Improving the Lifetime of Sensor
Networks via Intelligent Selection
of Data Aggregation Trees
Konstantinos Kalpakis, Koustuv Dasgupta, Parag Namjoshi
Department of Computer Science and Electrical Engineering
University of Maryland Baltimore County
{kalpakis, dasgupta, nam1}@csee.umbc.edu
CNDS ‘03
URL: http://www.csee.umbc.edu/~nam1
Sensor Networks – Goals and Challenges
Recent advances in micro-sensor technology and low-power
analog/digital electronics have led to the advent of wireless
networks of sensor devices
Sensor network – a tool for distributed sensing of physical
phenomena

Establish paths between point(s) of interest and observer(s)
One or more base stations



Comprises of relatively inexpensive sensor nodes
Readily deployable in physical environments to collect useful
information
Typically ad-hoc and multi-hop networks
Applications: military surveillance, object tracking, habitat
monitoring, search and rescue operations
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Sensor Networks – Goals and Challenges
Sensor networks are severely resource-constrained

Energy

Computing capabilities

Communication resources
Energy - the most critical resource


Each sensor is typically fitted with a finite nonreplenishable energy source (battery)
Replacing batteries in possibly harsh terrains might be
infeasible
The lifetime and hence the utility of the sensor
network is determined by energy usage
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Data Aggregation in Sensor Networks
Data aggregation


In-network fusion of data from different sensors to eliminate
redundant transmissions to the base station.
This significantly reduces the amount of data traffic as well as
the distances over which the data needs to be transmitted
In the process of in-network aggregation, the value generated
at each sensor in each round must influence the value that
reaches the base-station in that round !
Source 1
Sink
A
Source 2
2
1
Data
Aggregation
B
1+2
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Energy-Efficient Sensor Networks
Energy-aware routing protocols [Singh et al 1998]
LEACH [Heinzelman et al 1999]

Clustering-based protocol for transmitting data to the base station
Chang and Tassiulas [2001]

routing algorithms that maximize the time until the sensor energies drain
out
Bharadwaj et al [2001]
upper bounds on the lifetime of an energy-constrained sensor network
PEGASIS [Lindsey et al 2001]
 Chains formed among sensors to gather and aggregate data
 Sensors take turns to transmit to the base station

PEGASIS-based hierarchical scheme [Lindsey et al 2001]

Reduces
the delay incurred in each round of data gathering
TinyOS [Madden et al 2002]
 Implements the basic database predicates like COUNT, MIN, MAX, and
AVERAGE. These predicates are well suited to the in-network regime.
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Overview
System Model.
Maximum Lifetime Data Aggregation Problem.

Kalpakis, Dasgupta, and Namjoshi [2002]
A-Restricted MLDA.

An efficient algorithm for data gathering problem.
Experimental Results.
Conclusions.
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System Model
The locations of the sensors and base station are fixed and known a-priori
Each sensor has a finite, non-replenishable energy source
Any sensor can transmit to any other sensor or to the base station in one hop
 Sensors can adjust the antenna range to minimize the energy usage to
reach the intended recipient
Continuous data delivery

Each sensor observes a continuous phenomenon and produces some
information as it monitors its vicinity
A k-bit data packet is generated every time unit

Each time unit is referred to as a round

Data gathering
at each round, one data packet must be collected from each sensor
to be transmitted to the base station
the lifetime of the system is defined to be the number of rounds
until the first sensor is drained of its energy
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Energy Model for Sensors
Energy Model

First Order Radio Model

Each time sensor transmits or receives data, it expends some energy

Energy spent for transmitting k bits from sensor i to sensor j over dij meters is:

Energy spent for receiving k bits at sensor i is:
where,
εelec = 50 nJ/bit for driving transmitter/receiver circuitry
εamp = 100 pJ/bit/m2 for the transmitter amplifier
dij
CNDS ‘03
= distance between sensors i and j
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Maximum Lifetime Data Aggregation (MLDA) Problem
The MLDA problem is to find a data gathering schedule with
maximum lifetime for a sensor network which allows innetwork data aggregation

An aggregation tree is a directed tree rooted at the base station
and spanning all the sensors.
An aggregation tree specifies, how the data packets from all the
sensors are collected, aggregated and transmitted to base station.
There is one such aggregation tree for each round.

A schedule with lifetime T is a collection of up to T aggregation
trees
An aggregation tree may be used more than once in a schedule.
If an aggregation tree is used for f rounds, then it has lifetime f.
The lifetime of a schedule is the sum of the lifetimes of aggregation
trees in the schedule.

