Hybrid Delay-Minimization Scheduling Algorithm of FT and MPTS in WSN Data Aggregation

. The data acquisition of Internet of Things (IoT) is mostly brought out by wireless sensor networks (WSNs), and the ef ﬁ ciency of IoT is directly affected by the time delay in the process of data acquisition, which is researched mainly by the data aggregation of WSNs. Minimizing the delay in the data aggregation process is one of the most important operations. In order to reduce the data aggregation delay, a hybrid delay-minimization data aggregation scheduling (HDDAS) algorithm is proposed, which optimizes the delay from the two main aspects that affect the delay, namely, the transmission path and the collision rate. Accordingly, the algorithm is divided into two phases: the aggregation tree construction and the data transmission scheduling. In the aggregation tree construction phase, the fat tree (FT) is introduced to generate an optimal aggregation tree with the shortest path; in the data transmission scheduling phase, the maximum parallel transmission set (MPTS) is adopted to increase the amount of the collision-free data transmission. The simulation experiment results demonstrate that the HDDAS algorithm proposed in the paper has performed favorably in terms of the data aggregation delay.


Introduction
With the development of Internet of Things technology, wireless sensor network (WSN) is widely used in environmental monitoring, medical health, smart city, and other fields.Among them, the time delay has always been a challenge in WSN, due to the fact that the problem of time delay becomes more obvious when the network scale expands and the number of nodes increases.As for some applications, the requirements for time delay may be relatively less restrictive, such as environmental monitoring.Nevertheless, for other applications, the delay requirement may be more restrictive.For example, in industrial control systems, if WSN is used to control the actions of production lines or robots, the realtime requirements for data are fairly high.If the data transmission is delayed, it may lead to the slow response of the control system and may even lead to production accidents.
One of the main tasks of WSNs is the data collection.In order to accomplish the task, all the sensor nodes in the network need to periodically transmit their data to sink node.This many-to-one data transmission process is called the data aggregation [1].In the process of the data aggregation, the sensor node needs the transmission only once in one period, and its transmission link forms the tree topology, which is called the aggregation tree.The transmission of the collected data on the aggregation tree results in a large amount of data packet collisions, yielding long delays.In order to avoid data packet collisions and reduce delays, the data transmission scheduling is adopted, which is called the data aggregation scheduling.Through the data aggregation scheduling, the data transmission process is classified into many time slots, and the the collision-free data transmission is allocated in a time slot.Among the goals of the data aggregation scheduling, it is essential for the systems with the strict time requirements to minimize the delay of the data aggregation, which has become one of the most significant issues in the researches on WSNs and has been studied extensively.
By the analysis of our previous works, it can be concluded that in the process of the data aggregation scheduling, there exist two main factors that affect the delay, namely, the transmission path and the collision rate.Aiming at the two main factors, a hybrid delay-minimization data aggregation scheduling (HDDAS) algorithm is proposed in the paper, designed to optimize the data aggregation delay.The proposed HDDAS algorithm involves two phases: the aggregation tree construction and the data transmission scheduling.In the aggregation tree construction phase, first and foremost, the concept of the fat tree (FT) [2] is introduced, and the FT is constructed, which adopts sink node as the vertex.Then, the node transmission collision reduction is considered, the shortest path from the node transmission to sink node is examined, and the optimized shortest path aggregation tree based on the FT is generated; in the data transmission scheduling phase, the maximum parallel transmission set (MPTS) of the nodes is searched for each transmission time slot to reduce the transmission collision of the nodes, and the aggregation delay is minimized accordingly.
Our innovations lie in: (1) The FT is introduced into the data aggregation scheduling algorithm.We have linked all valid nodes into FT and then cut FT into the shortest path tree (SPT) with the optimal time delay.This inspiration is derived from the authors' leap in understanding through the long-term study of FT topology and WSN.
(2) The MPTS is introduced into the data aggregation scheduling algorithm.We have maximized the MPTS collection (the maximum number of elements in the collection) to reduce the collision rate of data transmission.
(3) We have combined FT and MPTS to solve the problem of long delay in the data aggregation scheduling process.
The rest of the paper is organized as follows.Section 2 reviews the previous works.In Section 3, we describe the HDDAS algorithm in detail, covering the system model of the algorithm, the FT construction, the aggregation tree generation from the FT, as well as the MPTS scheduling.The performance of the HDDAS algorithm is evaluated through simulation experiments in Section 4. Section 5 concludes the paper and future work.

