Panos Pardalos
Distinguished Professor
Center for Applied Optimization
Dept. of Industrial and
Systems Engineering,
University of Florida
DIMACS/
DyDAn
Workshop: Approximation Algorithms
in Wireless Ad Hoc and Sensor Networks
April 22

24, 2009
Sensors Everywhere
Introduction
Data Fusion
Sensor Network Design
Sensor Network Localization
Sensor Scheduling
Network Interdiction
Sensors Everywhere
Introduction
Data Fusion
Sensor Network Design
Sensor Network Localization
Sensor Scheduling
Network Interdiction
What are sensors?
A
sensor
is
a
device
that
responds
to
a
physical
stimulus
(e
.
g
.
heat,
light,
sound,
pressure,
magnetism,
or
motion)
.
It
collects
and
measures
data
regarding
some
property
of
a
phenomenon,
object,
or
material
.
Typical
sensors
are
cameras,
radiometers
and
scanners,
lasers,
radio
frequency
receivers,
radar
systems,
sonar,
thermal
devices,
seismographs,
magnetometers,
gravimeters,
and
scintillometers
.
The term "Remote Sensing" indicates that the measuring device
is not physically in close proximity with the phenomenon being
observed.
Each
year
hundreds
millions
of
sensors
are
manufactured
.
They
are
in
domestic
appliances,
medical
equipment,
industrial
control
systems,
air

conditioning
systems,
aircraft,
satellites
and
toys
.
Sensors
are
becoming
smarter,
more
accurate
and
cheaper
.
They
will
play
an
ever
increasing
role
in
just
about
every
field
imaginable
.
How can nanotechnology improve the performance of
sensors?
The
application
of
nanotechnology
to
sensors
should
allow
improvements
in
functionality
.
In
particular,
new
biosensor
technology
combined
with
micro
and
nanofabrication
technology
can
deliver
a
huge
range
of
applications
.
They
should
also
lead
to
much
decreased
size,
enabling
the
integration
of
nanosensors
into
many
other
devices
.
Sensor Networks
A
sensor
network
is
a
collection
of
some
(sometimes
even
hundreds
&
thousands)
smart
sensor
nodes
which
collaborate
among
themselves
to
form
a
sensing
network
.
Sensor Applications
Homeland security
Radiation detection and standards
X

ray detectors and imaging
Integrated System Health Management (ISHM)
Multisensor
Data Fusion
Nondestructive Evaluation and Remote Sensing
Commercial Development
Environmental sensing
Medical/healthcare sensing
Robotic and remote sensing Tomography
Domestic electronics and smart homes
Crime prevention
Automotive and aerospace
Leisure industry and toys
Food and agriculture
Marine
Energy and Power
Sensors Everywhere
Introduction
Data Fusion
Sensor Network Design
Sensor Network Localization
Sensor Scheduling
Network Interdiction
Data Fusion
Combine information from many sensors to have a better
picture than the sensors were used individually
More accurate, more complete, more reliable
Sensors fusion algorithms use machine learning
techniques:
Statistical inference and forecasting
Kalman Filter
Bayesian Networks
Neural Networks
Fuzzy Logic
Dempster

Shaffer
Sensor Network Design
Finding optimal network topology accounts the
following characteristics:
Fault tolerance
The ability to sustain sensor network functionalities
without any interruption due to sensor node failures
Scalability
A well designed architecture must be able to work with
large number of nodes
Costs constraints
Deployment, Maintenance, etc
Hardware constraints
Size, Weight, Transmitting, etc
Sensors Everywhere
Introduction
Data Fusion
Sensor Network Design
Sensor Network Localization
Sensor Scheduling
Network Interdiction
Sensor Network Localization
Network topology identification:
Ad hoc and dynamics networks;
Sensor’s parameters can depend on it’s location:
Transmission characteristics;
Energy consumption;
Reliability.
Installing GPS receivers in every sensor
–
too expensive;
Mathematical programming techniques often allow to
find efficient solutions.
Ad hoc positioning system using
angle of arrival
Typically, a few nodes of the network know their
location

landmarks (equipped with GPS);
The rest of the nodes can communicate to other nodes;
Every node has a capability to determine the angle of
the arriving signal;
Every node in the network has fixed main axis to
measure all angles against it.
Every node can only communicate with its neighbors
within the radio range (they may not know their
location).
Ad hoc positioning system using
angle of arrival
Nodes with angle of arrival (AOA) capability
Ad hoc positioning system using
angle of arrival
Nodes immediately adjacent to a landmark get their
angle directly from the landmark.
If a node has some neighbors with orientation for a
landmark, it will be able to compute its own
orientation with respect to that landmark, and forward
it further into the network.
Knowledge of orientation to two other nodes (which
are not on one line) allows to calculate location of the
node by triangulation.
Ad hoc positioning system using
angle of arrival
Node A computes its orientation to remote node L
using information from B and C
Ad hoc positioning system using
angle of arrival
Probability for a node to satisfy conditions
necessary for orientation forwarding
Ad hoc positioning system using
angle of arrival
The proposed method calculates position of nodes in
Ad hoc network where nodes can measure angle of
arriving signal;
All nodes have AOA capability and only a fraction have
self position capability
Simulations showed that resulted positions have an
accuracy comparable to the radio range between
nodes, and resulted orientations are usable for
navigational or tracking purposes.
Localization via Semidefinite
Programming
Tomorrow (April, 23)
Semidefinite Programming, Graph Realization, and
Sensor Network Localization. Yinyu Ye, Stanford
University
Reduction to Semidefinite Programming
Solution existence
Statistical interpretation of the formulation (distance
values are random with normally distributed
measurement errors)
Reference
Sorokin, A.; Boyko N.; Boginski V.; Uryasev S.; Pardalos P.
Mathematical Programming Techniques for Sensor
Networks. Algoritms, 2009, p. 565

