منابع مشابه
On a Cone Covering Problem
Given a set of polyhedral cones C1, · · · , Ck ⊂ R, and a convex set D, does the union of these cones cover the set D? In this paper we consider the computational complexity of this problem for various cases such as whether the cones are defined by extreme rays or facets, and whether D is the entire R or a given linear subspace R. As a consequence, we show that it is coNP-complete to decide if ...
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The Conditional Covering Problem (CCP) aims to locate facilities on a graph, where the vertex set represents both the demand points and the potential facility locations. The problem has a constraint that each vertex can cover only those vertices that lie within its covering radius and no vertex can cover itself. The objective of the problem is to find a set that minimizes the sum of the facilit...
متن کاملThe Covering Path Problem on a Grid
This paper introduces the covering path problem on a grid (CPPG) which finds the costminimizing path connecting a subset of points in a grid such that each point is within a predetermined distance of a point from the chosen subset. We leverage the geometric properties of the grid graph which captures the road network structure in many transportation problems, including our motivating setting of...
متن کاملOn a Covering Problem for Equilateral Triangles
Let T be a unit equilateral triangle, and T1, . . . , Tn be n equilateral triangles that cover T and satisfy the following two conditions: (i) Ti has side length ti (0 < ti < 1); (ii) Ti is placed with each side parallel to a side of T . We prove a conjecture of Zhang and Fan asserting that any covering that meets the above two conditions (i) and (ii) satisfies ∑n i=1 ti ≥ 2. We also show that ...
متن کاملA note on the Covering Steiner Problem
A randomized approximation algorithm for the undirected and directed covering Steiner Problems is presented. The algorithm is based on a randomized reduction to a problem called 12 -Group Steiner. For the undirected case, the approximation ratio matches the approximation ratio of Konjevod et al. [KRS01]. However, our approach is a lot simpler. For the directed covering Steiner this gives an O(n...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2011
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2010.07.004