Title: Efficient Algorithms for Maximum Lifetime Data Gathering and Aggregation in Wireless Sensor Networks Selected from Elsevier: Computer Networks
1Efficient Algorithms for Maximum Lifetime Data
Gathering and Aggregation in Wireless Sensor
NetworksSelected from Elsevier Computer
Networks
 Konstantinos Kalpakis,
 Koustuv Dasgupta,
 Parag Namjoshi
 Presentation by ShuPing Lin
2Outline
 Introduction
 The Data Gathering Problem
 Maximum Lifetime Data Gather with Aggregation
 Greedy CMLDA
 Incremental CMLDA
 Experimental Results
 Conclusions
3Outline
 Introduction
 The Data Gathering Problem
 Maximum Lifetime Data Gather with Aggregation
 Greedy CMLDA
 Incremental CMLDA
 Experimental Results
 Conclusions
4Introduction
 Rapid development of sensor results from advances
in  Microsensor technology
 Lowpower analog/digital electronics
 Bigger memory size
 Obstacles arise from
 Limited energy
 Computing capabilities
 Communication resources available
5Introduction (contd)
 In this paper authors consider a system of
sensors that are homogeneous and highly
energyconstrained.  Replenishing energy via replacing battery on
hundreds of nodes is infeasible.  The basic operation is systematic gathering of
sensed data to be eventually transmitted to a
base station.
6Introduction (contd)
 The key idea of data aggregation is to combine
data from different sensors to eliminate
redundant transmissions.  Addresscentric versus datacentric.
7Introduction (contd)
 This paper derives novel algorithms for data
gathering and aggregation in sensor networks.  A nearoptimal polynomialtime algorithm is
proposed, but it is computationally expensive for
large sensor networks.  Then two heuristics based on GREEDY and
INCREASMENTAL concept are derived.
8Outline
 Introduction
 The Data Gathering Problem
 Maximum Lifetime Data Gather with Aggregation
 Greedy MLDA
 Incremental MLDA
 Experimental Results
 Conclusions
9The Data Gathering Problem
 System Model
 A network of n sensor nodes and a base station
node t labeled n1 distributed over a region.  Each sensor produces one data packet whose size
is k bits per unit time as it monitors its
vicinity.  Each time unit is referred as a round.
 Each sensor has the ability to transmit data to
any other sensor in the network.  Each sensor i has a initial battery with finite,
nonreplenishable energy .
10The Data Gathering Problem (contd)
 Energy Model
 Energy model is based on the first order radio
model.  A sensor consumes to
run the transmitter or receiver circuitry and  for the
transmitter amplifier.  Energy consumed by a sensor i in receiving a
kbit packet is given by (1)  Energy consumed in transmitting a packet to
sensor j is given by
..(2) where di,j is the distance between
nodes i and j.
11The Data Gathering Problem (contd)
 Problem Statement
 Lifetime T of the system to be the number of
rounds until the first sensor is drained out.  A data gathering schedule specifies how the data
packets from all the sensor are collected and
transmitted to the base station.  The objective of data gathering problem is to
find a schedule that maximizes the system
lifetime T.
12Outline
 Introduction
 The Data Gathering Problem
 Maximum Lifetime Data Gathering with Aggregation
 Greedy MLDA
 Incremental MLDA
 Experimental Results
 Conclusions
13Maximum Lifetime Data Gathering with Aggregation
 Data aggregation performs innetwork fusion of
data packets in an attempt to minimize the number
and size of transmissions and thus save energy.  Aggregation can be performed when the data from
different sensor are highly correlated.  Simplistic assumption
 An intermediate sensor can aggregate multiple
incoming packets into a single outgoing packet.
14Maximum Lifetime Data Gathering with Aggregation
(contd)
 The Maximum Lifetime Data Aggregation (MLDA)
problem  Finding a gathering schedule with maximum
lifetime, where sensors are permitted to
aggregate incoming data packets.
15Maximum Lifetime Data Gathering with Aggregation
(contd)
 Let fi,j be the total number of packets that node
i transmits to node j in a schedule S with
lifetime T rounds.  The energy constraint for each sensor i is

 The schedule S induces a flow network G which is
a directed graph having edges (i,j) with capacity
fi,j whenever fi,j 0.
16Maximum Lifetime Data Gathering with Aggregation
(contd)
 Theorem 1
 Let S be a schedule with lifetime T, and let G be
the flow network induced by S. Then, for each
sensor s, the maximum flow from s to the base
station t in G is T.  Proof
 Each data packet transmitted from a sensor must
reach the base station.  In terms of network flows, this implies that
sensor s must have a maximum st flow of size T
to the base station in the flow network G.
17Maximum Lifetime Data Gathering with Aggregation
(contd)
t
t
t
Round 1
Round 2
Flow Network G
18Maximum Lifetime Data Gathering with Aggregation
(contd)
 A necessary condition for a schedule to have
lifetime T is that each node in the induced flow
network can push flow T to the base station t.  Now we must consider the problem of finding a
flow network G with maximum T, that allows each
sensor to push flow T to the base station, while
respecting the energy constraints at all sensor.
19Maximum Lifetime Data Gathering with Aggregation
(contd)
 Finding a nearoptimal admissible flow network
 flow variable indicating the flow that
k sends to the base station t over edge (i,j).
20Maximum Lifetime Data Gathering with Aggregation
(contd)
 Objective
 maximize T
(4)  Constraints

