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Optimally Decomposing Coverings with Translates of a Convex Polygon
TLDR
We show that any k-fold covering using translates of an arbitrary convex polygon can be decomposed into Ω(k) covers. Expand
Algorithms for Dominating Set in Disk Graphs: Breaking the logn Barrier - (Extended Abstract)
TLDR
We improve the status quo in two ways: for the unweighted case, we show how to obtain a PTAS using the framework recently proposed (independently) by Mustafa and Ray [16] and by Chan and Har-Peled [4]. Expand
On clustering to minimize the sum of radii
TLDR
We consider the problem of computing a minimum cost <i>k</i>-cover for a given set of balls, denoted cost(<i>P</i>, whose union covers (contains) a set of at most k balls. Expand
Decomposing Coverings and the Planar Sensor Cover Problem
TLDR
We show that a k-fold covering using translates of an arbitrary convex polygon can be decomposed into Omega(k) covers (using an efficient algorithm). Expand
Guarding Terrains via Local Search
TLDR
We obtain a polynomial time approximation scheme for the terrain guarding problem improving upon several recent constant factor approximations. Expand
An Approximation Scheme for Terrain Guarding
TLDR
We obtain a polynomial time approximation scheme for the terrain guarding problem improving upon several recent constant factor approximations and show the existence of a planar graph that appropriately relates the global optimum. Expand
Approximation Algorithms for Dominating Set in Disk Graphs
TLDR
We improve the status quo in two ways: for the unweighted case, we show how toobtain a PTAS using the framework recently proposed (independently) by Mustafa and Ray [16] and byChan and Har-Peled [4]; for the weighted case where each input disk has an associated rational weightwith the objective of finding a minimum cost dominating set. Expand
On Metric Clustering to Minimize the Sum of Radii
TLDR
We study a clustering problem motivated by applications in base-station coverage. Expand
Maximum Weight Digital Regions Decomposable into Digital Star-Shaped Regions
TLDR
We consider an optimization version of the image segmentation problem, in which we are given a grid graph with weights on the grid cells. Expand
The VC-Dimension of Visibility on the Boundary of a Simple Polygon
TLDR
In this paper, we prove that the VC-Dimension of visibility on the boundary of a simple polygon is exactly 6. Expand
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