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A feasible schedule is a schedule which respects the energy
constraints of the sensors
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Aggregation Trees
X
X
1
4
2
3
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1
4
2
3
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Maximum Lifetime Data Aggregation (MLDA) Problem…
Kalpakis, Dasgupta, and Namjoshi [ICN 2002] give a near
optimal solution to the MLDA problem.



The problem is formulated as a flow problem with linear objective
function and linear constraints.
An integer program is presented to solve the MLDA problem.
The linear relaxation of the integer program can be computed in
polynomial time.
MLDA problem can be shown to be NP-complete by reduction from
Hamiltonian Path problem.



CNDS ‘03
A integer solution is computed by flooring the flow variables given
by the linear program and re-computing the linear program with
the floored flows as constraints.
Experiments show that this solution is within 5 rounds of
fractional optimal solution.
MLDA approximation algorithm has a very high time complexity.
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A-Restricted MLDA
A-Restricted MLDA is an alternate formulation of
Maximum Lifetime Data Gathering problem.
Suppose that we are restricted to use a set of
aggregation trees A. (candidate set).
A-Restricted MLDA problem is to find the maximum
lifetime schedule using the aggregation trees from
candidate set only.

in other words, we must decide the lifetime of each
aggregation tree in A, such that sum of all lifetimes is
maximized.
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A few more definitions…
For an aggregation tree Ai, we define its energy vector E(i) as
a vector of size n indicating the energy consumed by each
sensor, in Ai.

Intuitively, energy vector denotes energy expended by each
sensor during one round of data gathering using tree Ai.

Given a candidate set comprising of m trees, let S be a schedule
that uses the aggregation trees only from candidate set.
 is a vector of size n indicating the initial energy of each
sensor.
To solve A-Restricted MLDA problem, we need to determine
the lifetime i of each tree in the candidate set in schedule S
such that lifetime of the system is maximized.
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A Linear Programming Formulation for
A-Restricted MLDA
The above integer program with linear constraints can be used
to solve A-Restricted MLDA problem.



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This integer program computes maximum lifetime schedule S
comprising of trees in candidate set
The energy constraint ensures that no sensor expends more than
its initial energy.
n constraints (one for each sensor) and m variables (one for each
tree in candidate set)
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A Linear Programming Formulation for
A-Restricted MLDA…
The linear relaxation of the integer program where i are
allowed to take fractional values, can be computed in
polynomial time.


We obtain the approximate solution by fixing the lifetime of each
aggregation tree to the floor of its lifetime obtained from linear
program.
This ensures that energy constraints are never violated by any
sensor.
If the candidate set contained all possible aggregation trees,
solution for A-Restricted MLDA problem is the solution for
MLDA problem.

Unfortunately, for a network with n sensors, number of such
aggregation trees is (2n).
The linear relaxation of the integer program provides us with
an approximation scheme for MLDA problem.
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A Linear Programming Formulation for
A-Restricted MLDA…
Better lifetimes can potentially be obtained by the
LP if a larger candidate set is used.

To be precise, if S1  S2, then lifetime for S1  the
lifetime for S2.
Thus, we are interested in finding easily computable
candidate sets with few ( O(nc) for some small
constant c ) aggregation trees, that provide us with
“good” lifetime.
We describe two approaches to construct the
candidate sets and discuss the performance of
these schemes.
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The A-LRS Algorithm
The LRS Protocol (PEGASIS-based hierarchical scheme)









CNDS ‘03
[Lindsey, Raghavendra and Sivalingam, 2001]
LRS protocol clusters sensors greedily based on their distances from each
other and the base-station.
Chains are formed among the nodes in the clusters at the lowest level of
the hierarchy.
Gathered data moves along the chain, gets aggregated and reaches a
designated leader of the chain i.e. cluster head.
The cluster heads from level one are again clustered into one or more
clusters (chains), and data is collected and aggregated in each chain in a
similar manner.
In the final level of the hierarchy, one sensor is chosen to transmit the
aggregated data packet for that round to the base station.
The leader in each round in each chain is selected in round robin manner.
The number of hierarchies is always 3.
Note that the manner in which chain leaders are selected in each level of
hierarchy, naturally defines an aggregation tree
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The A-LRS Algorithm…
LRS imposes an implicit ordering among the sensors in each cluster at
every level of the hierarchy.

clusters are arranged in a chain.

data always moves along the chain towards the leader.

