On Covering Points with Minimum Turns
نویسنده
چکیده
For the rectilinear version of the problem in which the lines must be axis-parallel, • Hassin and Megiddo (1991) observed that the problem in R reduces to vertex cover in bipartite graphs and hence is solvable in polynomial time, and proved that the problem in R in NP-hard by a reduction from 3SAT, • Gaur and Bhattacharya (2007) presented a (d − 1)approximation algorithm for the problem in R for all d ≥ 3. Hyperplanes For the more general problem of covering n points in R by k (not necessarily axis-parallel) hyperplanes, • Langerman and Morin (2005) presented FPT algorithms with both d and k as parameters. • Grantson and Levcopoulos (2006) and Wang, Li, and Chen (2010) improved the running times.
منابع مشابه
A Fast Algorithm for Covering Rectangular Orthogonal Polygons with a Minimum Number of r-Stars
Introduction This paper presents an algorithm for covering orthogonal polygons with minimal number of guards. This idea examines the minimum number of guards for orthogonal simple polygons (without holes) for all scenarios and can also find a rectangular area for each guards. We consider the problem of covering orthogonal polygons with a minimum number of r-stars. In each orthogonal polygon P,...
متن کاملOn Codes with Given Minimum Distance and Covering Radius
Codes with minimum distance at least d and covering radius at most d− 1 are considered. The minimal cardinality of such codes is investigated. Herewith, their connection to covering problems is applied and a new construction theorem is given. Additionally, a new lower bound for the covering problem is proved. A necessary condition on an existence problem is presented by using a multiple coverin...
متن کاملOn the Minimum Volume Covering Ellipsoid of Ellipsoids
We study the problem of computing a (1+ )-approximation to the minimum volume covering ellipsoid of a given set S of the convex hull of m full-dimensional ellipsoids in Rn. We extend the first-order algorithm of Kumar and Yıldırım that computes an approximation to the minimum volume covering ellipsoid of a finite set of points in Rn, which, in turn, is a modification of Khachiyan’s algorithm. F...
متن کاملOn the approximability of covering points by lines and related problems
Given a set P of n points in the plane, Covering Points by Lines is the problem of finding a minimum-cardinality set L of lines such that every point p ∈ P is incident to some line l ∈ L. As a geometric variant of Set Cover, Covering Points by Lines is still NP-hard. Moreover, it has been proved to be APX-hard, and hence does not admit any polynomial-time approximation scheme unless P = NP. In ...
متن کاملUsing the Particle Swarm Optimization Algorithm to Generate the Minimum Test Suite in Covering Array with Uniform Strength
Up to now, several useful algorithms have been proposed to generate covering array, which is one of the branches of combinatorial testing. The main challenge in generating such arrays is generation of the arrays with a minimum number of test cases (for efficiency) at a proper time (for performance), for large systems. Covering array generation strategies are often divided into two general categ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012