# Node Redeployment Algorithm Based on Stratified Connected Tree for Underwater Sensor Networks

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## Abstract

**:**

## 1. Introduction and Related Works

- (1)
- It takes full consideration of node drift with water environment during network operation. At every network adjustment moment, nodes can keep themselves in the monitored space through self-examination and adjustment, which helps to maintain good network monitoring quality.
- (2)
- At every network adjustment moment, the network is converted into a stratified connected tree through level-by-level stratifying, which can achieve full network connectivity and lower the network connectivity decrease speed during network operation.
- (3)
- The sink node performs centralized optimization adjustment on the locations of leaf nodes in the stratified connected tree with synthetically considering the network coverage and connectivity rates, and node movement distance. This can not only maintain excellent network monitoring performances, but also reduce node movement distance during node redeployment, as well as prolong the network lifetime.

## 2. Model, Definitions and Preliminaries

#### 2.1. Models

#### 2.1.1. 3D Underwater Space Model

#### 2.1.2. Node Energy Consumption Model

_{b}. T

_{p}denotes the transmitting time of the information package and S

_{v}is the transmission speed of the information package. On the one hand, we can calculate the transmitting time of the information package by the following formula:

_{tx}(d) and calculated by the following formula:

_{r}denotes the power threshold for a node to receive the information package. Moreover, supposing that the number of information package transmitting times for node s in the network redeployment process is t

_{n}, and the communication range for node s is R

_{t}, the communication energy consumption C

_{e}can be obtained by the following formula:

_{e}can be defined as the product of the movement distance m

_{d}and the energy consumption per movement distance m

_{u}, which can be also described as follows:

#### 2.1.3. Node Sensing Model

_{i},s

_{j}) denotes whether cube point p

_{i}can be covered by node s

_{j}:

_{j},y

_{j},z

_{j}) is the coordinate of node s

_{j}; (a

_{i},b

_{i},c

_{i}) is the coordinate of cube point p

_{i}, and R

_{s}is the sensing range of node s

_{j}. If the value of f(p

_{i},s

_{j}) is 1, cube point p

_{i}is covered by node s

_{j}. Otherwise, cube point p

_{i}is not covered by node s

_{j}. Based on function f(p

_{i},s

_{j}), coverage degree k(p

_{i}) of cube point p

_{i}can be defined as:

_{i}), the function f

_{0}(p

_{i}) describes whether cube point p

_{i}is covered or not:

_{0}(p

_{i}) is 1, cube point p

_{i}is not covered by any node.

#### 2.1.4. 3D Random Drift Model

_{e}is used to control the probability of node drift, and the higher P

_{e}means the larger node drift probability. If Equation (10) holds, the node drift model can be described as:

_{1}and m

_{x}are the coefficients to determine the maximum drift distance along the x direction, and P

_{dx}is the coefficient to determine the drift probability along the x positive direction. The higher P

_{dx}means the larger node drift probability along the x positive direction. rd(0,1) < P

_{dx}is a Boolean expression whose value is 1 when it holds and 0 otherwise. The meanings of the similar coefficients in the y or z directions are like those in the x direction, and we omit the corresponding description about them for simplicity.

#### 2.2. Definitions

#### 2.2.1. Network Coverage Rate

_{v}can be defined as the ratio of P

_{c}and P

_{t}, where P

_{c}is the number of the cube points covered and P

_{t}is the total number of all the cube points. Therefore, C

_{v}can be calculated as follows:

#### 2.2.2. Network Connectivity Rate

_{n}can be defined as the ratio of n

_{c}and n, where n

_{c}is the number of nodes that can communicate with the sink node through single-hop or multi-hop communication. C

_{n}can be calculated as follows:

#### 2.2.3. Network Adjustment Moment

_{r}, this network operation time is also called the network adjust moment T

_{ad}, when the locations of nodes should be examined and adjusted to maintain or improve network monitoring quality.

