An Energy Efficient and Minimum Latency Routing Protocol for Multihop WSNs

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1 An Energy Efficient and Minimum Latency Routing Protocol for Multihop WSNs Changyan Yi and Ken Ferens Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, Canada Abstract This paper presents a novel multihop routing protocol, which aims to simultaneously minimize data aggregation latency and maximize network lifetime. The protocol constructs a dynamic greedy growing tree (GGT) from sink to all sensor nodes. Latency and energy consumption minimization priority rules are applied to node selection at each step in the tree construction process. Latency minimization rules are applied first, and then energy consumption priority rules are applied to break any ties. The tree is constructed periodically to balance the energy consumption of nodes across the network. Priority Rules consist of the number of interfering neighbors, residual energy of senders and receivers, link quality, and load balancing. MATLAB simulations show that the proposed Energy Efficient Greedy Growing Tree (EEGGT) has the same latency performance as basic GGT. However, EEGGT significantly outperforms basic GGT, Static GGT (SGGT) and Dynamic GGT (DGGT) in terms of network lifetime. Keywords minimum delay routing, maximizing network lifetime, minimum delay data aggregation scheduling. I. INTRODUCTION A common difficulty encountered in the design of multi-hop routing protocols for wireless sensor networks (WSNs) is to minimize the delay and to simultaneously maximize network lifetime. These two goals seem to oppose one another. A routing protocol which aims to minimize delay usually achieves that goal by trading off network lifetime, and vice versa. On the one hand, a delay oriented routing protocol will typically chose the same subset of nodes in a portion of a route for data relaying purposes, simply because they represent distribution points in a least delay path. A such, these nodes will lose their energy before other nodes, since they have more work to do in terms of relaying radio messages and data processing. Consequently, the network suffers premature death. On the other hand, a network lifetime oriented protocol will typically choose a longer delay path, suitably because the nodes along that path have more energy than others. But, this network lifetime resultant path will consist of more hops than the least delay path; this results in a longer delay route. As such, more energy will be used, simply because there are more hops along the path. More nodes will be forced to perform radio relaying and data processing tasks, which means a higher total energy consumption amount, consequently leading to premature network death. A common goal in multi-hop routing protocols for wireless sensor networks (WSNs) is to achieve a compromise between minimizing the delay and maximizing network lifetime. An approach of achieving both goals simultaneously is to tie together the decision making rules of both goals with a common parameter that constrains the design of each. One such parameter is data aggregation. Data aggregation can be used to significantly reduce the amount of consumed energy in a network, since, in an aggregation enabled network, the nodes along a routing path work together to reduce the representation of sensor readings by performing averaging, min/max, data compression, data merging, etc. This significantly reduces the size of radio transmissions, albeit, at the cost of increased data processing, but, it is well known that the cost of radio transmission far exceeds that of data processing. By decreasing the amount of radio transmissions, this increases the network lifetime. A bridge connecting data aggregation and maximizing network lifetime with minimizing delay is to choose a minimum delay path such that the opportunity of parallel transmissions are maximized. When a protocol forms a minimum delay path, it should do so by choosing nodes in the path, which allow other nodes the opportunity to transmit simultaneously without interfering with the chosen nodes transmissions. In this way, there is more opportunity to perform data aggregation, resulting in decreasing the amount of consumed energy, while at the same time, minimizing the delay. Another benefit of maximizing parallel transmission is that the total amount of interference is reduced, thus saving the network even more energy by reducing the cost of retransmission due to collisions.

