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Abstract:
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A deep understanding of the structural properties
of wireless networks is critical for evaluating the performance of
network protocols and improving their designs. Many protocols
for wireless networks — routing, topology control, information
storage/retrieval and numerous other applications — have been
based on the idealized unit-disk graph (UDG) network model.
The significant deviation of the UDG model from many real
wireless networks is substantially limiting the applicability of
such protocols. A more general network model, the quasi unitdisk
graph (quasi-UDG) model, captures much better the characteristics
of wireless networks. However, the understanding on the
properties of general quasi-UDGs has been very limited, which
is impeding the designs of key network protocols and algorithms.
In this paper, we present results on two important properties
of quasi-UDGs: separability and the existence of power efficient
spanners. Network separability is a fundamental property leading
to efficient network algorithms and fast parallel computation. We
prove that every quasi-UDG has a corresponding grid graph
with small balanced separators that captures its connectivity
properties. We also study the construction of wireless backbones
through topology control for efficient communication and
present a distributed localized algorithm that builds a nearly
planar backbone in any quasi-UDG with low constant stretch
factor and degree. We demonstrate the excellent performance
of these properties through simulations and show, among many
applications, their application in efficient routing. |