n vertic...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2008
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2007.12.001