A Robust Spanning Tree Topology For Data Collection in

Sensor Networks

Ahmed EbaidComputer Science and Engineering

DepartmentMay, 1, 2008

2

Original Paper England, Darin, “A Robust Spanning Tree Topology

for Data Collection and Dissemination in Distributed Environments,” IEEE Transactions on Parallel and Distributed Systems, Volume 18, Issue 5,  May 2007.

3

Objective Overview on sensor networks. Evaluating a robust topology for applications that

operate on a spanning tree overlay network. Introducing a distributed algorithm used to construct

the topology. Evaluating the effect of this algorithm on data

collection for sensor networks.

Introduction Sensor Networks: A wireless network consists of

distributed autonomous devices that use sensors to monitor physical or environmental conditions.

4

5

Introduction (Cont’d) A sensor node is made up of four basic components. They might have application dependent components.

6

Introduction (Cont’d) They can provide coverage for a very large area

through the scattering of thousands of sensors. Sensor networks can also improve remote access to

sensor data by providing sink nodes that connect them to other networks.

They can work in hostile and unattended environments. Replenishment of power resources might be impossible

in sensor networks. Nodes expose the network to the potential for massive

data loss if they (or their upward links) happen to fail. Achieving a desirable trade-off for two opposing

metrics Power Consumption, and Data loss is essential.

7

Introduction (Cont’d) Many spanning trees are in use today. Which Spanning tree is better for a particular

application?. Spanning trees in use today such as:

1. Shortest Path (SP) (Dijkstra’s):2. Fewest hops (FH):

A Tree that is immune to data loss when node or links fail, and are able to maintain a good performance is

required, which is the very notion of robustness

8

A Robust Spanning Tree Topology (RB) Constructing a robust spanning tree considers a

weighted combination of hop count and path weight. (1)

where . Placing more importance on hop count means that the tree will be fat and shallow (FH), more importance on path weight means that the tree will be skinny and deep (SP).

tpath weigh × )-(1 +count hop

10

9

A Robust Spanning Tree Topology (Cont’d) An attempt is made to make the tree fat near the root and skinny further away

from the root.

The further a message has to travel to reach the root node, the more likely it is to encounter a failed parent somewhere along the way.

The weight is a function of a node’s depth in the tree. When an edge ( , ) is 𝜆 𝑖 𝑗being considered for inclusion in the tree and is the new vertex not already in 𝑖the tree, then

(2)

1

1

ii

h

10

A Robust Spanning Tree Topology (Cont’d) Where is the hop count of node from the root and 𝑖

is the eccentricity of the root node. The eccentricity

of a node is the largest of the shortest paths from that node to all other nodes.

Eccentricity is measured in number of hops, not path weight (depth of the deepest leaf in the SP tree).

Eccentricity can be thought of as a characteristic of the underlying graph not a property of the overlay network.

1ih

11

A Distributed Algorithm It is unrealistic to assume that any single node will have

complete knowledge of the network (Sensor Networks).A distributed algorithm is required where each node runs

the same algorithm and the tree is constructed after each node exchanges a series of messages with its neighbors.

Bellman Ford algorithm can be used in this manner to construct the SP, and FH trees.

Upon termination of this algorithm, each node will know:1. Its parent in both SP, and FH tree.2. Its distance to root in edge weights, and in number of

hops.

12

A Distributed Algorithm (Cont’d) The idea is that each node simply chooses a parent j 𝑖

based on the form of the weighted cost in (1). Hop count of a node is the number of hops to the root 𝑖

if node chooses node as its parent.𝑖 𝑗 The path weight of a node is the distance from node 𝑖 𝑖

to the root if node chooses node as its parent. 𝑖 𝑗 Each node scans its list of neighbors and chooses a 𝑖

parent according to:𝑗

(3))()1()1({min)( jijijiiAj

dzh

13

A Distributed Algorithm (Cont’d)

where is the weight on the link between nodes and , 𝑖 𝑗is node j’s estimate of its distance to the root node in path weight, is computed as

(4)

Each node sends a message to the root node using SP, where each message contains a counter that is incremented at each hop.

The root node scans the message and then determine the depth of the deepest leaf, and send the information back down the tree.

ijzjd

i

1

1

ii

h

14

Data Collection in Sensor Networks An edge between two nodes indicates that they can

communicate directly. The edge weight is the amount of power required to

transmit a single message between the two nodes. A larger weight indicates a greater distance or an

obstruction. node 1 is the root node which is the collection point to

which all other nodes must route their data.

15

Data Collection in Sensor Networks (Cont’d)

1

46 72

5

3

The SP, FH, and RB spanning trees for this network are shown in the following figures respectively.

1

1 2 1 1

1

1

5 76

2 3 4

3 1 3

4 2 1

1

5

76

2 3 4

3 1 3

2 1

1

1 4 7

2 3

5 6

11

1

1

1

1

3

3

4 2

1

SP FH RB

16

Data loss and Power Consumption Analysis The failure of a node is equivalent to the failure of the link to the

parent. This applies to every node in the tree except the root node. Consider a treeT with vertex setV(T) and edge set E(T). Let the number of nodes in the subtree rooted at node 𝑖

(including node itself) and let be the probability that node 𝑖 𝑖will fail. Then, the expected value of data loss given that exactly one node fails is

(5)

where (6)

imiq

iTVi

i qmfailsnodeoneexactlyLE )(

} |{

1)(

TVi

iq

17

Data loss and Power Consumption Analysis (Cont’d) It is assumed that all nodes have an equal probability of

failure. The expected value of data loss then becomes

(7) where n=|V(G)| is the number of nodes in the graph.

Using (7) The expected data loss of the SP spanning tree is 2.0. The expected data loss of the FH spanning tree is 1.5. The expected data loss of the RB spanning tree is 1.667.

)(1-n

1ies}probabilit equal with fails node one |{TVi

imexactlyLE

18

Data loss and Power Consumption Analysis (Cont’d) The amount of network power consumed when all nodes

send one message to the root node is the sum over all nodes of the product of the number of messages sent and the power required to transmit a single message.

The total network power required to collect a single data observation is

(8)

)(

,TVi

jii zmP

19

Data loss and Power Consumption Analysis (Cont’d)

The total network power for the SP tree equals to 14. The total network power for the FH tree equals to 17. The total network power for the RB tree equals to 16.

Expected Data Loss

Power Consumption

SP 2 14FH 1.5 17RB 1.667 16

20

Questions?