This ordering is determined during initialization, but remains fixed
thereafter.
LRS then simply alternates between the members of each chain in a
round-robin fashion to determine the leader(s) for a particular
round.
During the first n rounds of data gathering, LRS induces a set of n
distinct aggregation trees.


After the first n rounds, these n trees are used by the LRS protocol in
a round-robin manner.
We refer to these trees as the LRS aggregation trees.
The LRS trees form a suitable candidate set for the
A-Restricted MLDA.
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The A-Randomized-LRS Algorithm
A larger candidate set of aggregation trees can potentially
lead to a data gathering schedule with better lifetime.
We augment the LRS set of aggregation trees by permuting
the sensors in each cluster (chain) at the lowest level of the
LRS hierarchy.
Recall that, LRS imposes an implicit ordering among the
sensors within each cluster (chain) at the lowest level of the
hierarchy.
This ordering limits the number of distinct aggregation trees
used.
By using a different ordering of the sensors in one or more
clusters, one can easily construct a different set of
aggregation trees.
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A-Randomized-LRS Trees
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The A-Randomized-LRS Algorithm…
We start with a greedy clustering of the sensors into
chains,so that every sensor transmits to a close neighbor as in
LRS.
Using P random permutations of the sensors, where each
permutation randomly permutes the sensors within each cluster
at the lowest level of the hierarchy, we obtain additional P
orderings.
We can obtain additional ( P x n ) LRS aggregation trees by
running LRS for each of these orderings.
By choosing P to be a small constant, we can still solve the A-
Restricted MLDA problem efficiently, and potentially obtain
superior system lifetimes with respect to the A-LRS algorithm.
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Maximum Lifetime Data Routing (MLDR) Problem
Data aggregation is not applicable in all sensing environments.
In some environments, no aggregation may be feasible.


video images from distant regions of a battlefield with no overlap
this implies that the number and size of transmissions will
increase, thereby draining the sensor energies much faster.
Problem is to find an efficient schedule to collect and transmit
the data to the base station, such that the system lifetime T
is maximized.
This problem can be viewed as a maximum flow problem with
energy constraints at the sensors, subject to integral flows.
Note that MLDR schedule is a collection of paths to the base
station from each sensor.
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Maximum Lifetime Data Routing (MLDR) Problem…
The linear relaxation of the above integer program can be
computed in polynomial time.
A near-optimal solution to the MLDR problem can be obtained
by running the above linear program again and fixing the
values of the fi,j variables to the floor of their values
obtained in the previous step.

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The solution obtained in this second step is guaranteed to have
integer values for all the variables, since it is a max-flow
problem with integer capacities.
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Performance Evaluation
We will compares the performance of various
schemes for

unlimited aggregation,
MLDA, A-LRS, A-Randomized-LRS and LRS schemes

limited aggregation,
A-LRS, A-Randomized-LRS and LRS schemes
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Experimental Setup
We consider a network with sensors randomly distributed in
50m x 50m field
Number of sensors is varied between 40, 50, 60, 80 and 100
Each sensor has initial energy 1 Joule
The base-station is located at (25m, 150m)
Each sensor generated data packets of size 1000 bits
Energy model used is the First Order Radio Model
For each experiment, we measure the lifetime of the sensor
network for A-LRS and A-R-LRS algorithms
For A-R-LRS algorithm, we experiment with 10, 25, 50, 75,
100, 250, 500, 750, and 1000 permutations.
We compare our results with the LRS protocol [Lindsey et al
2001], MLDA and the fractional optimal.
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Results with Unlimited Aggregation
n=50
c=5
Algorithm
LRS
A-LRS
P=10
P=25
P=50
P=75
A-R-LRS P=100
P=250
P=500
P=750
P=1000
MLDA
Fractional Optimal
CNDS ‘03
T
5872
6490
6493
6490
6620
6692
6755
6782
6807
6805
6805
6808
6809
n=60
c=5
G
0
10.52
10.57
10.52
12.73
13.96
15.03
15.49
15.92
15.88
15.88
15.94
15.95
T
5466
6213
6465
6795
6811
6813
6813
6946
6946
7021
7021
7174
7176.2
n=80
c=10
G
0
13.66
18.27
24.31
24.6
24.64
24.64
27.07
27.07
28.44
28.44
31.24
31.28
T
6002
6545
6622
6677
6748
7223
7416
7645
7705
7827
7827
7945
7946.9
n=100
c=10
G
0
9.04
10.32
11.24
12.42
20.34
23.55
27.37
28.37
30.4
30.4
32.37
32.4
T
5526
6265
6541
6541
7005
7398
7440
7440
7593
7833
8082
8290
8292.6
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G
0
13.37
18.36
18.36
26.76
33.87
34.63
34.63
37.4
41.74
46.25
50.01
50.06
26
Comparisons for a 50 sensor network
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Comparisons for a 100 sensor network
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Limited Aggregation Model
Limited aggregation



Unlimited aggregation may not always be applicable.
We now consider a simple “limited” aggregation model and study
its effects on system lifetime.
Note that the MLDA algorithm cannot be used in this limited
aggregation model.
We define weight of a data packet W, to be the number of
sensors whose measurements are reflected in the information
in that data packet.


