The ultimate planar convex hull algorithm
SIAM Journal on Computing
Angle-restricted tours in the plane
Computational Geometry: Theory and Applications
Power consumption in packet radio networks
Theoretical Computer Science
On the performance of ad hoc networks with beamforming antennas
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
On the Complexity of Computing Minimum Energy Consumption Broadcast Subgraphs
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
Algorithmic aspects of topology control problems for ad hoc networks
Mobile Networks and Applications
Energy-Efficient Wireless Network Design
Theory of Computing Systems
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Communication in wireless networks with directional antennas
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
OPODIS'04 Proceedings of the 8th international conference on Principles of Distributed Systems
Do directional antennas facilitate in reducing interferences?
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Computational Geometry: Theory and Applications
Symmetric connectivity with directional antennas
Computational Geometry: Theory and Applications
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We study a combinatorial geometric problem related to the design of wireless networks with directional antennas. Specifically, we are interested in necessary and sufficient conditions on such antennas that enable one to build a connected communication network, and in efficient algorithms for building such networks when possible. We formulate the problem by a set P of n points in the plane, indicating the positions of n transceivers. Each point is equipped with an @a-degree directional antenna, and one needs to adjust the antennas (represented as wedges), by specifying their directions, so that the resulting (undirected) communication graph G is connected. (Two points p,q@?P are connected by an edge in G, if and only if q lies in p@?s wedge and p lies in q@?s wedge.) We prove that if @a=60^o, then it is always possible to adjust the wedges so that G is connected, and that @a=60^o is sometimes necessary to achieve this. Our proof is constructive and yields an O(nlogk) time algorithm for adjusting the wedges, where k is the size of the convex hull of P. Sometimes it is desirable that the communication graph G contain a Hamiltonian path. By a result of Fekete and Woeginger (1997) [8], if @a=90^o, then it is always possible to adjust the wedges so that G contains a Hamiltonian path. We give an alternative proof to this, which is interesting, since it produces paths of a different nature than those produced by the construction of Fekete and Woeginger. We also show that for any n and @e0, there exist sets of points such that G cannot contain a Hamiltonian path if @a=90^o-@e.