#### 2.2.4. Energy Threshold

_{i}is denoted as E

_{i}, and two kinds of energy threshold are defined in this paper. One is E

_{d}= E

_{tx}(R

_{t}) that is used to determine whether node s

_{i}is died. If E

_{i}is smaller than E

_{d}, we consider that node s

_{i}has almost depleted its energy and is hard to participate into the network monitoring, and we think that node s

_{i}is died. The other is E

_{y}= E

_{tx}(R

_{t}) × T

_{r}(T

_{r}is the network adjustment cycle) that judges whether a leaf node is strong. If the leaf node s

_{i}is a leaf node and its energy E

_{i}is smaller than E

_{y}, it is not strong enough and should be neglected during centralized optimization conducted by the sink node.

#### 2.2.5. Network Lifetime

_{f}, which is one of the important criteria to evaluate the algorithm energy efficiency [36,37]. In this paper, the network lifetime is defined as the operating rounds where the network coverage rate C

_{v}satisfies the condition (i.e., C

_{th}≤ C

_{v}≤ 1), and C

_{th}is the coverage rate threshold. If the network coverage rate is smaller than C

_{th}, the network has difficulty in monitoring the underwater space, and the network lifetime is over.

#### 2.3. Preliminaries

- (1)
- Inspired by the related assumptions or descriptions in references [18,22], the sink node and all the other nodes can freely move in all directions with the help of related technologies such as AUVs [38] and their real-time locations can be known during network operation with the help of related localization technologies [39].
- (2)
- Before the deployment, the destination location information of the sink node, i.e., the location information of the water surface center, has been stored in the memories of all the other nodes for them to gain information on the destination location of the sink node. Information on the 3D underwater space model and the number of nodes has also been stored in the memory of the sink node.
- (3)
- The communication range of the sink node is R
_{t}and the sink node can be recharged, whereas the sensing capability of the sink node is neglected. All the other nodes are homogeneous, meaning these nodes have the same sensing range R_{s}, same communication range R_{t}, and initial energy E_{in}. Furthermore, each of them has a unique I_{d}number.

## 3. Problem and Algorithm Description

#### 3.1. Problem Description

_{v}and connectivity rate C

_{n}at the cost of the probably least network energy consumption. For instance, as one of the typical node redeployment algorithms for UWSNs, the MRNR algorithm proposed that at every network adjustment moment T

_{ad}, the sink node repeatedly required the least important node, which made the smallest contribution to the network coverage rate, to move to the biggest coverage blind point through centralized optimization, aiming at achieving large network coverage rate improvement. However, this algorithm could not keep nodes in the monitored space effectively and did not consider how to improve the network connectivity rate. Moreover, it did not optimize the movement distance m

_{d}of the least important node during redeployment. Due to limited node energy and huge movement energy consumption M

_{e}in underwater environment, nodes die quickly upon running out of their energy (i.e., the left energy is smaller than E

_{d}), which shortens the network lifetime L

_{f}. Therefore, this paper proposes the NRBSCT algorithm. At every network adjustment moment, self-examination and adjustment on node locations are performed firstly. If a node finds it is outside the monitored space, it returns to the last location recorded in its memory along the straight line to maintain network monitoring quality. Later, the network is stratified into a connected tree that takes the sink node as the root node by broadcasting ready information level by level, which can improve the network connectivity rate during network operation. Finally, by synthetically considering the network coverage and connectivity rates, together with node movement distance, the sink node performs a centralized optimization on locations of leaf nodes in the stratified connected tree.

