Download Georgia State University: Wireless Sensor Networks & Medial Axis Routing - Prof. Yingshu L and more Papers Computer Science in PDF only on Docsity!
MAP: Medial Axis Based
Geometric Routingin Sensor Networks
J. Bruck, J. Gao, A. Jiang
By Shan Gao
Instructor: Dr. Yingshu Li
CSc 8910 Spring 2006
Department of Computer Science
Georgia State University
2
Introduction• Routing is elementary in all communication
networks.
- Networks with stable links and powerful nodes.– Networks with fragile links, constantly changing
topologies, and nodes with less resourcefulhardware.
Department of Computer Science
Georgia State University
3
Wireless sensor networks• Stationary• Deployed in a geometric space• Constrained power supply• P2P routing is required• Stable for static sensor nodes
Department of Computer Science
Georgia State University
4
Geometric proximity information
vs
Network topology
• Geographical forwarding• How to obtain the geographical locations
of a large number of sensors?
• Work well in a flat regular region with
simple geometry
Department of Computer Science
Georgia State University
5
Geometric proximity information
vs
Network topology (Cont.)
- Sensor fields in real world
- complex shape– Holes, obstacles, vulnerable nodes
- Other considerations
- Sensitive to location information– Load balance– Robust to network model
Department of Computer Science
Georgia State University
6
Geometric proximity information
vs
Network topology (Cont.)
A good infrastructure should:
- Abstract the geometric proximity of the sensors– Abstract the global geometric shape and topological
features of the sensor field
GLIDER
- Landmark-based naming & routing scheme– Delaunay triangulation– No theoretical way on how to select a good set of
landmark
Department of Computer Science
Georgia State University
7
Medial Axis• The set of points with at least two closest
neighbors on the boundaries of the shape
- A ‘skeleton’ of a region• Capture both geometric and topological
features
- Can be represented compactly by a graph
Department of Computer Science
Georgia State University
8
MAP•^
A medial axis based naming and routingprotocol
-^
Similar with GLIDER
- Also take a compact abstraction of the global
topology of the sensor field
•^
Difference - the choice of the abstraction
- The medial axis graph in MAP– The combinatorial Delaunay graph on landmarks in
GLIDER
Department of Computer Science
Georgia State University
13
MAP’s good properties•^
Location-free
-^
Expressive
-^
Compact
-^
Lightweight
-^
Efficient
-^
Load balancing
-^
Robust to network model
Department of Computer Science
Georgia State University
14
Medial axis based naming androuting•^
In continuous Euclidean domain
- For a continuous region in the Euclidean plane– Ideal situation -^
In a discrete sensor field
- A non-trivial re-design– Sensors have no geographical locations– Sensitive to noises on boundaries
Department of Computer Science
Georgia State University
15
Medial axis based naming androuting in continuous Euclideandomain•^
Concepts
- Medial axis– Chord– Medial ball– Medial node– Medial vertex– Medial edge– Medial radius– Canonical cell
Department of Computer Science
Georgia State University
16
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
17
Naming Scheme (Cont.)•^
N
( 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
18
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
19
Road System (Cont.)•^
The latitude and longitude curves provide aCartesian coordinate system for the pointsinside a cell
C
•^
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
20
Road System (Cont.)• For routing across cells• For points inside a medial ball of a medial
vertex
u
l-angular
curve
Department of Computer Science
Georgia State University
25
Construction of medial axis (Cont.)•^
Detect boundaries
- Dense sampling on the boundary (outer & holes’)
ε
-sample X
- By manual– By automatic detection
- Smaller sensor density• Breakage of wave propagation contours• Given sampling nodes
- Crust algorithm– Local flooding
Department of Computer Science
Georgia State University
26
Construction of medial axis (Cont.)• Construct MAG
- A node on the medial axis has equal hop
counts to two closest boundary nodes.
- Medial axis
- Sensitive to noises• Eliminate the unstable branches
Department of Computer Science
Georgia State University
27
Construction of medial axis (Cont.)• Construct MAG
- Identify medial nodes
- Boundary nodes initiate local flooding,
Messages with sender’s ID, boundary andhop counter
- Stop forwarding a packet, if its sender is
further away from current nearest boundarynode(s).
Department of Computer Science
Georgia State University
28
Construction of medial axis (Cont.)•^
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
Department of Computer Science
Georgia State University
29
Construction of medial axis (Cont.)•^
Construct MAG–^
Capture the geometric shape and thetopological properties of a sensor network.
Department of Computer Science
Georgia State University
30
Construction of medial axis (Cont.)• Assign names to sensors
- By a shortest path forest rooted at the medial
axis
- By which shortest path tree is stays on
Department of Computer Science
Georgia State University
31
Construction of medial axis (Cont.)•^
Assign names to sensors1.
Build shortest path
Majority vote to assign
T
( 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)
Department of Computer Science
Georgia State University
32
Construction of medial axis (Cont.)•^
Assign names to sensors–^
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*
Children of medial vertex have also polarcoordinates.
Department of Computer Science
Georgia State University
37
Medial axis based routing (Cont.)•^
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
38
Medial axis based routing (Cont.)• Routing under the polar coordinate system is
just the same
- All can be done by using one-hop neighbor
info. and target’s name.
Department of Computer Science
Georgia State University
39
Medial axis based routing (Cont.)• Improvements
- Keep a small routing table within 4 hops at
each node.
- Assign the polar coordinates to nodes in the
trees rooted at the medial nodes within a fewhops — e.g., 3 hops — from a medial vertex(rather than just the medial vertex itself).
Department of Computer Science
Georgia State University
40
Network dynamics• Add a node
- Connect to a one-hop shortest tree
- Delete a node
- Leaf, do nothing– Has descendants, re-add descendants– Medial node, neighbor medial nodes find
each other, assign new names
Department of Computer Science
Georgia State University
41
Network dynamics (Cont.)• Add a link
- Do nothing
- Lose a link
- Medial axis link, 2 ends connect by a
shortest path, build a new medial axis
- A path of a shortest path tree, re-add that
child/children
Department of Computer Science
Georgia State University
42
Simulation1.
Sensornetwork
Medial axis
Shortestpath forest
MAG
Department of Computer Science
Georgia State University
43
Simulation (Cont.)• MAP vs GPSR
- Comparable hops & Euclidean distance– Much better load balancing
- Robustness to network model
- Maintain stable performance on both the
construction of medial axis and routing
Department of Computer Science
Georgia State University
44
