On the Fundamental Limits of Topology Control in Ad Hoc Networks |
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Authors: | András Faragó |
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Affiliation: | (1) Department of Computer Science, Erik Jonsson School of Engineering and Computer Science, The University of Texas at Dallas, Richardson, TX 75080, USA |
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Abstract: | We prove two results that provide new fundamental limits for topology control in large ad hoc and sensor networks. First,
we show that it remains true under very general conditions that the maximum expected node degree must grow to infinity at
least logarithmically if we want to maintain asymptotic connectivity. This has been known so far only for much more special
models than ours. Building on this result, we prove a new fundamental limit regarding link dynamics, which means the worst case length ratio of the longest and shortest link adjacent to the same node. We prove that if link
dynamics remains bounded, then no topology control algorithm can keep a large network connected with high probability. Moreover,
bounded link dynamics prevents connectivity in the limit without any a priori assumption on node degrees or transmission ranges.
Our results hold in a model that is much more general than the frequently used assumption of uniformly distributed nodes in
a regularly shaped planar domain. Our more abstract setting also aims at finding (hopefully) more robust and elegant proofs
that have less dependence on the special geometry. Since link dynamics is expected to be bounded in practice, the results
strenghten the theoretical basis for the argument that a very large ad hoc or sensor network is unable to maintain connectivity
if it has a flat, random organization without additional structure.
Supported in part by NSF Grants ANI-0220001 and CCF-0634848. |
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Keywords: | Ad hoc network Topology control Random graph model Connectivity |
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