(5) 

(6) 

(7) 
(8) 

(9)  where k1,2,..,n and all variables are
nonnegative integers.
Flow Conservation Constraints
21Maximum Lifetime Data Gathering with Aggregation
(contd)
 The linear relaxation of this integer program can
be computed in polynomial time.  Then we can obtain a very good approximation for
the optimal admissible flow network by first
fixing the edge capacities to the floor of their
values obtained from the linear relaxation so
that the energy constrains are all satisfied.
Get edge capacities fi,j
22Maximum Lifetime Data Gathering with Aggregation
(contd)
 Finally we solve the linear program (4) subject
to constraints (6)(9) without requiring anymore
that the flows are integers.
23Maximum Lifetime Data Gathering with Aggregation
(contd)
 How to get a schedule from an admissible flow
network?  A schedule is a collection of directed trees that
span all the sensors and the base station, with
one such tree for each round.  These trees are called aggregation trees that may
be used for one or more rounds.
24Maximum Lifetime Data Gathering with Aggregation
(contd)
25Maximum Lifetime Data Gathering with Aggregation
(contd)
 Definition 1
 Given an admissible flow network G with lifetime
T and a directed tree A rooted at the base
station t with lifetime f.  (A, f)reduction G of G is the flow network that
results from G after reducing by f, the
capacities of all of its edges that are also in
A.  Definition 2
 An (A, f)reduction G of G is feasible if the
maximum flow from node v to the base station t in
G is T  f for each node v in G.
26Maximum Lifetime Data Gathering with Aggregation
(contd)
 If A is an aggregation tree with lifetime f and
the (A, f)reduction of G is feasible, then the
(A, f)reduced flow network G of G is an
admissible flow network with lifetime T f.  Therefore, we can devise a simple iterative
procedure to construct a schedule for an
admissible flow network G with lifetime T.
27Maximum Lifetime Data Gathering with Aggregation
(contd)
40
20
1
4
1
4
60
40
40
20
40
2
3
2
3
40
Infeasible!!
28Maximum Lifetime Data Gathering with Aggregation
(contd)
29Maximum Lifetime Data Gathering with Aggregation
(contd)
 Computing a maximum lifetime data gathering
schedule described above is referred to MLDA
algorithm.
30Maximum Lifetime Data Gathering with Aggregation
(contd)
 Worstcase running time of MLDA
 Lemma 1 an eoptimal solution to a linear
program with n variables can be found in
time.  Lemma 2 given a flow network G (V, E) with
integral edge capacities bounded by U, a maximum
st flow can be computed in
31Maximum Lifetime Data Gathering with Aggregation
(contd)
 Lemma 3 the lifetime of the sensor network is
.  Proof Let dmin be the minimum distance of a
sensor from the base station t. Based on Eqs. (1)
and (2), the minimum total energy expended by all
the sensors in on round is at least


32Maximum Lifetime Data Gathering with Aggregation
(contd)
 Theorem 3 The worstcase running time of the
MLDA algorithm is O(n15log n), where n is the
number of sensors.  Proof
 The linear program (4) has O(n3) variables and
using lemma 3 we know that the time to compute an
?approximate solution to the linear program (4)
is
33Maximum Lifetime Data Gathering with Aggregation
(contd)
 The GETSCHEDULE procedure makes O(T) calls to the
GETTREE routine.  GETTREE routine involves O(V2E) maxflow
computations whose running time is  O(n8/3 log n).
 Thus, the running time of GETSCEEDULE is

