Routing in Wireless Networks and Local Solutions for Global Problems
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Let P n be a set of points. The unit distance graph of P n is the graph with vertex set P n , in which two points are connected if their distance is at most one. Unit distance graphs of point sets can be used to model wireless networks in which the elements of P n represent the location the broadcast stations of our wireless networks. The stations are assumed to broadcast with the same power.
In recent years, it has been proved that many global problems for this type of networks can be solved by means of local algorithms, that is algorithms in which a node needs to communicate only with its neighbours. The first example of this, was the extraction of a planar connected subgraph of a unit distance wireless network, which was then used for a local type routing algorithm. In this talk we will survey several results in this area of research, and present recent results related to approximations of minimum weight spanning trees, snapshots of networks, etc.