Performance guarantees for the TSP with a parameterized triangle inequality
Information Processing Letters
Power consumption in packet radio networks
Theoretical Computer Science
Hardness Results for the Power Range Assignmet Problem in Packet Radio Networks
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Symmetric Connectivity with Minimum Power Consumption in Radio Networks
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
Communication in wireless networks with directional antennas
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
DCOSS '08 Proceedings of the 4th IEEE international conference on Distributed Computing in Sensor Systems
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Connectivity guarantees for wireless networks with directional antennas
Computational Geometry: Theory and Applications
Switching to directional antennas with constant increase in radius and hop distance
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
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Let P be a set of points in the plane, representing transceivers equipped with a directional antenna of angle @a and range r. The coverage area of the antenna at point p is a circular sector of angle @a and radius r, whose orientation can be adjusted. For a given assignment of orientations, the induced symmetric communication graph (SCG) of P is the undirected graph, in which two vertices (i.e., points) u and v are connected by an edge if and only if v lies in u@?s sector and vice versa. In this paper we ask what is the smallest angle @a for which there exists an integer n=n(@a), such that for any set P of n antennas of angle @a and unbounded range, one can orient the antennas so that (i) the induced SCG is connected, and (ii) the union of the corresponding wedges is the entire plane. We show (by construction) that the answer to this question is @a=@p/2, for which n=4. Moreover, we prove that if Q"1 and Q"2 are two quadruplets of antennas of angle @p/2 and unbounded range, separated by a line, to which one applies the above construction, independently, then the induced SCG of Q"1@?Q"2 is connected. This latter result enables us to apply the construction locally, and to solve the following two further problems. In the first problem (replacing omni-directional antennas with directional antennas), we are given a connected unit disk graph, corresponding to a set P of omni-directional antennas of range 1, and the goal is to replace the omni-directional antennas by directional antennas of angle @p/2 and range r=O(1) and to orient them, such that the induced SCG is connected, and, moreover, is an O(1)-spanner of the unit disk graph, w.r.t. hop distance. In our solution r=142 and the spanning ratio is 8. In the second problem (orientation and power assignment), we are given a set P of directional antennas of angle @p/2 and adjustable range. The goal is to assign to each antenna p, an orientation and a range r"p, such that the resulting SCG is (i) connected, and (ii) @?"p"@?"Pr"p^@b is minimized, where @b=1 is a constant. For this problem, we devise an O(1)-approximation algorithm.