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This document from georgia state university discusses wireless sensor networks, the importance of geometric proximity information versus network topology, and the use of a medial axis-based naming and routing protocol (marp) for efficient routing in such networks. Topics include the construction of the medial axis graph (mag), assigning names to sensors, and network dynamics.
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J. Bruck, J. Gao, A. Jiang
By Shan Gao
Instructor: Dr. Yingshu Li
CSc 8910 Spring 2006
Department of Computer Science
Georgia State University
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topologies, and nodes with less resourcefulhardware.
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Georgia State University
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Georgia State University
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Georgia State University
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Georgia State University
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A good infrastructure should:
features of the sensor field
landmark
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Georgia State University
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Medial Axis• The set of points with at least two closest
Department of Computer Science
Georgia State University
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MAP•^
A medial axis based naming and routingprotocol
-^
Similar with GLIDER
topology of the sensor field
Difference - the choice of the abstraction
GLIDER
Department of Computer Science
Georgia State University
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MAP’s good properties•^
Location-free
-^
Expressive
-^
Compact
-^
Lightweight
-^
Efficient
-^
Load balancing
-^
Robust to network model
Department of Computer Science
Georgia State University
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In continuous Euclidean domain
In a discrete sensor field
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Georgia State University
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Concepts
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Georgia State University
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Naming Scheme•^
Lemma 3.1.
For a point
p
not on the medial axis, if
p
is on
a chord
xy
, with
x
є A
,^
y
є ∂
R
, then
y
is
p
’s only closest
point on
∂
R
.
-^
Lemma 3.2.
If
p
is not on the medial axis, there is a unique
chord through
p
.
-^
Theorem 3.3.
Every point in
R
is assigned a unique name.
-^
Each point has a unique name.
Department of Computer Science
Georgia State University
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Naming Scheme (Cont.)•^
( p
x
( p
) , y
( p
d
( p
C(p)=(|ap|/r,
bap)
(
)
x
p
A ∈
(
)
{ }
y p
R
∈
∂
∪ ⊥
(
)
[0,1]
d p
∈
b
R
∈
∂
Department of Computer Science
Georgia State University
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Road System•^
h-latitude curve, 0<= h <= 1
-^
x-longitude curve
A chord in C with medial point x
Lemma 3.4.
Inside a canonical cell, any two chords have no
common intersection.
-^
Theorem 3.5.
For a canonical cell
C
partitioned by the medial
axis and all the chords of medial vertices, the collection ofpoints with height
h
, 0
<= h <=
1, is a continuous curve.
-^
So,
h
-latitude curve is also continuous.
Department of Computer Science
Georgia State University
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Road System (Cont.)•^
The latitude and longitude curves provide aCartesian coordinate system for the pointsinside a cell
Routing for two points inside the same cell canbe done efficiently by first following the latitudecurve to a point on the same chord as thedestination, then following the longitude curveto the destination.
Department of Computer Science
Georgia State University
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Road System (Cont.)• For routing across cells• For points inside a medial ball of a medial
l-angular
curve
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Georgia State University
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Detect boundaries
ε
-sample X
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Georgia State University
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counts to two closest boundary nodes.
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Georgia State University
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Messages with sender’s ID, boundary andhop counter
further away from current nearest boundarynode(s).
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Georgia State University
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Construct MAG1.^
Include a type I medial node into P
ij, if its closest boundaries
include
i, j
Include all nodes on P
ij^ into medial axis
For i, connect paths
P
ij^ , for all
j , into a cycle
Star-like tree connect all adjacent paths
Connect nearby medial nodes and nearby paths
Trim away short branches
Broadcast to every nodes
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Georgia State University
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Capture the geometric shape and thetopological properties of a sensor network.
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axis
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Build shortest path
Majority vote to assign
( u
) to which side of
v
Positive/negtive height values
Assign node name by its relative position tothe medial axis.
x
-range [
l(v), k(v)
], height
h(v)
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Georgia State University
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On one path
Medial nodes: ([3, 4], 0)•^
2 children, ranges are {(3, 3.2), (3.2, 3.4), (3.4,3.6), (3.6, 3.8), (3.8, 4)}
Other nodes: ([3.2, 3.4], h
max*
Department of Computer Science
Georgia State University
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How to route greedily towards the temporary goalin parallel with the medial edge
x
ixi
-^
Pick a neighbor of
v
,^ w
, that is ‘closer’ to the temporary
routing goal than
v
is as the next hop.
( k
( w
) -l
( x
i +
2
h
( w
) -h
p
2
k
( v
) -l
x i +
h
( v
) -h
( p
2
Never route to a descendant
Never route to the other side
Never route backward
Department of Computer Science
Georgia State University
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Georgia State University
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each node.
trees rooted at the medial nodes within a fewhops — e.g., 3 hops — from a medial vertex(rather than just the medial vertex itself).
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Georgia State University
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Network dynamics• Add a node
each other, assign new names
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Georgia State University
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Network dynamics (Cont.)• Add a link
shortest path, build a new medial axis
child/children
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Georgia State University
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Simulation1.
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Georgia State University
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Simulation (Cont.)• MAP vs GPSR
construction of medial axis and routing
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Georgia State University
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