Previous Works
A multitude of researches on the data aggregation delay optimization are carried out, based on the structure of the SPT.The SPT refers to a tree structure in which the distance from all the nodes to the root node is the shortest path.Huang et al. [3] and Wan et al. [4] studied the delay problem of the data aggregation tree structure, in which the centralized algorithm and the distributed algorithm were proposed, respectively, in which the SPT is based on to optimize the delay performance of data aggregation tree structure.In a study by Liang et al. [5], the expected amount of transmissions was adopted to define the length of the link in the network, so as to construct a SPT for each channel.In a study by Villas et al. [6], an intranetwork aggregation data routing algorithm was proposed, aiming to construct a routing tree with the shortest path that connected all the nodes and sink node.For WSN, since the aggregation tree construction with SPT is not unique, there is still a lot of the optimization space left for the aggregation tree construction.Certainly, there exist some related researches that used other types of data aggregation trees.In a study by Mehrjoo and Khunjush [7], the greedy incremental tree (GIT) was adopted.Arapoglu et al. [8] used the maximal independent set (MIS) to construct an aggregation tree.Sarangi and Bhattacharya [9] adopted minimum dominating set (MDS) to research the data aggregation by constructing an aggregation tree.
In a study by Chen et al. [10], the minimum data aggregation time (MDAT) was verified to be an NP-hard problem.Therefore, the research on optimizing the data aggregation delay is seeking for an approximate solution.For instance, Xu et al. [11] proposed an improved data aggregation scheduling (IAS) algorithm with better performance in the delay.The data aggregation process in the proposed algorithm was illustrated into two parts.In the first part, the transmission of the dominated node was taken into account first, and the noncollision transmission set was constructed as large as possible by adjusting the parent node of the dominated node.After the first part of transmission, the data of the dominated nodes were aggregated to the corresponding dominant nodes.In the second part, the dominant nodes were converged to the root node along the aggregation tree structure.In a study by Pan and Zhang [12], a scheduling algorithm based on the aggregation tree was proposed, which reduced the time required for the data collection through the aggregation convergence.In order to realize the lower limit of the small delay, the sum of the receiver depth and the number of subnumbers were taken as the cost of the transmission link, and then the link with the lowest iterative cost was added iteratively to construct the aggregation tree gradually.So as to adopt the time slot effectively, the neighbor degree sorting algorithm and the supplementary scheduling algorithm were employed to allocate the time slot for sensor nodes.The research on optimizing the data aggregation delay can not only seek the approximate solutions, but also simplify the problem by assuming the parameters or modifying the system scale.For instance, Le et al. [13] proposed a data aggregation delay scheme that minimized the duty cycle in WSN, examined the dormancy among the sensor nodes, and constructed the connection dominance set (CDS) tree in the first phase.In the second stage, CDS tree was used as the virtual backbone of effective data aggregation scheduling.The fastest available sensor node transmission time was allocated by scheduling to transmit all the data to the receiver without the collision.Chen et al. [14] studied the minimumlatency aggregation schedule (MLAS) problem in WSNs with a duty cycle, where nodes could only receive the active data, without considering the structure.The two distributed aggregation algorithms were proposed, in which the aggregation tree and the collision-free scheduling were generated at the same time to utilize the active time slot from all the neighbors and improve the aggregation delay and the utilization of the available time slot.In a study by Nguyen et al. [15], a distributed collision-avoidance scheduling (DCAS) algorithm was presented.The multidata aggregation scheduling and the multichannel (MLCAMDAS-MC) was avoided by the delay collision.When the sensor node was assigned a channel, and data compression with a aggregation ratio was carried out flexibly, minimum delay data aggregation was completed by the algorithm without the data collision in the distributed WSN.It is observed that reducing the node transmission collisions is the most effective scheduling method for obtaining the smallest data aggregation delay.

Hybrid Delay-Minimization Data
Aggregation Scheduling Algorithm 3.1.System Model of the Algorithm.The network G(V, E) is constructed, where V is the randomly distributed node, and E is the path of data transmission and aggregation.In network G, one sink node is set, which merely has the function of receiving data, and the transmission radius of other nodes for sending data and receiving data is r.The specific provisions are illustrated as follows: (1) In network G, the data acquisition has been completed by V. (2) In network G, the data aggregation generates on V, which is completely aggregated.(3) In network G, the additive aggregation operation is supported by the data aggregation.(4) In network G, V sending the data and receiving the data are completed within 1 hop.( 5) In network G, the time slots of the neighboring V broadcasting are equal (set as 1 time slot).If all the information of the network G is transmitted to the sink node after t time slots, then a convergence period ends.