2 Other parameters that can be used to unify the goals of minimizing delay in a network and maximizing network lifetime are choosing nodes to take part on routing based on their residual energy; choosing destination nodes based on link quality; and choosing nodes to maximize load balancing. This paper presents a novel routing protocol for WSNs, which aims to minimize the delay while simultaneously maximizing the network lifetime, by unifying the two goals with parameter constraining decision making processes based on data aggregation, residual energy, link quality, and load balancing. The remaining sections of this paper are organised as follows. Section 2 presents related work in routing protocols for minimizing the delay and maximizing network lifetime. Section 3 gives the system model. Section 4 discusses the proposed protocol, which incorporates node residual energy, edge link quality, and network wide load balancing into the decision making process of a modified minimum latency aggregation scheduling (MLAS) protocol [1], [2]. Section 5 describes the experiments and simulations which compare the proposed protocol with basic MLAS. Section 6 concludes the paper and gives future work. II. RELATED WORK Minimum latency aggregation scheduling (MLAS) is a wellknown problem of constructing minimum delay routes by minimizing the number of time slots in routes and incorporating data aggregation [1]. Most of the previous MLAS work use two consecutive independent phases, i.e., tree construction phase and edge scheduling phase (time slot scheduling phase) [1], [3], [4], [5]. Two notable approaches are Chen et al. s approach [4], which is based on the shortest path tree (SPT), and Huang et al. s [3] and Wan et al. s [1] approach, which is based on the dominating set tree (DST). However, two-phase approaches have some significant problems: First, the degree of latency varies greatly, even within the same algorithm, depending on the tree constructed initially. Second, the opportunity of parallel transmissions among nodes would decrease because the role of leaf nodes and non-leaf nodes are predefined. Therefore, Tian et al. [2] proposed a new aggregation scheduling by defining a greedy growing tree that only depends on one phase approach. This method easily assigns a minimum number of time slots for all the sender-receiver pairs. In all of the aforementioned works, the energy consumption of the network is largely ignored, and consequently, the network, while having minimum latency routes, dies prematurely, due to a large imbalance in node residual energy. This paper presents a novel routing protocol for WSNs, which starts with the work of MLAS [1], [2], and modifies this work by incorporating node residual energy, edge link quality, and network wide load balancing into the route formation decision making process. III. SYSTEM MODEL Consider a network G = (V, E) with V sensor nodes and E edges. There is only one sink node b V. Moreover, the communication graph of the network should be a digraph obtained from G by replacing each link in G with two oppositely directed edges u v and v u. That means all the sensor nodes are located in Euclidean plane and are equipped with omnidirectional antennas. Furthermore: 1. All nodes have the same fixed transmission radius r. 2. For simplify the problem, the interference range equals to the transmission radius, ρ = r. 3. Each node works in half-duplex mode, so that it can either send or receive at one time slot. Fig. 1 shows an example network. Two pairs of communication edges S1 D1 and S2 D2 are interference free because the two line segments (S1, D2) and (S2, D1) are both longer than ρ. However, S1 D1 and S2 D4 are exclusive interference edges that cannot be scheduled in the same time slot. In the subset of edges that belongs to interference free, multiple transmissions can be assigned in a same time slot. This model is referred to as the protocol interference model [6]. Fig. 1 Protocol interference model: Each node has a unit transmission radius and an interference radius. Energy Model The energy model used in this work is the same as in [7]: is the total energy consumption of the whole network. k is the number of bits received and sent by node i, r is the transmission distance. The and are the energy consumption in reception and transmission, respectively. is the electrical energy required for the circuits in receiver and transmitter. The amplification energy for transmission is denoted by. (1)

3 Latency Model Consider the network G = (V, E) with V sensors. Define C i as a subset of V. Therefore, the data aggregation process is a sequence of subsets C 1, C 2... C K, C K+1 that satisfy the following conditions. 