On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Perfect graphs and orthogonally convex covers
SIAM Journal on Discrete Mathematics
Covering orthogonal polygons with star polygons: the perfect graph approach
Journal of Computer and System Sciences
Linear time algorithms on circular-arc graphs
Information Processing Letters
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Algorithmic geometry
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
The 2-center problem with obstacles
Journal of Algorithms
Selecting forwarding neighbors in wireless ad hoc networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
On guarding the vertices of rectilinear domains
Computational Geometry: Theory and Applications
PTAS for geometric hitting set problems via local search
Proceedings of the twenty-fifth annual symposium on Computational geometry
A Scheme for Computing Minimum Covers within Simple Regions
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Covering points by unit disks of fixed location
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
| Hi-index | 0.00 |
Let $P$ be a simple polygon, and let $Q$ be a set of points in $P$. We present an almost-linear time algorithm for computing a minimum cover of $Q$ by disks that are contained in $P$. We then generalize the algorithm so that it can compute a minimum cover of $Q$ by homothets of any fixed compact convex set ${\cal O}$ of constant description complexity that are contained in $P$. This improves previous results of Katz and Morgenstern [Lecture Notes in Comput. Sci. 5664, 2009, pp. 447-458]. We also consider the minimum disk-cover problem when $Q$ is contained in a (sufficiently narrow) annulus and present a nearly linear algorithm for this case, too.