Constructing a Fat Tree.
The data aggregation requires scheduling on the branches (paths between nodes) of the aggregation tree and performing aggregation operations on nodes.In order to construct the shortest path aggregation tree, we introduce the FT.The FT is a structure with all the shortest paths, and some nodes have the multiple parent nodes, which is not the tree structure.On the node set, the FT is constructed, and the construction flow is shown in Figure 1.
The legend of FT construction is shown in Figure 2.

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As shown in Figure 2, r is taken as the transmission radius, the child nodes found by sink node S are node 1 and node 2; the child nodes found by node 1 are node 3 and node 4; the child nodes found by node 2 are node 4, node 5, node 6, and node 7. The constructed FT is shown in Figure 3.
The pseudocode of the constructed FT is presented in Algorithm 1.
It is worth noting that it is uncertain that all the nodes in G can be added to the FT, and the remaining nodes cannot communicate effectively with the surrounding nodes by broadcasting.For example, all the nodes marked as 0 by Algorithm 1, and these nodes are the isolated nodes, as well as the invalid nodes, which must be abandoned.

3.3.
Generating the Aggregation Tree from the Fat Tree.The FT contains all the shortest paths from the leaf node to the root node, but it is neither a true tree structure, nor an aggregation tree structure.Some nodes N in the FT have the multiple parent nodes.One parent node must be selected from these multiple parent nodes, which is called the true parent node, and the others are called the pseudoparent nodes.For the true parent node, the parent-child relationship with node N is retained; for the pseudoparent node, the parent-child relationship with node N is deleted.In this way, an aggregation tree from the FT is generated accordingly.
In the process of generating an aggregation tree from a FT, there is a key issue that needs to be solved, that is, how to select the true parent node.The principle of selecting the true parent node is to be beneficial to shorten the delay.First, no matter how the true parent node is selected, the path from the leaf node to the root node is the shortest path; second, after the true parent node is selected, the true parent node and the pseudoparent node receive the data and await the sum of time for the lowest decrease.An example is shown in Figure 4. Node 4 in the FT has two parent nodes, namely, node 1 and node 2. For them, node 1 receives the data of node 3 and node 4, and the waiting time slot for node 1 to receive data is 2 (one time slot is required for the transmission from node 3 to node 1, and one time slot is required for the transmission from node 4 to node 1); node 2 receives the data of node 4, node 5, node 6, and node 7. So, the waiting time slot for node 2 to receive data is 4 (one time slot is required for the transmission from node 4, node 5, node 6, and node 7 to node 2, respectively).If node 1 is selected as the true parent of node 4, then the relationship between node 4 and its pseudoparent node 2 must be deleted.At this time, the waiting time slot of the true parent node 1 is 2 and the waiting time slot of the pseudo parent node 2 is 3; if node 2 is selected to be the true parent node of node 4, then the relationship between node 4 and its pseudoparent node 1 must be deleted.At this time, the waiting time slot of the true parent node 2 is 4, and the waiting time slot of the pseudoparent node 1 is 1.To sum up, in this example, node 1 is selected as the true parent node of node 4. The reason is explained in Section 3.4.
The prerequisite for selecting the true parent node is to calculate the amount of the time slots that the node waits for.Suppose that the time slots that node i needs to wait for are T i to receive the data of all its child nodes, as shown in Formula (1).
where N Child is the number of the child nodes of node i and T MaxChild is the maximum value of waiting time slot after adjustment among the child nodes of node i. Sort the T values of the child nodes of node i in a stable order, and then compare the first element with the following elements one by one.If it is the same as the first element, add 1, and if it is different from the first element, start with the second element.The subsequent elements are compared one by one until the last element cannot be compared, and the last element is assigned to T MaxChild , which is the adjustment process.
The scheme of selecting the true parent node from two parent nodes is analyzed and examined through three cases.In the first case, the T value of both of the two parent nodes is N Child ; in the second case, the T value of one of parent nodes is N Child , and that of the other is T MaxChild + 1; in the third case, the T value of both of the two parent nodes is The center node of G is selected as sink node; 2: Initialization, all the nodes in G are marked as 0, and the FT is empty; 3: The mark of sink node is modified to be 1; 4: The information is sent to its neighboring nodes by the node marked as 1, and the information transmission radius is r; 5: The information is accepted by the node marked as 0, and the node that receives the information is connected to the node that sends the information as a child node and its mark is modified as 1; 6: The mark of the node that sends the information is modified as 2, and the node is added to the FT; 7: The steps 4-6 are repeated until there are no nodes marked as 1 in G; 8: The FT is obtained, which takes sink node as the only root node.ALGORITHM 1: FT construction.4 Journal of Sensors Note: When N Child of the parent node has the same value as the value of T MaxChild + 1, T MaxChild + 1 is selected as T value of the parent node; the solution is optimal, which is selected according to the probability; according to the Table 1, the number of parent nodes is equal to 2, which can be extended to the number of parent nodes >2.
Input: FT Output: Aggregation tree 1: Initialization, all the nodes in the FT are numbered, and the initial value of the attribute is empty; 2: For all the nodes K in the FT, the following operations are looped: 3: If K is a leaf node then T K = 0; 4: If K is a nonleaf node, then calculate the value of T K according to Formula (1); 5: If T K ¼ N Child , then the attribute of node K is set to A; 6: If T K ¼ T MaxChild + 1, then the attribute of node K is set to B; 7: For node K whose number of parent nodes ≥ 2, the following operations are looped: 8: If the attribute of all the parent nodes of K is A, then select the parent node with the smallest T value as the true parent node and calculate T value of the pseudoparent node according to steps 4-6; 9: If the attributes of all the parent nodes of K are B, then select the parent node with the largest T value as the true parent node and calculate T value of the pseudoparent node according to steps 4-6; 10: If the attributes of all the parent nodes of K have A and B, then select the parent node with the largest T value among all the nodes with attribute B as the true parent node and calculate the T value of the pseudoparent node according to steps 4-6; 11: Tree = FT.
ALGORITHM 2: Generating the aggregation tree from the FT.