1. C k1 C k2, 1 k 1 < k 2 K C 1 = V, and C K+1 = Sink 3. Data packets are gathered from all the sensors to the sink from C K to C K+1 in time slot K. Generally, the value of K is defined as the data aggregation latency. IV. ENERGY EFFICIENT GREEDY GROWING TREE The proposed algorithm modifies and extends the work done by Tian et al. [2]. In their paper, a Greedy Growing Tree (GGT) is proposed to schedule the aggregation process in a reverse order. In this algorithm, the spanning tree is constructed step by step, and the allocated time slot for each link is assigned along with the tree construction. In this way, the tree formation process starts from the sink. In the 1 st step, the sink acts as the parent (receiver), and the algorithm searches for a child (sender). A sender is chosen based on a set of priority rules. This sender is connected to the sink and assigned a specific time slot. Any other node that is out of the interference range of the chosen node, but in the transmission range of the sink, is assigned the same time slot. In the 2 nd step, the chosen node and any other nodes chosen (which was out of the interference range) in the 1 st step now act as parents, and the algorithm searches and chooses the next sender (child). Similarly, any other node that is out of the interference range of the chosen node, but in the transmission range of the previously chosen parent(s), is assigned the same time slot. This continues until all of the sensors are connected to the spanning tree and every link has been assigned a specific time slot. The basic idea of GGT is to construct larger and larger spanning trees rooted at the sink: It starts by considering the sink as the only node in the tree and tries to find the sender; in each subsequent round, all non-leaf nodes of the temporary spanning tree are the candidates of receivers; and all leaf nodes are the candidate of senders [2]. However, the GGT is only proposed to address the MLAS problem. In our system model, we also have to consider about the energy consumption by all the sensors. In order to expand the lifetime of the network, we have to balance the energy consumed by each node. Obviously, in the spanning tree of the network, non-leaf nodes consume more energy than the leaf nodes. A leaf node has only one link, i.e., for transmitting its own data packet. Thus, the energy consumed by leaf nodes can be represented as: (2) A non-leaf node has more than one link. There is one link for transmission, and i links for receiving data packets from all of its children nodes (e.g. the number of children is i, where (i 1 and i is an integer)). 1. The next step describes how to select the <sender, receiver> pairs in each round. The goal is to maximize the opportunity of parallel transmissions and balance the energy consumption by deciding which node should have larger value of i and which one should has smaller value of i. The proposed algorithm favors the minimization of latency by applying the priority rules of [2] firstly, and then, secondly, it applies the node residual energy, link quality, and load balancing constraints to the <sender, receiver> selection in each step of the tree construction process. Basic Greedy Growing Tree (GGT) The MLAS problem can be solved by using the priority rules with the GGT of [2]. This work asserts that the selection of <sender, receiver> pairs should be considered as beneficial for both current and later rounds, and the choices that benefit later rounds have priority. Thus, they define a Priority Rule for selecting proper <sender, receiver> pairs. To facilitate the discussion, the following definitions and notations are used: Neighbor (I, V ) NumNeigbor (I, V ) NumNeigbor (I, V \Z) Sizeof(V ) EnergyOf(i) EnergyOf(j) (3) The set of neighbors of a node i in a node set V of G. The number of neighbors of a node i in a node set V of G. The number of neighbors of a node i in a node set V but not in Z of G. the number of nodes in a node set V of G. the remaining energy of sender. the remaining energy of receiver. Now, consider the network G = (V, E), let r as round index and T r to be the temporary tree. The Priority Rules of GGT can be presented as follows: Priority Rule 1: First, sort all the nodes based on the increasing order of NumNeigbor (I, T r ). Priority Rule 2: For nodes with the same order by Rule 1, sort them based on the increasing order of NumNeigbor (I, T r \Z). Priority Rule 3: For nodes with the same order by Rule 1 and Rule 2, sort them based on lexicographic order.

4 The basic GGT algorithm uses he above rules to select <sender, receiver> pairs. As mentioned, this paper modifies and extends these rules to incorporate maximization of network lifetime. To better understand the extensions and modifications, the motivation and effect of the basic priority rules are explained first. Fig. 2 shows an example wireless sensor network with 20 nodes. In this network, there are only two nodes in the temporary tree which are represented by color black. Now, consider the order of nodes a; b; c; d with Priority Rule to decide the sequence of adding them in the tree. interfere with node b. Accordingly, we can say that b has more opportunity in parallel transmission than node a. Thus, node b has priority over node a. For Rule 2 (Comparing nodes b and c): Node b and c have the same number of neighbors in the tree. That is the reason why we need Rule 2. Node c has less number of neighbors outside of the tree than node b. That means if b or c acts as receiver after they join in the tree, choosing c may increase the opportunity of parallel transmission because it only has four potential senders. Only four potential transmissions would interfere with c in this way, but for b, the number of potential transmissions is seven. Rule 3 is actually only used for braking the ties; so, it provides no help in addressing the MLAS problem or the maximizing the network lifetime problem. With the above analysis of the Priority Rule, we find that each rule is reasonable for its particular situation. However, the reason why Rule 1 has higher priority than Rule 2 is not quite obvious. In fact, the following discussion shows that Rule 2 might have higher priority in