#### 3.2. Algorithm Description

#### 3.2.1. Description of Initial Network Distribution

_{j}(x

_{j},y

_{j},z

_{j}) for example and supposing that the coordinate of the sink node (i.e., the center of the water surface) is (x

_{sink},

_{ysink},0), the coordinate of node s

_{j}in the x direction follows the normal distribution whose mean is x

_{sink}and standard deviation is half of the x direction length of the monitored 3D underwater space. Similarly, the coordinate of node s

_{j}in the y direction follows the normal distribution whose mean is y

_{sink}and standard deviation is half of the y direction length of the monitored 3D underwater space. The depth of node s

_{j}(i.e., z

_{j}) can be calculated as follows:

_{h}means the depth of the monitored 3D underwater space. If the network follows the above distribution, the node distribution in the shallow area of the monitored 3D underwater space is denser than that in the deep area. Since the nodes closer to the sink node are usually burdened with heavier information packet forwarding task, this kind of distribution owns the effectiveness in balancing the network energy consumption.

#### 3.2.2. Algorithm Steps

_{r}and node drift cycle T

_{m}are initialized to be two different non-zero constants, and the value of T

_{r}should be larger than that of T

_{m}.

_{r}) which means the remainder of dividing t by T

_{r}is 0 or not. If it is, the network operation time reaches the adjustment moment, and the algorithm turns to Step 3 for network topology adjustment; otherwise, the algorithm turns to Step 6.

_{i}has not received any ready information M

_{r}, it moves to the sink node along the straight line. During the movement, it opens its data receiving module to catch the ready information M

_{r}and stops moving upon the reception of M

_{r}. At the same time, the network is stratified level by level from the sink node. The corresponding description is shown in Figure 4. The process and result are shown in Figure 5 (a network comprised of 9 nodes is taken as the example). After finishing the network stratification, the whole network topology is changed into a stratified connected tree that takes the sink node as the root node, which helps to achieve full network connectivity. In the stratified connected tree, if node s

_{i}has received any acknowledging information M

_{a}, it has one or more child nodes and is considered as a backbone node; otherwise, node s

_{i}has no child node and is considered as a leaf node.

_{1}comprising cube points in the 3D underwater space model, which are less than R

_{t}away (this is helpful to guarantee full network connectivity after centralized optimization) from the backbone nodes in the network. Next, it determines the set C

_{y}comprising the strong leaf nodes in the network. Then, new locations of leaf nodes in C

_{y}are calculated one by one according to the descending order of their residual energy. Taking leaf node s

_{i}for example, p

_{i}and o

_{i}are used to denote its probably new location and old location respectively. First, the sink node calculates its furthest movement distance d

_{m}(i) according to Equation (15):

_{1}ensures that s

_{i}is still a strong leaf node after reaching the probably new location and d

_{2}ensures that s

_{i}will not consume excessive energy during the movement (r

_{g}is the control coefficient). Both of them limit the movement energy consumption of the leaf node from different perspectives (d

_{1}is from the left energy perspective and d

_{2}is from the consumed energy perspective), therefore, the node movement distance is reduced. Second, the sink node determines set C

_{2}comprising cube points in the sphere Q

_{i}, whose center is the old location (i.e., o

_{i}) of node s

_{i}and radius is d

_{m}(i). The set C

_{d}= C

_{1}∩C

_{2}is calculated. Next, the sink node considers cube points in C

_{d}one by one. Taking cube point p

_{i}for example, the network coverage rate is C

_{v}(o

_{i}) when node s

_{i}is at its old location o

_{i}, and would be C

_{v}(p

_{i}) if node s

_{i}moved to its probably new location p

_{i}. The distance between o

_{i}and p

_{i}is denoted as d(o

_{i},p

_{i}). The target cube point p

_{d}(s

_{i}) (i.e., final destination location of node s

_{i}) is calculated according to Equation (16). The sink node returns the result information to node s

_{i}, and node s

_{i}moves to p

_{d}(s

_{i}) along the straight line. Then, the sink node considers the next strong leaf node until all the strong leaf nodes have been studied. After this, all the nodes record the real-time locations into their own memories.

