Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Capacity of Ad Hoc wireless networks
Proceedings of the 7th annual international conference on Mobile computing and networking
Wireless Communications: Principles and Practice
Wireless Communications: Principles and Practice
The capacity of wireless networks
IEEE Transactions on Information Theory
Providing location privacy in assisted living environments
Proceedings of the 1st international conference on PErvasive Technologies Related to Assistive Environments
An Almost Linear Time 2.8334-Approximation Algorithm for the Disc Covering Problem
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Covering a line segment with variable radius discs
Computers and Operations Research
Small-world effects in wireless agent sensor networks
International Journal of Wireless and Mobile Computing
| Hi-index | 14.98 |
Consider an infinite square grid G. How many discs of given radius r, centered at the vertices of G, are required, in the worst case, to completely cover an arbitrary disc of radius r placed on the plane? We show that this number is an integer in the set \{3,4,5,6\} whose value depends on the ratio of r to the grid spacing. One application of this result is to design facility location algorithms with constant approximation factors. Another application is to determine if a grid network design, where facilities are placed on a regular grid in a way that each potential customer is within a reasonably small radius around the facility, is cost effective in comparison to a nongrid design. This can be relevant to determine a cost effective design for base station placement in a wireless network.