certain circumstances. Let s consider a special case as shown in Fig. 3. Fig. 2 Example network for Priority Rules. Based on the properties of node a; b; c; d as shown in the Table, we can use the Priority Rules to determine the order of adding in the tree for nodes a; b; c; d. Step1. Increasing order by Rule1: b = c = d < a Step2. Increasing order by Rule2: c = d < b Step3. Lexicographic order by Rule3: c < d Step4. Final order: c < d < b < a Therefore, node c has the highest priority and node a has the lowest priority among these four nodes. Accordingly, the algorithm would choose node c as the child of the parents, and node c becomes the parent for the next step. In next section, this example will be used again to explain the rationality of Priority Rule. Rationale of GGT According to the example network shown in Fig. 2, the GGT algorithm may be analyzed as follows: For Rule 1 (Comparing nodes a and b): Node a has two parents in the tree, but b only has one. For node a, all the neighbors of its two parents might be the sender in subsequent rounds. All of them would interfere with a, because two parents are definitely in a s transmission range. However, only neighbors of one parent would Fig. 3 Special case for Priority Rule. Considering the scenario indicated by Fig. 3, node b would be given higher priority than node a, with the help of Rule 1. But, it is apparent that more collisions might occur if node b was chosen. Special Node Processing in Basic GGT The basic GGT algorithm proposed in [2] applies a higher priority to special nodes, such as the so called Articulation, Pilot and Critical nodes. Their rationale behind the special treatment stems from their concern that the network might become partitioned if these special nodes were not treated with higher priority than Priority Rule 1. They define an Articulation node as a node through which the traffic of a subset of other nodes T G must pass in order to be received by the sink. And, if this articulation node is not given higher priority, then the subset T would be cut-off

5 from the sink. However, our simulations show that the Articulation, Pilot, and Critical nodes are not necessary to consider first. Therefore, all the nodes can be treated equally and ordered simply by the Priority Rule if we only consider addressing the MLAS problem. So in our new routing protocol, the special treatment of nodes has been removed and the simulation shows no ill effects on the aggregation latency. Energy Efficient Extension to Basic GGT Since the network lifetime is significant in WSNs, we now take the energy consumption into account. There are two limitations in GGT algorithm: First, Rule 3 has no contribution in minimizing latency. Choosing a lexicographic order means that the order of the nodes would remain the same all the time. However, the order made by Rule 3 can be more useful if it is based on the remaining energy of the nodes. Second, GGT does not mention anything about the link selection; it only focuses on node selection. That means even if a node is chosen in a specific step, the link selection among all the possible links for this node is random. This process can also be modified if the quality of the link can be taken into account. Notice that if we do not change Rule 1 and Rule 2, the latency would not be changed (This latency is denoted as τ ). Energy Efficient Extensions 1. The static GGT can be easily changed to dynamic if the tree is reconstructed periodically. The minimum time of this periodic interval is set to the time required to completely gather the data from all the sensor nodes in the network; as such, this interval is the latency for one round τ. After every interval τ, the GGT is reconstructed. The added benefit of this modification is that the sensor load and energy consumption may be more balanced, different nodes will generally take part in the routes, since the link selection is random in the Priority Rules. 2. Rule 3 can be replaced by sorting the nodes in decreasing order of the remaining energy of each node. In this case, the node which has higher remaining energy would be chosen first. Since a node entering the tree has a higher chance to be a non-leaf node than the remaining nodes, with this extension, better energy balancing can be achieved, since a non-leaf node requires more energy in its role. (The number of links on a specific node is proportional to the priority of the node.) 3. Alternatively, Rule 3 can be replaced by sorting the nodes in decreasing order of link quality. The link quality is defined as min{energyof(i), EnergyOf(j)}. The rationale behind this extension is that it would make more energy conserving sense to choose the node with the higher link quality than other contenders. For instance, if a node had higher residual energy, but its receiver had very low residual energy, then choosing that node would not be a good choice. Instead of choosing the node with higher remaining energy, this extension proposes to choose the best link between sender and receiver nodes. 4. Moreover, Rule 3 can be replaced by sorting the nodes in decreasing order of receiver residual energy. This extension proposes to sort the nodes in decreasing order of max{energyof(j)}, where j is the index of nodes in the tree which can act as the receiver of this specific new sender. 