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T MaxChild + 1.The specific discussion and analysis are given in Table 1.
The pseudocode for generating the aggregation tree from the FT is shown in Algorithm 2.

Maximum Parallel Transmission Set Scheduling.
In the scheduling phase, the total amount of the data collected by all the nodes of the aggregation tree is fixed.If the data are to be aggregated to sink node with the lowest delay, then the data need to be transmitted in each transmission time slot as much as possible, and the transmission collisions are not caused for the data.In the tth transmission time slot, one of the leaf nodes that are brothers to each other is selected and put into S t , in which S t is the MPTS in the tth time slot.Therefore, a MPTS scheduling algorithm is proposed in the paper, which has constructed a scheduling sequence set S with the MPTS as the elements, that is, S ¼ fS 1 ; S 2 ; S 3 ; ⋯; S t g.The data of the scheduling sequence set are converged by the shortest path in the aggregation tree to sink node, and the scheduling sequence set is satisfied as follows: (1) where, condition (1) guarantees that each node sends the information only once; condition (2) guarantees that the information collected by all the nodes are aggregated to sink node.
The MPTS scheduling process is shown in Figure 5.
The MPTS scheduling can be described by assigning time slots to the nodes.As shown in Figure 5, the aggregation period is four time slots: in the first time slot, node 3 and node 5 are in the transmitting state, and the corresponding node 1 and node 2 are in the receiving state and S 1 ¼ f3; 5g; in the second time slot, node 4 and node 6 are in the transmitting state, and the corresponding node 1 and node 2 are in the receiving state and S 2 ¼ f4; 6g; in the third time slot, node 1 and node 7 are in the transmitting state, and the corresponding node S and node 2 are in the receiving state and S 3 ¼ f1; 7g; in the fourth time slot, the node 2 is in the transmitting state, and the corresponding node S is in the receiving state and S 4 ¼ f2g.Thus, the MPTS is S 1 ; S 2 ; S 3 , and S 4 , the scheduling sequence set of the network is S ¼ fS 1 ; S 2 ; S 3 ; S 4 g, the aggregation delay is regarded as the number of time slots involved in an integrated data aggregation period [16], and the transmission delay is 4.
From the scheduling process, it can be detected that the MPTS and the network transmission delay are related to the selection of the true parent node in the FT.As shown in Figure 4, when node 2 is selected as the true parent node of node 4, the network transmission delay is 5; when node 1 is selected as the true parent of node 4, the network transmission delay is 4.
The pseudocode of the MPTS scheduling algorithm is elaborated in Algorithm 3.

