منابع مشابه
On the Shortest Separating Cycle
According to a result of Arkin et al. (2016), given n point pairs in the plane, there exists a simple polygonal cycle that separates the two points in each pair to different sides; moreover, a O( √ n)-factor approximation with respect to the minimum length can be computed in polynomial time. Here we extend the problem to geometric hypergraphs, and obtain the following characterization of feasib...
متن کاملThe Shortest Separating Cycle Problem
Given a set of pairs of points in the plane, the goal of the shortest separating cycle problem is to find a simple tour of minimum length that separates the two points of each pair to different sides. In this article we prove hardness of the problem and provide approximation algorithms under various settings. Assuming the Unique Games Conjecture, the problem cannot be approximated within a fact...
متن کاملComputing the Shortest Essential Cycle
An essential cycle on a surface is a simple cycle that cannot be continuously deformed to a point or a single boundary. We describe algorithms to compute the shortest essential cycle in an orientable combinatorial surface in O(n2 log n) time, or in O(n log n) time when both the genus and number of boundaries are fixed. Our results correct an error in a paper of Erickson and Har-Peled [DCG 2004].
متن کاملOn Finding a Cycle Basis with a Shortest Maximal Cycle
The Shortest Maximal Cycle Basis (SMCB) problem is that of finding a cycle basis B of a given graph G such that the length of the longest cycle included in B is the smallest among all bases of G. We show that any cycle basis B’ of G such that the sum of the lengths of the cycles included in B’ is the smallest among all cycle bases of G constitutes a solution to the SMCB problem. Finding a basis...
متن کاملShortest cycle through specified elements
We give a randomized algorithm that finds a shortest simple cycle through a given set of k vertices or edges in an n-vertex undirected graph in time 2n.
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2020
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2020.101612