5. Finally, the link quality between the sender and receiver may not be the most energy efficient choice, particularly when the receiver is over loaded. The basic GGT does not consider the number of links on the existing nodes in the growing tree. When a node is chosen by the Priority Rules in a certain step of the GGT algorithm, an arbitrary parent of the growing tree is chosen as the receiver of the chosen node s traffic. Perhaps, this is the closest parent. Many such nodes may also be sending their sensor data to this same arbitrarily chosen parent, and this parent would consume more energy than other parents in the range of the chosen node, thus leading to premature network death. It would be better to incorporate the number of links currently being handled by the parent into the decision making process. This extension proposes to use set the priority of parent node selection to be proportional to its remaining energy and inversely proportional to its connections. More details would be discussed in simulation part based on Fig. 13. Algorithm for Energy Efficient GGT Table 1 gives the one-round of the tree construction process proposed in the paper. Table 1 Modified basic GGT construction algorithm. Step Action Initialization: Start from the sink node by regarding 0 it as the only node in the T r, r 1. Adopt Rule 1: Choose the node which has highest 1 priority in Rule 1 as the next member. Single Node Case: If only one node is chosen by 2 Rule 1, go to Step 6. Otherwise, continue. Adopt Rule 2: Choose the node which has highest 3 priority in Rule 2 as the next member. Single Node Case: If only one node is chosen by 4 Rule 2, go to Step 6. Otherwise, continue. Remaining Energy judgement: Choose the node along with the best link by choosing the one which has higher min{energyof (i), EnergyOf (j)}. If more 5 than one node is chosen, determine the selection based on max{energyof (i)}. If the final decision is still uncertain, choose the link randomly. Goto Step 7. Link selection: Connect the best link which has max{energyof (j)} or max{energyof (j)/(number of 6 j s childs + 1)}. If more than 1 link has the highest remaining energy, then choose it randomly. Iteration Rule: r r + 1, if r V, go to Step 1. 7 Otherwise Stop.

6 The algorithm shown in Table 1 indicates one-round tree construction. In simulation, the tree would be reconstructed every time period τ. The details of the algorithm for Rule 1, Rule 2 and interference judgement can be found in [2]. So next, only the detailed algorithm for energy judgement is listed in the following. Table 2 Energy balancing algorithm. Step Action Initialization: The initial energy of each node is set 0 as E0 and energy of sink is assumed to infinity. Attribute update of each potential candidate: After finding out the potential candidate for the tree 1 (based on the transmission range), update their attribute of energy from its own remaining energy to min{energyof (i), EnergyOf (j)}. New Rule: If a winner cannot be obtained after Rule 1 and 2, then compare their attributes of 2 energy derived from step 1. If multiple nodes still have the same attribute of energy, then perform a random selection. Decide its parent in the Tree: Two different ways: 1: choose the parent which has max{energyof (j)}. 3 2: choose the parent which has max{energyof (j)/(number of j s childs + 1)}. Complete the tree construction and start transmitting: Data aggregation starts after the tree 4 is constructed. At the end of each round, calculate the remaining energy of each node. Renew status: After each round of transmission, remove the dead ones and renew the status of each 5 node for next tree construction process. And go back to Step 1. There would be 2 main phases in the whole process. In the 1 st phase, the tree construction process is performed time4- slot-by-timeslot until all the nodes are added in the tree. In the 2 nd phase, data transmission is performed. After each round of data transmission, the tree is reconstructed. Fig. 4 Initial network for tree construction. In the first round, the tree construction starts from the sink. Obviously, node a; b; c are the next potential members in the tree. By adopting Rule 1, three nodes get the same order. Then we need to use Rule 2, a and c have higher priority because they have less number of neighbors not in the temporary tree. In order to determine the selection between node a and c, the remaining energy judgement in step 5 is necessary. With all the criteria illustrated above, a sink is chosen in the first time slot s1. Next, the node b, c, d, and e become the candidates of potential members. With Rule 1, we get an order c = d = e < b. Since some nodes have the same order, Rule 2 is applied to figure out a new order, thus we have c < d < e < b. Apparently, the next member c can be chosen and d can be chosen simultaneously in time slot s2 because of the interference free judgement. This tree construction process continues regarding to the Energy Efficient GGT algorithm until all the nodes are connected in the spanning tree. This process is completely shown in Fig. 5 (A). EEGGT for Example Network Consider an example network with 12 sensor nodes and one sink. Small letters indicate the index of all the nodes and their remaining energy are represented by different numerical numbers. Assume that the remaining energy of the sink is positive infinite and energy consumed in transmission and reception are 2 units and 1 unit respectively. The initial network is shown in Fig. 4. Fig. 5 (A)Tree constructed in 1st round. (B)Tree constructed in 2nd round.