_{m}) (remainder of dividing t by T

_{m}) is 0 or not determines whether the node drift with water environment occurs in the current network operation time. If the value of Rem(t,T

_{m}) is 0, all the nodes drift according to the 3D random drift model; otherwise, the algorithm turns to Step 7.

#### 3.2.3. Detailed Description for Algorithm Important Parts

_{r}and node drift cycle T

_{m}are initialized to be 50 rounds and 5 rounds respectively. The network operation time just comes to 50 rounds, i.e., the first adjustment moment. At this time, the algorithm will turn to Step 3 which is mentioned in the previous part for network topology adjustment. We will take the scenery at this time as an example to describe for simplicity.

#### Self-Examination and Adjustment of Nodes Outside the Monitored Space

_{e}as the example, as is shown in Table 2, it gradually drifted outside the monitored space, so it returns to the location recorded in its memory at the last network adjustment moment. Since the network operation time is just the first adjustment moment, the last network adjustment moment means the operation starting time (i.e., when t = 0). Therefore, node s

_{i}will move from (125, 43, 21) to (115, 37, 16), which makes itself come back into the monitored space to help maintain good network monitoring quality.

#### Network Connectivity Rate Improvement

_{d}(s

_{i}) (i.e., final destination location of strong leaf node s

_{i}) belong to the set C

_{d}= C

_{1}∩C

_{2}, which means it also belongs to the set C

_{1}and is less than R

_{t}away from the backbone nodes in the network, which is helpful to guarantee full network connectivity after centralized optimization. The scenery shown in Figure 5 can also be the example. Figure 5 shows that after the network stratification, nodes s

_{2}, s

_{3}, s

_{8}and s

_{9}are the leaf nodes. Supposing that their left energy are distributed as Table 3 shows (the simulation value at the 50 round time is much bigger than the supposition value in Table 3), since the energy threshold E

_{y}= E

_{tx}(R

_{t}) × T

_{r}is 65 J in the currently supposed simulation scenery, nodes s

_{2}and s

_{8}can be treated as the strong leaf nodes. Therefore, based on Equations (15) and (16), the sink node firstly determine the final destination location for node s

_{2}, and then for node s

_{8}.

#### Node Movement Distance Limit

_{8}as the example, in Equation (15), the calculation of d

_{1}(value is 8 m) limits the movement distance by ensuring that node s

_{8}is still strong after the current movement; while the calculation of d

_{2}(value is 10 m) limits the movement distance by ensuring that node s

_{8}will not consume excessive energy during the current movement. By using Equation (16), the node movement distance is also limited when requiring the node to move toward its final destination location to improve the network coverage rate. As is shown in Figure 6, point p

_{1}and p

_{2}belong to the set C

_{d}= C

_{1}∩C

_{2}. If node s

_{8}chooses p

_{1}as its final destination location, it should move 6 m to gain 0.035 network coverage rate improvement; however, if node s

_{8}chooses p

_{2}as its final destination location, it should move 4 m to gain 0.025 network coverage rate improvement. Since moving toward p

_{2}can gain more network coverage rate improvement per movement distance, node s

_{8}will prefer to choose p

_{2}rather than p

_{1}.

#### Overall Summarization for Main Mathematical Symbols

#### 3.2.4. Algorithm Analysis

_{i}, it has to calculate C

_{v}(o

_{i}) and C

_{v}(p

_{i}), and the time complexities for these two calculations are the same, i.e., O(P

_{t}× n). The smaller w means the larger P

_{t}, and then results in the higher time complexity.

