Journal of the ACM (JACM)
On k-Nearest Neighbor Voronoi Diagrams in the Plane
IEEE Transactions on Computers
Covering a line segment with variable radius discs
Computers and Operations Research
Coverage restricted to an angle
Operations Research Letters
Solving a 2-covered path problem with variable radii for wireless sensor networks
ICA3PP'12 Proceedings of the 12th international conference on Algorithms and Architectures for Parallel Processing - Volume Part II
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In this paper we describe and solve the following geometric optimisation problem: given a set S of n points on the plane (antennas) and two points A and B, find the smallest radial range r@?@?^+ (power transmission range of the antennas) so that a path with endpoints A and B exists in which all points are within the range of at least two antennas. The solution to the problem has several applications (e.g., in the planning of safe routes). We present an O(nlogn) time solution, which is based on the second order Voronoi diagram. We also show how to obtain a path with such characteristics.