7 However, after one round data aggregation process, the remaining energy of the nodes changes to the situation in Fig. 5 (B). We can easily find out the difference of the output of (A) and (B). The tree reconstructs in a different way because the factor of remaining energy affect the node selection and link selection. For instance, node h is chosen in the last order in both (A) and (B), but they select different link for h. In (A), node d has the highest remaining energy of 9, so it is more suitable to be the receiving node of h. In (B), node e has the highest remaining energy of 6 because d consumed more energy in the first round than e, which means h e becomes a better choice. This example shows that the Energy Efficient GGT algorithm does really balance the energy consumption among all the nodes by periodically reconstructing the data gathering tree. Moreover, the latency caused in (A) and (B) is the same in 7 time slots. In other words, Energy Efficient GGT algorithm maintains the latency of traditional GGT algorithm in solving MLAS problem, but, it improves the GGT algorithm by increasing the network lifetime. V. SIMULATION First, randomly deploy N sensors into a square region with edge length L; the density of node is determined by O(N/L 2 ). Besides, the sink and all the sensors have a same transmission range λ. In multi-hop communications, the networks are considered to be fully connected when all the nodes are reachable. The connectivity depends on the radio range; thus, the radio range of the nodes should be configured optimally. In the simulation, we choose N = 50, L = 50 so that O(N/L 2 ) = In order to ensure the network connectivity, λ has 3 different values 15; 20; 35. Since the network deployment and the location of sink have great impact on the performance, two different sensor networks with sink located at the corner and center, respectively, were setup. The remaining simulations are all based on the networks shown in Fig. 6 and Fig. 7. Fig. 7 Random deployed sensors network with sink located at the center. The location of the sink does not only affect the time scheduling for data aggregation, but also leads a great difference in performance of network lifetime. Figure 8 examines the correctness of my idea that considering special nodes is almost useless. Modified GGT shows almost the same performance in aggregation latency with traditional GGT; however it simplifies the time scheduling process by removing the step for considering local optimization which may be caused by some special nodes. Fig. 8 With sink at the center, the performance of aggregation latency. Fig. 6 Random deployed sensors network with sink located at the corner. Traditional GGT is considered as a static transmission process which means that the tree would never be changed, it is denoted as SGGT. On the other hand, the tree construction can be re-built every round based on the remaining energy of the sensors, this process is called DGGT. EEGGT is an energy efficient GGT which is based on our proposed algorithm; the MLAS problem, remaining energy of each child node and parent node, the link quality and energy balancing are all taken into account. Simulation

8 ends when there is no path to the sink, meaning that all neighbors of sink are out of energy. In Fig. 9, we can easily find that EEGGT has longer network lifetime that it runs more rounds based on the same random sensor network. And in this situation, only EEGGT makes all sensors exhausted; this implies the energy balancing performance of the protocol. The difference would be more obvious for lower network nodes density. pairs are highly limited by the transmission range λ = 15. If the tree construction process is static, the network breaks down very fast. However, for DGGT and EEGGT, since they will reconstruct the tree in every round, they can choose different new < sender, receiver > based on current remaining energy of nodes. In this case, SGGT shows significant inferiority in network stability and lifetime. Whereas, EEGGT still performs better. Fig. 9 With sink at the corner, the performance of network lifetime. Consider the sink located at the center of the field in Figure 10. Using EEGGT still has advantage in expanding network lifetime and we can find that SGGT has more live nodes remaining when the network has been already collapsed (neighbors of sink are all running out of energy). However, the EEGGT method best balances the energy