Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6875762 | Theoretical Computer Science | 2017 | 16 Pages |
Abstract
Let P be a set of points in the plane, each equipped with a directional antenna that covers a sector of angle α and range r. In the symmetric model of communication, two antennas u and v can communicate to each other, if and only if v lies in u's coverage area and vice versa. In this paper, we introduce the concept of fault-tolerant spanners for directional antennas, which enables us to construct communication networks that retain their connectivity and spanning ratio even if a subset of antennas are removed from the network. We show how to orient the antennas with angle α and range r to obtain a k-fault-tolerant spanner for any positive integer k. For αâ¥Ï, we show that the range 13 for the antennas is sufficient to obtain a k-fault-tolerant 3-spanner. For Ï/2<α<Ï, we show that using range 6δ+19 for δ=â4/|cosâ¡Î±|â, one can direct antennas so that the induced communication graph is a k-fault-tolerant 7-spanner.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
M.A. Abam, F. Baharifard, M.S. Borouny, H. Zarrabi-Zadeh,