منابع مشابه
Unit Disk Cover Problem
Given a set D of unit disks in the Euclidean plane, we consider (i) the discrete unit disk cover (DUDC) problem and (ii) the rectangular region cover (RRC) problem. In the DUDC problem, for a given set P of points the objective is to select minimum cardinality subset D∗ ⊆ D such that each point in P is covered by at least one disk in D∗. On the other hand, in the RRC problem the objective is to...
متن کاملOn the Discrete Unit Disk Cover Problem
Given a set P of n points and a set D of m unit disks on a 2-dimensional plane, the discrete unit disk cover (DUDC) problem is (i) to check whether each point in P is covered by at least one disk in D or not and (ii) if so, then find a minimum cardinality subset D∗ ⊆ D such that the unit disks in D∗ cover all the points in P. The discrete unit disk cover problem is a geometric version of the ge...
متن کاملApproximation algorithms for the unit disk cover problem in 2D and 3D
Given a set P of n points in the plane, we consider the problem of covering P with a minimum number of unit disks. This problem is known to be NP-hard. We present a simple 4-approximation algorithm for this problem which runs in O(n log n)-time. We also show how to extend this algorithm to other metrics, and to three dimensions.
متن کاملA PTAS for the Weighted Unit Disk Cover Problem
We are given a set of weighted unit disks and a set of points in Euclidean plane. The minimum weight unit disk cover (WUDC) problem asks for a subset of disks of minimum total weight that covers all given points. WUDC is one of the geometric set cover problems, which have been studied extensively for the past two decades (for many different geometric range spaces, such as (unit) disks, halfspac...
متن کاملThe Within-Strip Discrete Unit Disk Cover Problem
We investigate the Within-Strip Discrete Unit Disk Cover problem (WSDUDC), where one wishes to find a minimal set of unit disks from an input set D so that a set of points P is covered. Furthermore, all points and disk centres are located in a strip of height h, defined by a pair of parallel lines. We give a general approximation algorithm which finds a 3d1/ √ 1− h2e-factor approximation to the...
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ژورنال
عنوان ژورنال: Journal of Discrete Algorithms
سال: 2015
ISSN: 1570-8667
DOI: 10.1016/j.jda.2015.05.002