Analysis of fundamental limits for partial connectivity in wireless networks
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Increased connectivity at lower cost: The case for multi-radio nodes in multi-hop wireless networks
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Structural properties of random graph models
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Asymptotically optimal trade-off between local and global connectivity in wireless networks
Performance Evaluation
Network topology models for multihop wireless networks
ISRN Communications and Networking
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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.