## 4. Simulation Evaluation

#### 4.1. Algorithm Comparison and Evaluation Metrics

- (1)
- The MRNR algorithm does not propose effective measures to prevent nodes from drifting out of the monitored space because of water environment. However, the NRBSCT algorithm can make nodes outside the monitored space return back through self-examination and adjustment on node locations, which is goodfor maintaining good network monitoring quality.
- (2)
- The MRNR algorithm only considers how to improve the network coverage rate, but ignores the network connectivity rate improvement. However, at the network adjustment moment, the NRBSCT algorithm can firstly establish a stratified connected tree that takes the sink node as the root node, and then ensure that in the centralized optimization conducted by the sink node, the final destination location of node s
_{i}will not be R_{t}away from the backbone nodes, which achieves full network connectivity and also helps to maintain a relatively high network connectivity during network operation. - (3)
- The MRNR algorithm does not consider how to shorten the movement distance when requiring the least important node to move toward the biggest coverage blind point to improve the network coverage rate. However, the centralized optimization conducted by the sink node in the NRBSCT algorithm considers limiting node movement distance from the left and consumed energy perspectives, which can shorten the total movement distance of nodes during redeployment and prolong the network lifetime.

#### 4.2. Simulation Scenario and Parameter Settings

_{x}= m

_{y}= m

_{z}= 1 and λ

_{1}= 0.8. Node drift probability P

_{e}is set to be 0.3, and drift probabilities along the positive directions of x, y and z axes are controlled by setting P

_{dx}= P

_{dy}= P

_{dz}= 0.5. In the NRBSCT algorithm, the value of r

_{g}is 0.2. Other main parameter settings of the MRNR and NRBSCT algorithms are enumerated in Table 5.

#### 4.3. Simulation Results and Analysis

_{ad}, the network connectivity exhibits the decrease because of the node drift caused by water environment and node death caused by energy depletion. While, if the network operation time is just the network adjustment moment T

_{ad}(such as 50 rounds, 100 rounds, 150 rounds), the NRBSCT algorithm can firstly establish a stratified connected tree that takes the sink node as the root node, and then ensure that in the centralized optimization, the final destination location of node s

_{i}will not be R

_{t}away from the backbone nodes, which achieves full network connectivity and makes the value of the network connectivity bigger than that of the former or latter network operation time (i.e., the network connectivity exhibits the fluctuation phenomenon).

## 5. Conclusions and Future Work

- (1)
- The 3D random drift model adopted to simulate the node drift caused by the water environment is relatively simple, considering the complex flow changes for realistic conditions.
- (2)
- In the description of the energy consumption calculation for transmitting information, the attenuation model of acoustic propagation is relatively rough considering the reasonable uncertainty bounds for realistic conditions.
- (3)
- The movement energy consumption calculation method is also relatively idealized considering the complex current effects for realistic conditions.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 7.**Comparison of number of nodes outside monitored space during network operation: (

**a**) different algorithms and same network distribution (D1); (

**b**) different algorithms and same network distribution (D2); (

**c**) different network distribution and same algorithm (NRBSCT); and (

**d**) different network distribution and same algorithm (MRNR).

**Figure 8.**Comparison of network coverage rate during network operation: (

**a**) different algorithms and same network distribution (D1); (

**b**) different algorithms and same network distribution (D2); (

**c**) different network distribution and same algorithm (NRBSCT); and (

**d**) different network distribution and same algorithm (MRNR).

**Figure 9.**Comparison of network connectivity rate during network operation: (

**a**) different algorithms and same network distribution (D1); (

**b**) different algorithms and same network distribution (D2); (

**c**) different network distribution and same algorithm (NRBSCT); and (

**d**) different network distribution and same algorithm (MRNR).

**Figure 10.**Comparison of total movement distance of nodes during network operation: (

**a**) different algorithms and same network distribution (D1); (

**b**) different algorithms and same network distribution (D2); (

**c**) different network distribution and same algorithm (NRBSCT); (

**d**) different network distribution and same algorithm (MRNR).

**Figure 11.**Comparison of network lifetime: (

**a**) different algorithms and same network distribution (D1); (

**b**) different algorithms and same network distribution (D2); (

**c**) different network distribution and same algorithm (NRBSCT); and (

**d**) different network distribution and same algorithm (MRNR).

Literature/Algorithm | Node Mobility | Consideration of Node Drift with Water Environment |
---|---|---|

