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A range assignment to the nodes in a wireless ad hoc network induces a topology in which there is an edge between two nodes if and only if both of them are within each other's transmission range. The critical transmission radius for k-connectivity is the smallest r such that if all nodes have the transmission radius r, the induced topology is k -connected. In this paper, we study the asymptotic critical...
Topology control in ad-hoc networks tries to lower node energy consumption by reducing transmission power and by confining interference, collisions and consequently retransmissions. In other words, we are given the communication graph G obtained when all the nodes transmit at maximum power, the goal is to identify a sparse subgraph G (also called power spanner) of G such that only energy-efficient...
This paper studies the combinatorial properties of geometric structures, known as k-locally Delaunay graphs, introduced in the application of wireless ad hoc networks. Given a network that models the connections among its sensors as a k-locally Delaunay graph, we investigate which topologies are allowed for such a network. We show that the family of regular series-parallel graphs, a subfamily of two-terminal...
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