# Topology Control

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```					  Topology Control of Multihop
Wireless Networks Using Transmit
Paper By:   Ram Ramanathan, Regina Resales-Hain
Slides adapted from R. Jayampathi Sampath
Presenter: Shahram Mohrehkesh, CS852, ODU, Spring 2011
Outline
lNTRODUCTION

PROBLEM STATEMENT

STATIC NETWORKS: OPTIMUM CENTRALIZED ALGORITHMS
CONNECT
Separation Edges and Vertices
Biconnected Graph
BICONN-AUGMENT

MOBILE NETWORKS : DISTRIBUTED HEURISTICS
LINT Description
LILT Description

EXPERIMENTAL RESULTS
lNTRODUCTION
set of communication links between node pairs used
explicitly or implicitly by a routing mechanism.

uncontrollable factors: mobility, weather, noise
controllable factors: transmit power, antenna direction

This paper addresses the problem of controlling the
topology of the network by changing the transmit powers
of the nodes.

Controlling the set of neighbors to which a node talks to is
the basic approach.
lNTRODUCTION(Contd.)
Why do we need to control the topology?
Draw back of a wrong topology
Reduce the capacity
Increase the end-to-end packet delay
Decrease the robustness to node failures
Example 1 – Too sparse network
A danger of network partitioning
High end to end delays
Example 2 – Dense network
Many nodes interfere with each other
Recompute routes even if small node movements
PROBLEM STATEMENT
Definition 1: A multihop wireless network is represented
as M = (N, L), where N is a set of nodes and L
is a set of coordinates on the plane denoting the locations
of the nodes.

Definition 4: The least-power function gives the
minimum power needed to communicate a distance of d.

Definition 6: Problem Connected MinMax Power (CMP).
Given an M = (N, L), and a least-power function   find a
per-node minimal assignment of transmit powers
such that the induced graph of (M, p) is connected, and
is a minimum.
PROBLEM STATEMENT (Contd.)
Definition 7: Problem Biconnectivity Augmentation with
MinMax Power (BAMP). Given a multihop wireless net M =
(N, L), a least-power function     and an initial assignment
of transmit powers                   such that the induced
graph of (M,     p) is connected, find a pernode minimal set
of power increases         such that the induced graph of
is biconnected, and
is a minimum.
STATIC NETWORKS: OPTIMUM
CENTRALIZED ALGORITHMS

s-p

step number          power assigned
d(s)

distance            step number
Algorithm CONNECT (Contd.)

side-effect edge

A side effect edge may form a loop with other edges and
may allow the lowering of some power levels and the
elimination of some edges added previously.
Per Node Minimalize
reduction of power of A and B to 1 again.

A      B
Separation Edges and Vertices
Definitions
Let G be a connected graph
A separation edge of G is an edge whose removal disconnects G
A separation vertex of G is a vertex whose removal disconnects G
Applications
Separation edges and vertices represent single points of failure in a
network and are critical to the operation of the network
Example
3, 5 and 6 are separation vertices
(3,5) is a separation edge

4
1                                       7

6

2                3                 5                8
Biconnected Graph
Equivalent definitions of a bi-connected graph G
Graph G has no separation edges and no separation vertices
For any two vertices u and v of G, there are two disjoint
simple paths between u and v (i.e., two simple paths between
u and v that share no other vertices or edges)
For any two vertices u and v of G, there is a simple cycle
containing u and v
Example

4
1                                7

6

2              3             5              8
Algorithm BICONN-AUGMENT
Identify the bi-connected
components in the graph
induced by the power
assignment from
algorithm CONNET
This is done using method
based on depth-first
search
Node pairs are selected in
non-decreasing order of
their mutual distance and
joined only if they are in
different bi- connected
components
This is continued until the
network is biconnectd.
Implementation
40 nodes spread out with a density of 2 nodes/sq mile
MOBILE NETWORKS :
DISTRIBUTED HEURISTICS
The topology is continually changing
Solution: continually readjust the transmit powers of
the nodes to maintain the desired topology.
The solution must use only local or already available
information. Eg. Positions

Centralized solutions not available in a mobile
context.

Present two distributed heuristics
Local Information No Topology (LINT)

Zero overhead protocols; they do not use any
special control messages for their operation
LINT
Uses locally available information collected by a routing
protocol
Attempt to keep degree of each node bounded.
if d(Ni)>dh
reduce transmit power
if d(Ni)<dl
increase transmit power
dh High threshold on the node degree
dl Low threshold on the node degree
dd desired degree, dc current degree
Gamma is factor of propagation loss function based on
environment, between 2 and 5 , set 4 in emulations
New power
LILT
significant shortcomings of LINT
Unaware of network connectivity
Danger of a network partitioning

LILT uses global information available in locally to recognize and
repair network partitions

Two main parts
Neighbor reduction protocol (NRP)
LINT mechanism

The purpose triggering is to override the high threshold bounds
and increase the power if the topology change indicated by the
routing update results in undesirable connectivity.
Experiment
Emulation by a prototype of Rooftop communication nodes
40 nodes
3 min of simulation
In mobile scenarios, random movement with speed of 72
miles/hour
256 bytes packet
12 stream
Arrival rate of 4Kbps per stream
EXPERIMENTAL RESULTS- static

AVG

BICONN better   BICONN uses more power
EXPERIMENTAL RESULTS -mobile

-LINT is better. Not an ideal scenario
- Density 1 is where the network is connected   No significant changes
and increase in density cause drop in           Delay is calculated only for
throughput
successful transferred
-Bkz of hidden terminal and inaccurate link     messages
state information LILT start to downgrade
Thanks

Questions ???

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