consumption. Fig. 11 With λ = 15, the performance of network lifetime. Figure 12 indicates another problem of the network. When λ is relatively high, the simulation can last for many rounds even the number of live nodes is very small. Since the sink can reach most of the nodes in this extreme case, the network turns to be very similar to direct transmission after some long distance nodes died. Fig. 10 With sink at the corner, the performance of network lifetime. Keep the sink located at the corner and change the transmission range λ = 15 and 35 to see the difference. The longer transmission range leads to more choices for selecting new < sender, receiver > pair. In Fig. 11, the choices of choosing new node and adding new < sender, receiver > Fig. 12 With λ = 35, the performance of network lifetime. Actually, when we have already made the decision on which new node to add in the tree, it is not optimal for energy consumption if we choose to connect the parent which has higher remaining energy. Because, the tree is reconstructed at the beginning of next round, the data transmission and tree construction is not working simultaneously, which means that maybe a lot of nodes would choose the same parent in

9 one tree construction process. So, some nodes would deplete its energy very fast. We can also consider the number of child nodes of these potential parents, which should be inversely proportional to the priority of parent selection. As in 2- EEGGT, each new added node chooses its receiver which has max{energyof (j)/(number of j s childs + 1)}, the performance is enhanced in a certain extent as shown in Fig. 13. REFERENCES [1] P. J. Wan, C. H. Huang, L. Wang, Z. Wan and x. Jia, "Minimum latency aggregation scheduling in multihop wireless," in Proceedings of the tenth ACM international symposium on Mobile adhoc networking and computing, New York, [2] C. Tian, H. Jiang, C. Wang, Z. Wu, J. Chen and W. Liu, "Neither shortest path nor dominating set: Aggregation scheduling by greedy growing tree in multihop wireless sensor networks," IEEE Transactions on Vehicular Technology, vol. 60, pp , [3] S. H. Huang, P. J. Wan, C. Vu, Y. Li and F. Yao, "Nearly constant approximation for data aggregation scheduling in wireless sensor networks," in 26th IEEE International Conference on Computer Communications, Fig. 13 The performance with different parent searching method. VI. CONCLUSION AND FUTURE WORK In this paper, a modified greedy growing tree EEGGT is proposed. It simplifies the original GGT by removing the process of differentiating special nodes. And EEGGT does not only aim to minimize the aggregation latency in multihop wireless sensor networks, but also balance the energy consumption so that expanding the lifetime of the network. Though minimizing data aggregation time is still considered in the first place, the proposed novel protocol shows good energy efficiency. Simulation demonstrates that EEGGT has nearly the same performance in minimizing latency as traditional GGT. Furthermore, this modified protocol has much better energy saving and balancing. Moreover, numerical experiment also indicates that different parent searching method would lead to a great difference in the performance of network lifetime. However, the Minimum Aggregation Latency Problem and Energy Efficiency Problem are considered separately with different priority in this work. Future work can consider to set up joint rules for finding new <sender, receiver> pairs for these two goals. Besides, the transmission range is assumed fixed and same for all the sensors in this paper. For a more general case that sensors could adjust their transmission radius, the tree construction process would be much more complicated for the difficulty in interference judgement. And it needs to be considered as a Minimum Spanning Tree. [4] X. Chen, X. Hu and J. Zhu, "Minimum data aggregation time problem in wireless sensor networks," in Proceedings of the First international conference on Mobile Ad-hoc and Sensor Networks, Heidelberg, Berlin, [5] V. Annamalai, S. Gupta and L. Schwiebert, "On treebased convergecasting," vol. 3, pp , March [6] P. Gupta and P. Kumar, "The capacity of wireless networks," Transactions on Information Theory, vol. 46, pp , March [7] W. Heinzelman,, A. Chandrakasan, and H. Balakrishnan, "Energy efficient communication protocol for wireless microsensor networks," in Proceedings of the 33rd Annual Hawaii International Conference, 2000.