# A Distributed Greedy Algorithm for Constructing Connected Dominating Sets in Wireless Sensor Networks

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TL;DR: This paper presents a distributed greedy algorithm for constructing a CDS that is up to 30% smaller in size than K2 that operates in two phases, first constructing a dominating set and then connecting the nodes in this set.

Abstract: A Connected Dominating Set (CDS) of the graph representing a Wireless Sensor Network can be used as a virtual backbone for routing in the network. Since sensor nodes are constrained by limited on-board batteries, it is desirable to have a small CDS for the network. However, constructing a minimum size CDS has been shown to be a NP-hard problem. In this paper we present a distributed greedy algorithm for constructing a CDS that we call Greedy Connect. Our algorithm operates in two phases, first constructing a dominating set and then connecting the nodes in this set. We evaluate our algorithm using simulations and compare it to the two-hop K2 algorithm in the literature. Depending on the network topology, our algorithm generally constructs a CDS that is up to 30% smaller in size than K2.

## Summary (2 min read)

### 1 INTRODUCTION

- Wireless Sensor Networks (WSNs) have attracted considerable research interest in the past decade (Iyengar and Brooks, 2004) (Akyildiz et al., 2002) (Chong and Kumar, 2003).
- They have evolved from research to deployment with many environmental, security, energy and other applications.
- Each sensor serves as both a data gathering source and a router, forwarding messages from other nodes.
- A key approach to solve the problem of data gathering and communication involves the construction of a connected dominating set (CDS) that serves as a virtual backbone for the network.
- The construction of a CDS provides the network with a virtual backbone over which routing, multicast and broadcast can be performed since every node is either in the backbone or has a neighbor in the backbone.

### 3 Greedy Connect Algorithm for CDS construction

- Distributed algorithm for constructing a connected dominating set.the authors.
- The authors also assume every sensor node to have a unique identifier.
- The sensor nodes fields as used in their algorithm are shown in Table 1.

### 3.1 Phase 1: Greedy construction of a dominating set

- Phase 1 uses node coloring to implement its greedy approach.
- Initially the authors start out with all nodes being colored white.
- At this point, the node with the highest white neighbor count adds itself to the dominating set by changing its color to black and changing the color of its white neighbors to grey.
- The second pass looks at only those nodes that are still white and essentially repeats the process to ensure that the set is dominating.
- Request the white neighbor count for every neighbor u ∈ N(v) if v.

### 3.2 Phase 2: Connecting the Dominating Set

- In this subsection the authors will present their connection algorithm.
- Assume there is a component separated from all other components by at least three vertices at the end of the algorithm, also known as Lemma Proof.
- The authors can visualize this scenario as COMP1− a− b− c−COMP2 where a,b,c are the three vertices separating COMP1 and COMP2.
- The authors make the assumption that every sensor has a unique identifier associated with it.
- As can be seen from the algorithm below, the authors initialize the component id of each grey sensor to -1 and for every connected dominating component, they initialize its component number to that of the highest id sensor in that connected component.

### 3.3 An example

- The figure shows the sensors and the resulting graph representing the network.
- As mentioned in (Zhang and Hou, 2005), the transmission radius is double the sensing radius.
- In the first round of Phase 1 each vertex checks if it has the highest (or tied highest) white neighbor count in its neighborhood.
- At this point the authors have a Dominating Set with two components (each of the two black nodes being a separate component).
- This node will assume the component id of the higher of these two nodes (i.e., 5) and this component id will propagate across the CDS resulting in all the black nodes having a component id of 5 as shown in the second figure of Figure 3.

### 4 Results

- For their simulation setup, the authors create networks of sensors with 100 nodes scattered randomly in a 100x100m area.
- Each data point in the figure represents an average of the ten graphs generated for that size.
- The authors plot the size of the CDS for both algorithms in each of the random networks they generated with this range.
- As can be seen from the figure, their algorithm is consistently better than K2.
- One major point to note is that the authors have not yet conducted simulation studies on the impact of their algorithm on the lifetime of the network.

### 5 CONCLUSIONS

- In conclusion, in this paper the authors present a 2-phase algorithm that starts with greedy coloring scheme to form a dominating set which they then connect using the sensor id’s of the disconnected component.
- In simulation studies their approach has been shown to result in a smaller CDS than a popular 2-hop algorithm in the literature.

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##### Citations

151 citations

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### Cites background or methods from "A Distributed Greedy Algorithm for ..."

...Greedy Connect by [9] creates a minimised connected dominating set in a greedy fashion....

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...Therefore, descriptions presented below slightly deviate from the original descriptions in [9], [10], [11]....

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### Cites background from "A Distributed Greedy Algorithm for ..."

...While the topic of dominating sets has several years of research behind it in particular for backbone formation in Wireless Sensor Networks [7] [8] [9], the problem of Positive Influence Dominating Sets (PIDS) in social networks has been studied relatively recently....

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2 citations

##### References

13,726 citations

### "A Distributed Greedy Algorithm for ..." refers background in this paper

...Wireless Sensor Networks (WSNs) have attracted considerable research interest in the past decade (Iyengar and Brooks, 2004) (Akyildiz et al., 2002) (Chong and Kumar, 2003)....

[...]

3,178 citations

1,788 citations

### "A Distributed Greedy Algorithm for ..." refers background in this paper

...In order to keep their cost low, the sensors are equipped with limited energy (Feeney and Nilsson, 2001) (Feeney, 2001) and computational resources....

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1,522 citations

### "A Distributed Greedy Algorithm for ..." refers background in this paper

...tioned in (Zhang and Hou, 2005), the transmission radius is double the sensing radius....

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...As mentioned in (Zhang and Hou, 2005), the transmission radius is double the sensing radius....

[...]

...We also assume that the transmission range is at least twice the sensing range since as shown in (Zhang and Hou, 2005) a covered network is also connected if this is true....

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1,454 citations

### "A Distributed Greedy Algorithm for ..." refers background in this paper

...The resulting graph is known as a Unit-Disk Graph (UDG) (Clark et al., 1990) since the uniform transmission range results in edges of equal (or unit) weight....

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...However this has been shown to be a NP-hard problem in (Clark et al., 1990)....

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