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Georgia State University: Wireless Sensor Networks & Medial Axis Routing - Prof. Yingshu L, Papers of Computer Science

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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MAP: Medial Axis Based
Geometric Routing
in 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 resourceful
hardware.
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?
GPS, algorithms
Work well in a flat regular region with
simple geometry
pf3
pf4
pf5
pf8
pf9
pfa

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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?

  • GPS, algorithms

• 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

  • Continuous -^

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).

  • Assumption

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

  • Others, do nothing

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