MASSIMO FRANCESCHETTI

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Theoretical tools for sensor networks
MASSIMO FRANCESCHETTI NEST retreat, January 2003
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Where is all this theory? Is it useful? How can
we use it?
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NEST, the temple of the real world
Dont think a wireless network is like a bunch
of discs on the plane (David Culler)
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The geometric disc abstraction
Connectivity (continuum percolation theory)
Capacity (Gupta and Kumar, 2000)
Routing
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Introduced by
Ed Gilbert (1961) to improve upon the Erdös and
Rényi random graph model
to model wireless multi-hop networks
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Ed Gilbert (1961)
P Prob(exists unbounded connected component)
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Example
l0.3
l0.4
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(No Transcript)
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2003 Technology
1960s theory?
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Unreliable connectivity
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Rotationally asymmetric ranges
Start with simplest extensions
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Random connection model
Connection probability
Let
define
such that
x1-x2
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Squishing and Squashing
Connection probability
x1-x2
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Example
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A Theorem for connectivity
For all
it is easier to reach connectivity in an
unreliable network
longer links are trading off for the
unreliability of the connection
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Shifting and Squeezing
Connection probability
x
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Example
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Do long edges help percolation?
Mixture of short and long edges
Edges are made all longer
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for the standard connection model (disc)
CNP
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Do long edges help routing?
A fundamental trade off shortest path vs. number
of retransmissions
S
D
D
S
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Do long edges help routing?
Mininize the expected numnber of retransmission
(Alec) Existing routing algorithms perform better
when allowing unreliable (long) links ?
S
D
D
S
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Non-circular shapes
Among all convex shapes the triangle is the
easiest to percolate Among all convex shapes the
hardest to percolate is centrally
symmetric Jonasson (2001), Annals of Probability.
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Conclusion
To the engineer have faith in theory To the
theoretician build the right tools
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Some references
Critical power for asympototic connectivity in
wireless networks P. Gupta, P.R. Kumar (1998)
The capacity of wireless networks P. Gupta, P.R.
Kumar (IEEE Trans. on Inf. Theory, 2000)
Continuum Percolation R. Meester, R. Roy
(Cambridge University press, 1995)
Critical power for connectivity in clustered
wireless networks L. Booth, J. Bruck, M.
Franceschetti, R. Meester (ISIT, 2002)
Covering algorithms continuum percolation and the
geometry of wireless networks L. Booth, J. Bruck,
M. Franceschetti, R. Meester (Annals of applied
probability, in press)
Ad hoc wireless networks with noisy links. L.
Booth, J. Bruck, M. Franceschetti, M. Cook
(preprint)
massimof_at_EECS.berkeley.edu