# Topology Control of Multihop Wireless Networks using Transmit

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Topology Control of Multihop Wireless Networks

INFOCOM 2000

Ram Ramanathan, Regina Rosales-Hain

Bae Chi-Sung
Jan. 20, 2005
Network Systems Lab.

KAIST
No.1                                        Network Systems Lab.
Outline
 Introduction
 Problem formulation
 Centralized Algorithms
 Connected Min-Max Power (CMP)
 Bi-Connectivity Augmentation with Min-Max Power
 Distributed Heuristic Algorithms
 LINT (Local Information No Topology)
 LILT (Local Information Link-state Topology)
 Simulation Result
 Summary
 Critique

KAIST
No.2                                            Network Systems Lab.
Introduction
 Topology
The set of communication links between node pairs used by routing
mechanism
 Uncontrollable factor: Mobility, Weather, Interference, Noise
 Controllable factor: Transmit power, Antenna direction.

 Drawback of Wrong Topology
 Reduce the capacity
 Increase interference
 Increase end-to-end packet delay
 Decrease the robustness to node failure

 Consider transmit power adjustment problem in a multi-
hop wireless network to create a desired topology
KAIST
No.3                                                  Network Systems Lab.
Topology Control

KAIST
No.4               Network Systems Lab.
K-vertex/edge-connected
A graph is k-vertex/edge-connected if and only if
there are k vertex/edge-disjoint paths between
every pair of vertices

(a)1-vertex/edge-connected   (b) 2-vertex/edge-connected
(connected)                  (bi-connected)     KAIST
No.5                                          Network Systems Lab.
Problem formulation
 Connected Min-Max power
 Given an M=(N, L)

 Find a per-node minimal assignment of transmit powers p : N  Z
such that (1) the induced graph of (M,  ,p) is connected
(2) MAX uN ( p(u )) is minimum.

 Bi-connectivity Augmentation with Min-Max Power
 Given M=(N,L), and initial transmit power p : N  Z  such that
the induced graph (M,  , p) is connected
 Find a per node minimal set of power increases  (u)
such that (1) induced graph of (M,  , p(u )   (u )) is bi-connected
(2) MAX uN ( p(u )   (u )) is minimum

KAIST
No.6                                                      Network Systems Lab.
Algorithm CONNECT
Input: (1) Multi-hop wireless network M= (N, L)
(2) Least-power function
Output: Power levels for each node that induces
a connected graph

Begin
1. Sort node pairs in non-decreasing order of
mutual distance
2. initialize |N| clusters, one per node
3. for each (u,v) in sorted order do
4. if cluster(u)cluster(v)
5.          p(u)=p(v)=(d(u,v))
6.          merge cluster(u) with cluster(v)
7.          if number of cluster is 1
then end
8. perNodeMinimalize(M,,p,1)
end
KAIST
No.7                                              Network Systems Lab.
Per Node Minimize

Procedure perNodeMinimalize(M,,p,k)
Begin
1. let S = sorted node pair list
2. for each node u do
3. T={(n1,n2)S: u=n1 or u=n2}
4. sort T in no-increasing order of distance
5. discard from T all (x, y) such that
(d(x,y))>p(u)
6. for (x, y)  T using binary search do
7. if graph with p(u)=(d(x,y)) is not k-
connected, Stop
8. else p(u)= (d(x,y)
end

KAIST
No.8                                             Network Systems Lab.
Algorithm BICONN-AUGMENT
Input: (1) Multi-hop wireless network M= (N, L)
(2) Least-power function
(3) Initial power assignment inducing connected network
Output: Power levels for each node that induces a bi-connected graph.

Begin
1. sort node pairs in non-decreasing order of distance
2. G=graph induced by (M,,p)
3. For each (u,v) in sorted order do
4. if biconn-comp(G,u) biconn-comp(G,v)
5.       q= (d(u,v))
6.       p(u)=max(q,p(u))
7.       q(u)=max(q,p(v))
9. perNodeMinimalize(M,, p, 2)
end
KAIST
No.9                                                 Network Systems Lab.
Example

(a) Connected Networks   (b) Bi-connected Networks (c) Without Topology Control

KAIST
No.10                                                     Network Systems Lab.
Local Information No Topology Algorithm (LINT)

 Use locally available neighbor propagation model
information                     (r )   (rthr ) if r  rthr

 Attempts to keep the degree  (r )   (rthr )  10 log( r ), if r  rthr
rthr
of each node
If node degree > dh
reduces transmit power        d c  D rc 2
If node degree < dl              d d  D rd2
increases transmit power                                     rc
pc  ( (rthr )  10 log(        ))  T
rthr
 Power update equation                   pd  ( (rthr )  10 log(
rd
))  T
dd
pd  pc  5 log(      )                                       rthr
dc                                dd
pd  pc  5 log(      )
dc
KAIST
No.11                                                      Network Systems Lab.
Local Information Link-state Topology Algorithm (LILT)

 Uses freely available neighbor information and global
topology information
 Triggered whenever an event driven or periodic link-state
update
 A node determine topology states and take following
action
 Bi-connected
No Action
 Connected but not Bi-connected
1. Finds its distance form the closest articulation point
2. Set a timer for a value t
3. If acter time t the network is still not bi-connected, the node
increase its power to the maximum possible.
 Disconnected
Increases its transmit power to maximum possible value
KAIST
No.12                                                    Network Systems Lab.
Experiment Environment
 40 node network, 3 minutes simulation time
 Use Utilicom Logranger 2020
 900MHz ISM band (raw data rate 300Kbps)
 Transmission range: 6Miles
 Use software emulation of radio and its MAC layer Protocol
 Mobility and Propagation model
 Mobility: pseudo-random mobility model (72miles/hour)
h1
 Propagation model:   (d )  156  40log(d )  15log( )  ( g1  g 2)
h2
 12 data stream (random chosen source-destination pair,
mean rate is 4kbps)

KAIST
No.13                                                              Network Systems Lab.
Simulation Result (static networks)
 For grater than 1.5nodes/sq,
interference reduces spatial
reuse
 BICONN gives the best
changing density

 BICONN uses significantly more
power than CONNECT

KAIST
No.14                             Network Systems Lab.
Simulation Result (mobile networks)
 Above a density of 1 node/sq mile
increased density causes a decrease in
throughput
 Both LINT and LILT appropriately
reduce interference and improve
throughput
 LINT does better than LILT

 Only slight gains in delay performance

KAIST
No.15                                Network Systems Lab.
Concluding remarks
 Propose Centralized algorithms and distributed heuristics
for transmit power control
 Relevant to Commercial
 Static network algorithms improve the throughput and
battery life of infrequently mobile instant infrastructure
networks (Metricom’s Ricochet networks)

KAIST
No.16                                        Network Systems Lab.

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