Transcript Slides PPT

Function Computation over Heterogeneous
Wireless Sensor Networks
Xuanyu Cao, Xinbing Wang, Songwu Lu
Department of Electronic Engineering
Shanghai Jiao Tong University, China
Function Computation over Heterogeneous Wireless Sensor Networks
Outline
 Introduction
 In-Network Computation
 Related Works
 Motivation
 System Model
 Main Results
 Proof Sketch
 Conclusion
Computation over Heterogeneous Wireless Sensor Networks
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In-Network Computation
 Scaling law for pure information delivery
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Unicast, Multicast, Convergecast.
Homogeneity, Heterogeneity.
Static, Mobile.
Ad hoc, Hybrid.
 Scaling law for function computation
 Symmetric function, Identity function, Divisible Function, Typethreshold function, Type-sensitive function, etc.
 Noiseless or Noisy environment.
 Broadcast Network and Multihop Network.
 Energy and Latency
 Motivation for function computation
 Sink node is only interested in a function of the data, but not all the
raw data.
Computation over Heterogeneous Wireless Sensor Networks
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In-Network Computation
Performing in-network computation could help save
both energy and time in terms of scaling law.
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Related Works
 Seminal work [1]
 Multihop and broadcast network.
 Symmetric function, type-sensitive function, type-threshold
function.
 Noiseless environment.
 Maximum throughput.
[1] A. Giridhar and P. Kumar, “Computing and communicating functions over
sensor networks,” IEEE Journal on Selected Areas in Communications, vol. 23,
no. 4, pp. 755-764, 2005.
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Related Works
 Noisy Networks [2][3]
 Multihop transmission.
 Symmetric function, Divisible function.
 Minimum energy consumption
[2] L. Ying, R. Srikant and G. E. Dullerud, “Distributed symmetric function
computation in noisy wireless sensor networks,” IEEE Trans. Inf. Theory, vol.
53, no. 12, pp. 4826-4833, 2007.
[3] C. Li and H. Dai, “Towards efficient designs for in-network computing with
noisy wireless channels,” INFOCOM, pp. 1-8, 2010.
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Related Works
 Grid Networks [4] (most related one)
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Binary input data.
Noiseless and noisy networks.
Symmetric and identity function.
Energy and time complexity.
Matching upper and lower bound.
Intra-cell and Inter-cell protocols.
[4] N. Karamchandani, R. Appuswamy, M. Franceschetti, “Time and energy
complexity of function computation over networks,” IEEE Trans. Inf. Theory,
vol. 57, no. 12, pp. 7671-7684, 2011.
Computation over Heterogeneous Wireless Sensor Networks
Motivation
Previous works on in-network computation are all
for homogeneous networks.
However, the distribution of sensor nodes can be
highly heterogeneous in practice [5][6].
[5] G. Alfano, M. Garetto and E. Leonardi, “Capacity scaling of wireless networks
with inhomogeneous node density: upper bounds,” IEEE Journal on Selected
Areas in Communications, vol. 27, no. 7, pp. 1147-1157, 2009.
[6] G. Alfano, M. Garetto and E. Leonardi, “Capacity scaling of wireless networks
with inhomogeneous node density: lower bounds,” IEEE/ACM Trans. Netw.,vol.
18, no. 5, pp. 1624-1636, 2010.
Computation over Heterogeneous Wireless Sensor Networks
Motivation
 Two fundamental questions arise:
 What is the impact of heterogeneity on energy consumption for
function computation?
 How much energy consumption reduction can we get by
performing in-network computation in heterogeneous networks?
Computation over Heterogeneous Wireless Sensor Networks
Outline
Introduction
System Model
 Network Model
 Function Model
 Objective
Main Results
Proof Sketch
Conclusion
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Network Model
 The total number of nodes is n.
 The network area is a circle centered at the sink with

radius n ,   0 is the network extension exponent.
 Each node independently choose a position in the network
area according to the following probability density function:
f ( ) 

s(  )
r
r
s (|| x ||) d x
where  is the distance from the sink,  is the network
area. s (.) is specified as follows:
s (  )  min 1,   
where   2 is the heterogeneity exponent.
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Network Model
 Due to the heterogeneity of the nodes’ distribution, we
assume nodes have different transmission range r . The
energy consumption of transmitting one bit with range r

is r , where   2 is the path loss exponent.
Illustration of heterogeneous wireless sensor networks
Computation over Heterogeneous Wireless Sensor Networks
Function Model
 At one instant, each node gets one binary input data.
 We consider symmetric function and identity function:
 A function f is a symmetric function iff for any permutation
we have:

f ( y1, y2 ,..., yn )  f ( y (1) , y (2) ,..., y (n) )
where y i is arbitrary binary data. Equivalently speaking,
symmetric function merely depends on the value but not the
identity of the input data.
 The output of identity function is all the raw input data. Hence,
computing identity function is equivalent to gather all the raw
data.
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Objective
 The objective of this paper is to design energy
efficient algorithms which can compute the goal
function at the sink node with the minimum total
energy usage.
 We prove that the proposed algorithm is energy
optimal (except for poly-logarithmic terms) by
deriving matching lower bounds.
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Outline
Introduction
System Model
Main Results
Proof Sketch
Conclusion
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Main Result
Energy consumption vs. path loss exponent
(\gamma), network extension exponent (\alpha),
heterogeneity exponent (\delta).
Identifying three heterogeneous regimes: 1)
slightly heterogeneous; 2) significantly
heterogeneous; 3) highly heterogeneous
Symmetric function computation
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Identity function computation
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Outline
Introduction
System Model
Main Results
Proof Sketch
 Tessellation
 Transmission scheme
Conclusion
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Tessellation
 The key question is how to tessellate the network in order
to minimize the energy consumption.
Transmission Scheme
 We invoke intra-cell/inter-cell transmission scheme.
Outline
Introduction
System Model
Main Results
Proof Sketch
Conclusion
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Conclusion
 We have studied the optimal energy consumption of
function computation in heterogeneous networks.
 For both symmetric function and identity function, we
 design energy efficient algorithm for computation.
 prove the optimality of the proposed algorithm by deriving a
matching lower bound.
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Thank you !
Computation over Heterogeneous Wireless Sensor Networks