 Total worstcase running time of MLDA is
34Outline
 Introduction
 The Data Gathering Problem
 Maximum Lifetime Data Gather with Aggregation
 Greedy CMLDA
 Incremental CMLDA
 Experimental Results
 Conclusions
35Greedy CMLDA
 Let sensors be partitioned into m clusters
 each consisting of at most c
sensors.  We refer to each cluster as a supersensor.
 Let supersensor consist only of the base
station t.  Greedy heuristic is to compute a maximum lifetime
schedule for the supersensor  with base station, and then use this schedule
to construct aggregation trees for the sensors.
36Greedy CMLDA (contd)
37Greedy CMLDA (contd)
38Greedy CMLDA (contd)
39Greedy CMLDA (contd)
O(n2)
O(n2)
O(m15log m)
O(n)
O(n3)
40Greedy CMLDA (contd)
 The worstcast running time of GREEDY CMLDA
heuristic is O(m15 log m n3).  By appropriately choosing the number of
supersensors m, we can achieve a significant
reduction in the actual time.  For example, for m n3/16, the worstcast
running time is O(n3).
41Greedy CMLDA (contd)
 The rationale is to greedily construct the tree
by choosing minimum energy consumption edge at
every iteration.
42Outline
 Introduction
 The Data Gathering Problem
 Maximum Lifetime Data Gather with Aggregation
 Greedy CMLDA
 Incremental CMLDA
 Experimental Results
 Conclusions
43Incremental CMLDA
 In solving MLDA problem, we are essentially
interested in provisioning the (edge) capacities
of an admissible flow network G.  This proposed heuristic builds such a flow
network by incrementally provisioning capacities
on its edges.  INCREMENTAL MLDA heuristic consists of four
phases .
44Incremental CMLDA (contd)
 Phase I
 The same with GREEDY heuristic
 The only difference is that we do not compute
schedule w.r.t. supersensor, only linear
relaxation of the integer program of MLDA is run.  After running the linear relaxation we get the
capacity between every pair of supersensor
and , such that the system of supersensors
has a lifetime T.
45Incremental CMLDA (contd)
 In phase II we determine the capacity provisions
between s and the remaining sensors within the
same supersensor, as well as between s and each
of the supersensor , such that  The sum of provisioned capacities from all the
sensors in to each supersensor equals  obtained from Phase I.
 each sensor s in can push T packets to the
remaining supersensors.
46Incremental CMLDA (contd)
 Our objective is to minimize the maximum energy
consumed by any sensor within the supersensor
, thereby extending the lifetime of the sensors.
47Incremental CMLDA (contd)
Energy required for transmission within the same
supersensor i
Energy required for transmission between other
supersensor j
Flow sent from supersensor i to j must equal to
48Incremental CMLDA (contd)
Total flow sent from supersensor i equals to T
49Incremental CMLDA (contd)
 From phase II, we obtain the capacity provisions
between any sensor s and all other sensors in the
same supersensor.  In phase III, we need to determine the capacities
that need to be provisioned between individual
sensors in different supersensors.
50Incremental CMLDA (contd)
 Consider two distinct supersensor and
 We provision capacities between pairs of sensors
from and , while ensuring that  Total capacity provisioned from each sensor
 to all the sensors in equals the
provisioning obtained from Phase II.  Total capacity provisioned from each sensor
 to all the sensors in equals the
provisioning obtained from Phase II.
51Incremental CMLDA (contd)
52Incremental CMLDA (contd)
 Note that these capacities obtained from Phase
III are fractional nonnegative numbers.  We scale the provisioned capacities by a factor
of , where ?max is the maximum energy
consumed by any sensor.  Then we floor all the capacities to obtain flow
network with integer capacities.
53Incremental CMLDA (contd)
 Using this flow network we finally compute the
integral system lifetime by MLDA algorithm, and a
data gathering schedule S using the GETSCHEDULE
algorithm.
54Incremental CMLDA (contd)
55Incremental CMLDA (contd)
 Worsecase analysis
 Phase I O(m15 log m)
 Phase II O(c5m10 log (cm))
 Phase III O(c10 log c)
 Worstcase running time of Incremental CMLDA is
 O(m15 log m) O(c5m10 log (cm)) O(c10 log c)
56Outline
 Introduction
 The Data Gathering Problem
 Maximum Lifetime Data Gather with Aggregation
 Greedy CMLDA
 Incremental CMLDA
 Experimental Results
 Conclusions
57Experimental Results
 Consider a network of sensors randomly
distributed in a 50mX50m field.  The number of sensor in the network is varied to
be 40, 50, 60, 80 and 100.  Performance ration RM is defined as the ratio of
the system lifetime achieved using MLDA to the
lifetime given by the LRS protocol.
58Experimental Results (contd)
 The depth of a sensor v is defined to be its
average number of hops from the base station in
the schedule.  Construct initial cluster
 Pick a sensor i farthest from the base station
and form a cluster that includes i and its c1
nearest neighbors.
59Experimental Results (contd)
60Experimental Results (contd)
 The lifetime of a schedule obtained using the
INCREMENTAL CMLDA heuristic is always within 3
of optimal solution.  The lifetime of a schedule give by the MLDA
algorithm nearoptimal.  The algorithms proposed in this paper outperform
the LRS protocol in terms of system lifetime.
61Experimental Results (contd)
 The average depth of a data gathering schedule
attained by these heuristics is slightly higher
than that of the LRS.
62Experimental Results (contd)
63Experimental Results (contd)
64Experimental Results (contd)
 The GREEDY and INCREMENTAL CMLDA heuristics
significantly outperform the LRS protocol.  The average depth of a data gathering schedule
attained by these heuristics is only slightly
higher than that of the LRS.
65Conclusions
 This paper proposed a polynomialtime
nearoptimal algorithm (MLDA) for solving the
maximum lifetime data gathering problem for
sensor networks.  Three heuristics are proposed and formulated as
linear programming problem.  Future research
 Aggregation rate should be included.
 Depth (delay) constraint is considered.