constructing a message-pruning tree with minimum cost for tracking moving objects in wireless sensor...

Constructing a Message-Pruning Tree with Minimum

Cost for Tracking Moving Objects in Wireless Sensor

Networks Is NP-Complete and an Enhanced Data

Aggregation Structure

Constructing a Message-Pruning Tree with Minimum

Cost for Tracking Moving Objects in Wireless Sensor

Networks Is NP-Complete and an Enhanced Data

Aggregation StructureIEEE TRANSACTIONS ON COMPUTERS, VOL. 57, NO. 6, JUNE 2008

Presented By Yen-Yi, Hsu

Contents

1. Introduction2. Related Work3. Preliminaries4. Reference 15. Reference 26. Hardness of Min-Cost Message-Pruning

Tree7. New Data Aggregation Structure8. Performance Study9. Conclusion

2

Introduction

WSNs be used in a wide range of applicationsex: environment monitoring, battlefield surveillance, health care

One of the most important areas of research─ object tracking

Two basic operation：Update and QueryThe Object’s location stored in the sink or notConstruct the message-pruning tree with

shortcuts

3

Related Works

How to monitor the objectThis paper:

address now to aggregate the sensed dataDual prediction using the moving historyTree topologyDistributed database and a message-

pruning tree:attempt to prune redundant message

4

Preliminaries

Voronoi graph Assume that the sensor that

receives the strongest signal from an object is responsiblefor reporting the object’s location

5

Preliminaries

Undirected Weighted Graph Assumed that the event rate

between any two neighboringsensors can be statisticallycalculated

Assumed that the sensor’s transmission range is largeenough such that any twoneighbors can directlycommunicate with each other

Represented as G(VG,EG,wG)

6

Preliminaries

Undirected Weighted Graph Assumed that the event rate

between any two neighboringsensors can be statisticallycalculated

Assumed that the sensor’s transmission range is largeenough such that any twoneighbors can directlycommunicate with each other

Represented as G(VG,EG,wG)

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Preliminaries

Message-Pruning Tree T(VT,ET,wT), rooted at the sink

wT(u,v): minimum hop count between u and v in G.

VT=VG and ET EG

8

Preliminaries

Database Update Each node v maintains a list

v.DL=(L0, L1, L2, …, Lk), wherek is the number of v’s children

For example, L0=L2=NIL and L1={Car1} in b.DL

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Preliminaries

Database Update When a object o moves from

u to neighbor v• dep(o, u, v)

• arv(o, u, v)

• Along to the tree path to lca(u, v)

distT(g, h) = wT(g, d)+wT(d, b) +wT(b, e)+wT(e, i) +wT(i, h)=5

The cost of updating the database is 10

Object Query Forwarding path for Car1

• (a, b, d, g)(a, b, d) When a sensor receives a

query for object o, it forwardsthe query to its ith child ifo Li and it’s ith child is not a leaf

The cost of a query for objectis double the sum of wTs of edges on the reduced forwardingpath

Preliminaries

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Preliminaries

Object Query For example: the cost of a

query for Car1 is 2 x distT(a, d) = 4

The cost of querying objects is

where q(v) denotes the query rate of sensor v

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Reference

Efficient In-Network Moving Object Tracking in Wireless Sensor Networks Chih-Yu Lin, Student Member, IEEE, Wen-Chih

Peng, Member, IEEE, and Yu-Chee Tseng, Senior Member, IEEE

IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 5, NO. 8, AUGUST 2006

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Update Cost

counting the average number of messages transmitted in network per unit time

(2)

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vp(v)

Deviation-Avoidance Tree

1. We would expect that distT(u, sink)= distG(u, sink)

otherwise, u deviates from its shortest path to the sink

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Deviation-Avoidance Tree

2. minimize the wT(u, v) by selecting neighboring sensors as parents avg. of distT(u, lca(u, v))+distT(v, lca(u, v))

can be minimized

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Deviation-Avoidance Tree

3. an edge with higher wG(u, v) should be included into T as early as possible highest-weight-first principle

For two edges (u, v) and (u’, v’) EG such that wG(u, v) > wG(u’, v’), it’s desirable that

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Deviation-Avoidance Tree

T is always a subgraph of G

wT (u, v)=1

18

Zone-Based DAT

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Zone-Based DAT

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Query Cost Reduction

QCR tries to adjust the tree T obtained by DAT or Z-DAT in a bottom-up manner

Two observation1. Placing a node as a leaf can save the query cost

2. We should choose a node closer to the sink as v’s parent,

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Query Cost Reduction

1. if a node v is not a leaf

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Query Cost Reduction

2. if a node v is a leaf node

23

Reference

Message-Efficient In-Network Location Management in a Multi-sink Wireless Sensor Network Chih-Yu Lin and Yu-Chee Tseng, Ten H. Lai

24

Multi-sink WSNs

Naïve way to extend a single-sink system to multi-sink system is to construct a virtual treefor each sink x

Three issues need to be addressed when multiple trees coexist 1. Update and query mechanisms 2. Multi-tree construction 3. The number of trees used

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Update and Query Mechanisms

We denote a WSN with n sensors, m of which are designated as sinks (σi , i =1, ..., m)

rooted at σi has constructed form GEach sensor x keeps two tables

Subtree_Member SX :

• An m x n table to indicate whether another sensor is a descendant of x in a certain tree

Detected_List DLX :

• k+1 entries, each entry maintain a set of objects26

For Example Subtree_Member

• SD(TB,F)=1

• SD(TA,F)=0

Detected_List• Car2 DLA(D)