581
Sensors Everywhere
Introduction
Data Fusion
Sensor Network Design
Sensor Network Localization
Sensor Scheduling
Network Interdiction
Sensor Scheduling
Scheduling problem
–
m
sensors,
n
sites to observe,
n>m
. The problem is to find the schedule that reduces
potential loss of limited observations.
Single sensor scheduling
Multiple sensor schedule using percentile type
constrains
Sensor Scheduling
Scheduling problem
–
m
sensors,
n
sites to observe,
n>m
. The problem is to find the schedule that reduces
potential loss of limited observations.
Single sensor scheduling
Multiple sensor schedule using percentile type
constrains
Single Sensor Scheduling
The simplest case is to model one sensor that observes
a group of sites at discreet time point
Time for changing a site being observed is negligibly
small
Assume we need to observe
n
sites during
T
time
periods
During every period a sensor is allowed to watch only
at one of
n
sites
Decision variable:
Penalty for not observing site
i
at time
t
:

fixed penalty;

variable penalty;

time of last observing site
i
before time moment
t
;
is set to t if and only if the sensor is observing site
i
at time
t
otherwise it remains constant

only one site may be observed at a time
i
a
t
i
b
,
t
i
y
,
t
i
y
,
Single Sensor Scheduling
Problem Formulation:
Single Sensor Scheduling
Reference
This problem was first formulated for one sensor in
M. Yavuz and D.E. Je
ff
coat. Single sensor
scheduling for multi

site surveillance. Technical
report, Air Force Research Laboratory, 2007.
Sensor Scheduling
Single sensor scheduling
Multiple sensor schedule using percentile type
constrains
Multiple Sensor Scheduling
Next talk: Vladimir Boginski will present sensors
scheduling problem
Multiple sensors
Stochastic Setup
Robust formulation using Conditional Value at Risk
(CVaR)
Joint work with N. Boyko, T. Turko, D.E. Jeffcoat, S. Uryasev,
P.M. Pardalos
Sensors Everywhere
Introduction
Data Fusion
Sensor Network Design
Sensor Network Localization
Sensor Scheduling
Network Interdiction
Network Interdiction
An important issue in military applications is to
neutralize the communication in the sensors network
of the enemy
Given a graph whose arcs represent the
communication links in the graph.
(Offense) Select at most k nodes to target whose
removal creates the maximum network disruption.
(Defense) Determine which of your nodes to protect
from enemy disruptions.
Problem
Definition
Decision Version:
K

CNP
Input: Undirected graph
G = (V,E)
and integer
k
Question: Is there a set
M
, where
M
is the set of
all maximal connected components of
G
obtained by deleting
k
nodes or less, such that
where
σ
i
is the cardinality of component
i
, for all
i
in
M
?
M
i
i
i
K
2
)
1
(
Theoretical Results
Lemma 1
: Let
M
be a partition of
G = (V,E)
in to
L
components obtained by deleting a set
D
, where
D = k
Then the objective function
with equality holding if and only
σ
i
=
σ
j
, for all
i,j
in
M
, where
σ
i
is the size of
i
th
component of
M
.
Objective function is best when components are of
average size.
M
i
i
i
L
k
V
k
V
2
1


)

(
2
)
1
(
Theoretical Results
Lemma 2:
Let
M
1
and
M
2
be a two sets of
partitions of
G = (V,E)
obtained by deleting a set
D1 and D2
sets of nodes respectively, where
D
1

= D
2
 = k.
Let
L
1
and
L
2
be the number of
components in
M
1
and
M
2
respectively, and
L
1
≥
L
2
. If
σ
i
=
σ
j
, for all
i,j
in
M
1
, then we obtain a better
objective function value by deleting
D
1
.
Proof
of NP

Completeness
NP

complete: Reduction from
Independent Set
Problem
by a simple transformation and the result
follow from the above Lemmas.
Formulation
Let
u
i,j
= 1
, if
i
and
j
are in the same component of
G(V
\
A)
, and
0
otherwise.
Let
v
i
= 1
, if node
i
is deleted in the optimal solution,
and
0
otherwise.
We can formulate the CNP as the following integer
linear program
Formulation
Formulation
If
i
and
j
in different
components and
there is an edge
between them, at
least one must be
deleted
Formulation
Number of nodes
deleted is at most
k
.
Formulation
For all triplets
(i,j,k)
, if
(i,j)
in
same comp and
(j,k)
in same comp,
then
(i,k)
in same
comp.
Heuristics
We implement a heuristic based on Maximal
Independent Sets
Why? Because induced subgraph is empty
Maximum Independent Set provides upper bound on #
of components in optimal solution.
Greedy type procedure
Enhanced with local search procedure
Results are excellent
Heuristic obtains optimal solutions in fraction of time
required by CPLEX
Runs in
O(k
2
+ Vk)
time.
Results
•
This is the case you just saw!!
•
Optimal solutions computed for all values of k for this graph
•
The solutions are computed very quickly
Conclusions and Future Work
Identified nodes of sparse
Breakdown communication
Integer Programming and Heuristics
Approximation algorithms
Weighted version of the problems
Reference
A. Arulselvan, C.W. Commander, P.M. Pardalos, and
O. Shylo. Managing network risk via critical node
identification.
Risk Management in
Telecommunication Networks
, N. Gulpinar and B.
Rustem (editors), Springer, 2009
Conclusions
Applications
Health care
Military
Security and law enforcement
Satellite surveillance
… essentially Everywhere!
Research Directions
Computational complexity
Stochasticity
Robustness
…
Thank You!
Questions?
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