Simulation Experiments and Result Analysis
In order to verify the performance of the HDDAS algorithm proposed in the paper in terms of the aggregation delay, three types of simulation experiments are carried out: the experiments on the impact of parameters on the delay, the time delay comparison and ablation experiments of aggregation tree, and the comparison experiments of the delay among the algorithms.In the simulation environment, the node positions have the random distribution, all the sensor nodes own the transmission radius, which are the same, and the delay of the aggregation tree construction is not covered in the aggregation delay examined in the paper.
All the simulation results in this paper are based on the average of 200 valid experimental results.When the number of experiments is small, the randomness of the experimental results is larger.As the number of experiments increases, the average of experimental results tends to be stable.Input: Aggregation tree Output: Scheduling sequence set S 1: Initialization, S ¼ ∅, j = 1; 2: While sink node has the child node 3: The leaf nodes of aggregation tree are numbered from 1 to n; 4: For i = 1 to n do 5: If there not exist the brother node of v i in S j 6: Then S j ← v i 7: S ← S j 8: Delete all the nodes of S j in the aggregation tree; 9: j = j + 1; 10: End while 11: Return S ALGORITHM 3: MPTS scheduling algorithm.6 Journal of Sensors time slots.The delay comparison of the HDDAS algorithm under different transmission radii is shown in Figure 6.The delay comparison of the HDDAS algorithm under different amounts of nodes is shown in Figure 7.
As shown in Figure 6, with different amounts of nodes, the curves of the transmission delay are compared, which varies with transmission radius r, and the value of transmission radius r is 20, 30, and 40 m, respectively.It can be observed from Figure 6 that first, with the same amount of nodes, as the transmission radius r of the node increases, the network delay increases rapidly.For example, when 500 nodes are used, the aggregation delay under the three transmission radii is 28, 37, and 60, which is increased with 32.1% and 62.2%, respectively.Second, with the same transmission radius r, the different amount of nodes have the significant impact on the delay growth rate.At the same time, with different transmission radii, the delay growth rate is also different.For example, when the transmission radius r is 20 m, the delay of the network increases with 78.6% when the amount of nodes is increased from 500 to 1,000, and when the transmission radius r is 40 m, the value is 203.3%.
As shown in Figure 7, the delay changes with different amounts of the nodes are compared.When the node radius r is smaller, the transmission delay of the network has little difference.For example, when the transmission radius r is 10 m, the delay difference under the three different kinds of amounts of nodes is only a few time slots; as the transmission radius r increases, the delay difference under the different amounts of nodes increases obviously.When the transmission radius r is 50 m, the delay with 1,000 nodes is increased with about 2.2 times compared with that of 500 nodes.

Comparison Experiments of the Delay of the Aggregation
Tree.The experiment results from the existing researches present that the performance of the data aggregation trees constructed by different algorithms varies greatly in terms of the delay, which is resulted from the aggregation tree structure.Therefore, the MPTS scheduling scheme proposed in the paper is used to simulate and compare the delay under different aggregation tree structures.Among them, there exist the center at nearest source (CNS) algorithm, the SPT algorithm, the GIT algorithm, and the algorithm proposed in the paper base on fat tree (BFT).The simulation experiment results are shown in Figure 8.
In order to show the significance and performance of introducing FT and MPTS into the HDDAS algorithm proposed in this paper, we have designed the ablation experiment of the HDDAS, that is, the HDDAS without FT (random construction of the aggregation tree), the HDDAS without MPTS (random transmission scheduling), and the complete HDDAS is compared for aggregation delay.The experimental results are shown in Figure 9.
The experimental parameters of these two experiments are set as follows: the experimental area is 200 × 200 m, the transmission radius of sensor nodes is r = 20 m, the number of nodes is n (100-500), and the time delay is expressed by time slots.

