To what extent can one "prune" the links in a wireless network while retaining (almost) the same connectivity achieved when each node is connected to all nodes within its communication radius? In a nutshell, if each node explores a portion of its neighborhood sufficient to reach ≈ log(1/ε) other nodes in expectation, w.h.p. all but a fraction ε of the network joins the same connected component. Each node can then "locally" choose to maintain (at most) 4 links, and the network still retains w.h.p. essentially the same level of connectivity.
(More) Efficient Pruning of Wireless Ad Hoc Networks
PESERICO STECCHINI NEGRI DE SALVI, ENOCH
2009
Abstract
To what extent can one "prune" the links in a wireless network while retaining (almost) the same connectivity achieved when each node is connected to all nodes within its communication radius? In a nutshell, if each node explores a portion of its neighborhood sufficient to reach ≈ log(1/ε) other nodes in expectation, w.h.p. all but a fraction ε of the network joins the same connected component. Each node can then "locally" choose to maintain (at most) 4 links, and the network still retains w.h.p. essentially the same level of connectivity.
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