[19,20] | Static | No |

[21,22,27] | limited | Additional |

[28] | limited | No |

[23,25,29,30,31] | Free | No |

[26] | Free | Additional |

[32], NRBSCT | Free | Full |

Round | 0 | 40 | 49 | 50 (after Adjustment) |
---|---|---|---|---|

Location | (115, 37, 16) | (123, 41, 19) | (125, 43, 21) | (115, 37, 16) |

Inside/Outside | Inside | Outside | Outside | Inside |

Node | s_{2} | s_{3} | s_{8} | s_{9} |
---|---|---|---|---|

Left energy (J) | 75 | 61 | 77 | 57 |

Inside/Outside | Inside | Outside | Outside | Inside |

Strong leaf node | Yes | No | Yes | No |

Symbols | Meanings |
---|---|

w | cube side length |

d | transmitting distance of information package |

M_{b} | size of information package |

T_{p} | transmitting time of information package |

S_{v} | transmission speed of information package |

f | carrier acoustic signal frequency |

α(f) | water absorption coefficient |

A(d) | energy attenuation |

λ | energy spreading factor |

E_{tx}(d) | energy consumption for transmitting information |

P_{r} | power threshold for receiving information package |

t_{n} | information package transmitting times for a node |

R_{t} | communication range |

C_{e} | communication energy consumption |

M_{e} | movement energy consumption |

m_{d} | movement distance |

m_{u} | energy consumption per movement distance |

P_{e} | controlling probability of node drift |

C_{v} | network coverage rate |

P_{c} | number of cube points covered |

P_{t} | total number of all cube points |

C_{n} | network connectivity rate |

n_{c} | number of nodes being able to communicate with sink node |

n | number of all nodes |

t | network operation time |

T_{r} | network adjustment cycle |

T_{ad} | network adjust moment |

E_{i} | energy of node s_{i} |

E_{d} | energy threshold judging death of node |

E_{y} | energy threshold judging whether leaf node is strong enough |

L_{f} | network lifetime |

C_{th} | coverage rate threshold |

E_{in} | node initial energy |

R_{s} | sensing range |

T_{m} | node drift cycle |

M_{r} | ready information |

M_{a} | acknowledging information |

r_{g} | control coefficient |

Parameter Names | Parameter Values |
---|---|

Initial energy of node (E_{i}) | 500 J |

Network coverage rate threshold (C_{th}) | 0.1 |

Energy consumption per movement distance (m_{u}) | 1.5 J/m |

Size of information package (M_{b}) | 1 Kbit |

Receiving Power threshold (P_{r}) | 0.05 w |

Frequency of carrier acoustic signal (f) | 25 kHz |

Transmission speed of information package (S_{v}) | 5 kbps |

Energy spreading factor (λ) | 1.5 |

Sensing range of node (R_{s}) | 15 m |

Communication range of node (R_{t}) | 25 m |

Network adjustment cycle (T_{r}) | 50 round |

Node drift cycle (T_{m}) | 5 round |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, J.; Jiang, P.; Wu, F.; Yu, S.; Song, C.
Node Redeployment Algorithm Based on Stratified Connected Tree for Underwater Sensor Networks. *Sensors* **2017**, *17*, 27.
https://doi.org/10.3390/s17010027

**AMA Style**

Liu J, Jiang P, Wu F, Yu S, Song C.
Node Redeployment Algorithm Based on Stratified Connected Tree for Underwater Sensor Networks. *Sensors*. 2017; 17(1):27.
https://doi.org/10.3390/s17010027

**Chicago/Turabian Style**

Liu, Jun, Peng Jiang, Feng Wu, Shanen Yu, and Chunyue Song.
2017. "Node Redeployment Algorithm Based on Stratified Connected Tree for Underwater Sensor Networks" *Sensors* 17, no. 1: 27.
https://doi.org/10.3390/s17010027