CNDS ‘03
Recall that, in our unlimited aggregation model, we allow each
sensor to aggregate any number of incoming packets into one
single outgoing packet of same size.
Thus, in the unlimited aggregation case, the weight of a data
packet is not bounded by any constant.
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Limited Aggregation Model…
In our Limited Aggregation Model each data packet has a
capacity to carry a fixed weight, K.
In any single round, if a sensor receives incoming packets of
total weight W, it will need to send as many packets as
required to hold weight W+1.

Thus,  (W+1)/K  data packets will be sent.
the total weight of all the outgoing packets equal to W+1.
each outgoing packet weighs no more than K.

The aggregation ratio is K:1.

A-Restricted MLDA and therefore the A-LRS and A-R-LRS
algorithms can be used to solve the data aggregation problem
even in the limited aggregation case.

CNDS ‘03
Note that we do not claim applicability of this particular Limited
Aggregation model in all cases and the schemes presented here
are independent of this particular model.
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Experimental Setup
We consider a network with sensors randomly distributed in
100m x 100m field.
Number of sensors is varied between 100 to 500.
Each sensor has initial energy 1 Joule.
The base-station is located at (50m, 300m).
Each sensor generated data packets of size 1000 bits.
Energy model used is the First Order Radio Model.
For each experiment, we measure the lifetime of the sensor
network for A-LRS and A-R-LRS algorithms.
For the A-R-LRS algorithm,

Aggregation ratios range from :1 to 2:1.

Number of permutations P, is fixed to 100.
We compare our results with the LRS protocol.
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Results with Limited Aggregation
A- LRS
n
c
100
100
100
100
100
10
10
10
10
10
200
200
200
200
200
10
10
10
10
10
300
300
300
300
300
15
15
15
15
15
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AR
∞:1
100:1
10:1
4:1
2:1
∞:1
100:1
10:1
4:1
2:1
∞:1
100:1
10:1
4:1
2:1
A-R -LRS
LRS
T
G
T
G
2454
2454
2315
2083
1516
2983
2983
2883
2624
1966
21.55
21.55
24.53
25.97
29.68
3902
3902
3770
3549
2593
59
59
62.85
70.37
71.04
2854
2840
2489
2041
1372
3748
3725
3333
2709
1826
31.35
31.16
33.9
32.73
33.09
4449
4442
3886
3430
2281
55.88
56.4
60.15
68.05
66.25
3119
3011
2714
2230
1607
3969
3819
3576
2949
2110
27.25
26.83
31.76
32.22
31.26
5037
4738
4255
3583
2532
61.49
57.35
56.8
60.67
57.55
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Results with Limited Aggregation…..
A- LRS
n
c
400
400
400
400
400
20
20
20
20
20
500
500
500
500
500
25
25
25
25
25
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AR
∞:1
100:1
10:1
4:1
2:1
∞:1
100:1
10:1
4:1
2:1
A-R -LRS
LRS
T
G
T
G
3090
2893
2605
2154
1470
4098
3866
3437
2851
1929
32.62
33.63
31.95
32.49
31.26
5263
4867
4327
3588
2426
70.3
68.25
66.12
66.59
65.04
2996
2852
2563
1981
1117
4061
3864
3484
2711
1534
35.55
35.48
35.92
36.85
37.42
4939
4601
4102
3312
1899
64.85
61.33
60.05
67.22
69.96
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33
Conclusions and Future Directions
A approximation algorithm for the Maximum
Lifetime Data Aggregation problem in sensor
networks.
Our scheme significantly improves the system
lifetime when compared to one of the best known
existing protocols and is close to optimal.
Solves Maximum Lifetime Data Aggregation problem
in the limited aggregation case.
Future directions …

CNDS ‘03
We plan to investigate modification which would allow
addition (removal) of sensors from the network, without
having to re-compute the schedule.
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Thank You !!!
CNDS ‘03
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35