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As shown in Figure 8, under the aggregation trees constructed by all the algorithms, the aggregation delay has an increasing tendency with the increase of the nodes.When the amount of the nodes is smaller, the GIT algorithm and the BFT algorithm of the paper are basically the same in terms of the delay, while the CNS algorithm and the SPT algorithm have the higher delay than the two previous algorithms; as the amount of the nodes increases, the delay of the aggregation tree constructed by the BFT algorithm of the paper is significantly lower than that of the other three algorithms.
As shown in Figure 9, the aggregation delay of all the algorithms increases with the increase of number of nodes.The delay of the HDDAS algorithm is significantly lower than that of the HDDAS without FT and that of the HDDAS without MPTS, which indicates that the introduction of FT and MPTS is of great significance to improve the delay performance of the HDDAS algorithm.Among them, the delay of the HDDAS without FT is the largest, which shows that it is more effective to introduce FT.Theoretically, FT is cut into an aggregation tree with the shortest path, and the balance in the cutting process increases the MPTS in the later scheduling, and the collision rate is obviously reduced.

Comparison Experiments of the Delay among Algorithms.
The HDDAS algorithm of the paper, the conventional IAS algorithm, the conventional DAS algorithm, and the most advanced SVM algorithm are compared in the terms of the aggregation delay.The comparison results are shown in Figures 10 and 11.
Experimental parameter setting: The experimental area is 200 × 200 m, the same transmission radius r = 20 m, the same number of nodes n = 500, and the time delay is represented by time slots.
As shown in Figure 10, with the same transmission radius, as the amount of the nodes increases, the aggregation delay of all the algorithms increases distinctively, and the delay of the proposed HDDAS algorithm is the optimal.The delay of the IAS algorithm and the delay of the DAS algorithm are the same basically and the worst.When the node density is small, the latency of SVM algorithm is similar to that of IAS; when the node density is high, the delay of the SVM algorithm is close to that of the algorithm in this paper.When the nodes in the IAS algorithm increase from 500 to 1,000, the value of the delay increases from 31 to 61 correspondingly, an increase of 96.8%; the delay of the SVM algorithm increases from 30 to 55, an increase of 83.3%; the delay of the HDDAS algorithm proposed in the paper increases from 28 to 50, an increase of 78.6%.Therefore, the delay of the proposed HDDAS is greatly lower than those of three other algorithms.
As shown in Figure 11, the delay of different transmission radii is compared and shown by the changing curves.It can been verified that as the transmission radius of the nodes increases, the collision increases, the amount of the parallel transmission nodes in each time slot decreases, and the delay of the network increases.In this case, when the transmission radius r is smaller (≤ 20 m), the delay among the HDDAS Journal of Sensors algorithm of the paper, the IAS algorithm, and the SVM algorithm is a bit different.But as the transmission radius r increases, the delay of the proposed HDDAS algorithm is significantly lower than that of the IAS algorithm and the SVM algorithm.

Conclusion
On the basis of analyzing and researching the main factors affecting the data aggregation delay, as well as the related algorithms, the HDDAS algorithm is proposed, in which the FT is introduced to generate the aggregation tree, and the MPTS scheduling scheme is combined to reduce the delay of the data aggregation scheduling process.From the simulation experiments, it has been verified that when the transmission radius is larger and the amount of nodes is larger, the advantages of the FT structure can be fully reflected, and the data aggregation delay of the entire network is lower.In addition, the proposed HDDAS algorithm of the paper is the data aggregation research under the condition of the equal time slot transmission.For WSN with the unequal transmission time slot, as long as the maximum transmission time of nodes is taken as one time slot, the HDDAS algorithm still remains practical, but the delay is increased to some extent, and the further research is needed in the future.

Begin
Select the center point of G as the sink node Select the sink node as the starting point Seek the child node with transmission radius r Whether the child node of the starting point is found?Complete the FT construction End No Yes Link the child node of the starting point into the FT Select each child node as a new starting point

FIGURE 4 :
FIGURE 4: Schematic diagram of selecting the true parent node.

4. 1 .
Experiments on the Impact of Parameters on the Delay.In the experimental environment, since the nodes are randomly distributed, the delay of the HDDAS algorithm of the paper is affected by the transmission radius r and the number n of nodes.Experimental parameter setting: the experimental area is 200 × 200 m, different sensor specifications have different transmission radii r (10-50 m), the number of nodes n (500-1,000), and the time delay is represented by

FIGURE 6 :
FIGURE 6: Comparison of the delay of the HDDAS algorithm under different transmission radii.

FIGURE 7 :FIGURE 8 :
FIGURE 7: Comparison of the delay of the HDDAS algorithm with different amounts of nodes.

FIGURE 10 :FIGURE 11 :
FIGURE 10: Delay comparison of the various algorithms with the same transmission radius.

TABLE 1 :
Selection of the true parent node between the two parent nodes.