A PTAS for a Disc Covering Problem Using Width-Bounded Separators
نویسندگان
چکیده
In this paper, we study the following disc covering problem: Given a set of discs of 6 various radii on the plane, find a subset of discs to maximize the area covered by exactly one 7 disc. This problem originates from the application in digital halftoning, with the best known 8 approximation factor being 5.83 (Asano et al., 2004). We show that if the maximum radius 9 is no more than a constant times the minimum radius, then there exists a polynomial time 10 approximation scheme. Our techniques are based on the width-bounded geometric separator 11 recently developed in Fu and Wang (2004), Fu (2006). 12
منابع مشابه
Theory and application of width bounded geometric separators
We introduce the notion of the width bounded geometric separator and develop the techniques for the existence of the width bounded separator in any fixed ddimensional Euclidean space. The separator is applied in obtaining 2O( √ n) time exact algorithms for a class of NP-complete geometric problems, whose previous algorithms take nO( √ n) time . One of those problems is the well known disk cover...
متن کاملApproximation Schemes for Planar Graph Problems
Many NP-hard graph problems become easier to approximate on planar graphs and their generalizations. (A graph is planar if it can be drawn in the plane (or the sphere) without crossings. For definitions of other related graph classes, see the entry on Bidimensionality (2004; Demaine, Fomin, Hajiaghayi, Thilikos).) For example, maximum independent set asks to find a maximum subset of vertices in...
متن کاملApproximation Schemes for Deal Splitting and Covering Integer Programs with Multiplicity Constraints
We consider the problem of splitting an order for R goods, R ≥ 1, among a set of sellers, each having bounded amounts of the goods, so as to minimize the total cost of the deal. In deal splitting with packages (DSP), the sellers offer packages containing combinations of the goods; in deal splitting with price tables (DST), the buyer can generate such combinations using price tables. Our problem...
متن کاملLayered Separators in Minor-Closed Families with Applications
Graph separators are a ubiquitous tool in graph theory and computer science. However, in some applications, their usefulness is limited by the fact that the separator can be as large as Ω( √ n) in graphs with n vertices. This is the case for planar graphs, and more generally, for proper minor-closed classes. We study a special type of graph separator, called a layered separator, which may have ...
متن کاملTheory and Application of Width Bounded Geometric Separator
We introduce the notion of the width bounded geometric separator and develop the techniques for the existence of the width bounded separator in any d-dimensional Euclidean space. The separator is applied in obtaining 2 √ n) time exact algorithms for a class of NPcomplete geometric problems, whose previous algorithms take n √ n) time [2,5,1]. One of those problems is the well known disk covering...
متن کامل