The ultimate planar convex hull algorithm
SIAM Journal on Computing
Communication in wireless networks with directional antennas
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Strong connectivity in sensor networks with given number of directional antennae of bounded angle
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Connectivity guarantees for wireless networks with directional antennas
Computational Geometry: Theory and Applications
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What is the minimum angle @a0 such that given any set of @a-directional antennas (that is, antennas each of which can communicate along a wedge of angle @a), one can always assign a direction to each antenna such that the resulting communication graph is connected? Here two antennas are connected by an edge if and only if each lies in the wedge assigned to the other. This problem was recently presented by Carmi, Katz, Lotker, and Rosen (2011) [2] who also found the minimum such @a namely @a=@p3. In this paper we give a simple proof of this result. Moreover, in our construction each antenna can be assigned one of two possible directions and the diameter of the resulting communication graph is at most four. Our main tool is a surprisingly basic geometric lemma that is of independent interest. We show that for every compact convex set S in the plane and every 0