• D is a neighbor of A

• SD(TA,G)=1 and Car1 is tracked by G I

D

F

J

A

B

C

E

G H

K Car1

Car3

Car2

Update and Query Mechanisms

27

1. The Location Update Mechanism Update message should be sent from a and b to

lcai(a, b) In a system with m trees, a sensor x need to

maintain pi(x) for each Because the number of neighbors of x may be

smaller than m, some of the pi(x) may be duplicate and thus can be update together

Thus, update mechanism comprise two parts:• (1.) Forwarding Rule

• (2.) Updating Rule

Update and Query Mechanisms

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(1.)Forwarding Rule

If there is a tree making Eq.1 true, the update message should be sent to pi(x)

If two trees both satisfy Eq.1 and pi(x) = pj(x), then only one update message needs to be sent

(2.)Updating Rule

Update and Query Mechanisms

29

Update and Query Mechanisms

30

Update and Query Mechanisms

31

2. The Location Query Mechanism Assume user can issue a query from any

sensor• (1) o does not appear in any of the entries of DLX

– x will forward the query to the closest sink

– If an intermediate node y finds that o appears in DLy,then the second scenario will be initiated immediately

• (2) o appears at least in one of the entries of DLX

– Model the WSN responsible for tracking object o as a directed query graph

Update and Query Mechanisms

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Update and Query Mechanisms

33

Update and Query Mechanisms

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Multi-Tree Construction

1. The MT-HW Algorithm(with the high-weight-first property)

an edge (u, v) with higher weight will be considered for being included into a tree earlier

candidate parents : distG(σi , x) = distG(σi , y) +1 and y is x’s neighbor

Each sensor x will sort its neighbors in a decreasing order according to the event rates

Then, for each sink σi , x will pick one neighbor y as its parent that has the highest event rate among x’s candidate parents for σi and set y= pi(x)

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Multi-Tree Construction

2. The MT-EO Algorithm(with the edge-overlap-first property)

If we can increase the number of the tree edges that overlap with each other, SC(v)↑ and U↓

Each of x’s neighbors is associated with an overlap counter for x

Then, x select the neighbor y whose overlap counter is the largest

Until x has determined its paents for all sinks

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Simulation Results

Comparison of Update Costs

37

Simulation Results

Comparison of total costs under different query rate

38

Simulation Results

Comparison of total cost (single vs. multiple)

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Simulation Results

Two implicit results should be addressed 1. multi-sink system has a faster query

response time

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Simulation Results

2. multi-sink system can achieve a better load balance factor

41

Hardness of MC-MPT

Exact 3-cover problem Given a S= {σ1,…, σs} of triplets of elements from a

set L={τ1,… , τ3t}, is there a subcollection S’ S of size t that covers L?

Ex: L={ }, S={ } is given, S’={ } is a solution of this problem

Minimum-Cost Message-Pruning Tree G(VG, EG, wG, qG), a sink sink, integer M≥0

Determine whether there exist a T(VT, ET) rooted at sink with VT=VG whose cost U(T)+Q(T) is at most M

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Hardness of MC-MPT

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Hardness of MC-MPT

44

New Data Aggregation Structure

When Car1 moves: g→ h Reduced forwarding path:

(a, b, e ,i) The cost of a query is 6

This paper’s idea: Add a shortcut (d→ h)

45

New Data Aggregation Structure

After add a shortcut: Reduced forwarding path:

(a, b, d) The cost of updating the

database:wT(g, d)+wT(d→ h)=2

The cost of a query for Car1:2x( wT(a, b)+wT(b, d))=4

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New Data Aggregation Structure

The Structure The shortcut (u→ v) will be

• u’s outgoing shortcut and • v’s incoming shortcut

wT(u→ v) = distG(u, v)

For example, wT(d→ h) = 1

(u1, u2, …, un) is a downward path if

• ui is the parent of ui+1

• (ui →ui+1) is a shortcut

(b, d, h) is a shortest downward path from b to h47

The Structure v.DL( )

• k is the number of v’s children

• p is the number of v’s outgoing shortcut

• q is the number of v’s incoming shortcut

d.DL(NIL, NIL, {Car1})

New Data Aggregation Structure

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The Structure Extended_ancestor:

ex: a, b, d, e, i and h are extended_ancestor of h

u.prec(o)ex: h.prec(Car1) = d can be evaluated by checking DL

u.succ(v)ex: d.succ(h) = h and b.succ(h) = d

New Data Aggregation Structure

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Object Query

New Data Aggregation Structure

50

Example sink a receive query(Car1))

The cost of a query(o) is 2 x dist(r fpath(query(o)))

The cost of queries for all objectsis 2 x

New Data Aggregation Structure

51

Database Update

New Data Aggregation Structure

52

Example

New Data Aggregation Structure

The cost of updating the database for all events

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Addition of Shortcuts Add shortcut (u→ v) with the property

• 1. distT(sink,u)+wT(u→v)≦ distT(sink,v)

• 2. (u, v) EG-ET

• 3. u is not a leaf

New Data Aggregation Structure

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Performance Study

256 sensors, 32 x 32 sensing fieldRandom & regular deploymentZ-DAT and Z-DAT+QCR were constructedα and δ are set to 4 and 0the tree root in Z-DAT or Z-DAT+QCR is

located in either the corner or the center

averaging the data of 1000 simulations

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Performance Study

The Cost of Updating the Database

56

Performance Study

The Cost of Updating the Database

57

Performance Study

The Cost of Updating the Database

58

Performance Study

The Cost of Updating the Database

59

Performance Study

The Cost of Querying Objects

60

Performance Study

The Cost of Querying ObjectsdistT(sink,u)+wT(u→v)=distT(sink,v)

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Conclusion

Total cost = Update cost + Query CostMultiple sink is important when the

network scale is large or when the query rate is high

It proposed a data aggregation structure that is constructed by adding shortcuts to MPT

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