Unmanned aerial vehicle network arbitrary multicast algorithm based on air route perception

Abstract

The invention provides an unmanned aerial vehicle network arbitrary multicast algorithm based on air route perception. Any multicast is a very important communication normal form in which a source communicates with a plurality of potential destinations within a multicast group. Arbitrary multicast provides significant advantages in load balancing, redundancy and reliability improvement over conventional multicast and unicast. As we know, any multicast algorithm research about an unmanned aerial vehicle network does not exist at present. Considering that the highly dynamic nature of an unmanned aerial vehicle network forms a great challenge to formalization and solution of any multicast, the space-time trajectory diagram of unmanned aerial vehicle flight is constructed by using predetermined trajectory information, and the dynamically changing network topology is converted into a static diagram beneficial to analysis. Benefited from the space-time topological graph, any multicast problem in the unmanned aerial vehicle network can be formalized and converted into a known Steiner tree problem. Finally, the invention provides an efficient search algorithm to solve the problem and find an optimal transmission path.

Description

Technical Field

[0001] The invention designs an arbitrary multicast algorithm for unmanned aerial vehicle networks based on route perception, and belongs to the field of wireless networks and mobile computing in the field of computers. Background Art

[0002] With the development of monolithic integrated circuit (MIC) and imaging technology, UAVs have greatly expanded their functions in both civil and military fields [1]. In order to complete the designated tasks, UAVs need to share information through the network and receive instructions from decision-making units. To support these operations, it is very important to design reliable routing protocols.

[0003] Existing routing protocols for UAV networks can be roughly divided into unicast, broadcast, multicast, and anycast. In unicast, a single node sends a traffic stream to a single recipient, which is called one-to-one transmission. In broadcast, a series of packets are sent to all nodes on the network, which is called one-to-all transmission. In multicast, a server directs copies of a single data stream and routes them to a multicast group, which is called one-to-many transmission. In anycast, a packet is sent to one of the members of any anycast group, which is called one-to-any transmission. While unicast and multicast routing in UAV networks have been systematically studied in recent years, research on anycast is still in a relatively early stage [2]. This paper focuses on a more common scenario and introduces the problem of anycast in UAV networks. In anycast, it is desired to deliver a packet to any k of all possible destinations [3]. Anycast is obviously different from traditional multicast. First, the destinations are potential rather than predetermined. Second, the goal of anycast is to try to deliver the packet to exactly k destinations. In other words, the number of recipients is strictly limited in advance. Anycast and multicast are two special cases of any-multicast, where k is equal to 1 or n (the total number of multicast group members).

[0004] Typically, after collecting information, the drone will send the data to a ground station for analysis. Other drones will act as relays to deliver the data packets. However, in a large-scale drone network, if all drones send their data to one receiving end, there will be a bottleneck problem [4]. To solve this problem, scenarios with multiple sites and distributed storage systems are considered [5, 6]. Such networks require the source drone to transmit the collected data to all storage nodes or any k of the ground stations. In order to improve reliability, load balancing and security considerations, it is very useful to design an arbitrary multicast routing protocol in the drone network to effectively find a route from the source to any k of the n possible destinations. It is well known that the replication mechanism is very important in distributed systems, involving fault tolerance, load balancing and security. For example, Web services usually deploy multiple replicas of servers and share the client load among a group of mirrors. In addition, large CDNs tend to replicate objects among multiple servers within the cluster, thereby reducing the miss rate and providing fault tolerance. In drone networks, arbitrary multicast can provide high-quality services in dynamic environments. In the event of network partitions due to high mobility or single point failures, drones can still obtain services within accessible servers. In addition, in some special network applications, a group of nodes with different functions, but a threshold number of nodes can provide the same function. Efficient any-multicast routing is needed to meet these requirements. For example, in a distributed storage system using erasure coding, users can recover the original data from any K blocks among K+P blocks.

[0005] Although unicast and multicast routing in UAV networks have been extensively studied in recent years, these traditional schemes cannot fully support and utilize multiple aggregation points and distributed applications in the network. To address these challenging issues, it is necessary to design an arbitrary multicast routing protocol that can effectively route data from a source to any k destinations. Although some arbitrary multicast routing protocols have been designed in mobile ad hoc networks (MANETs), most of them are extensions of current unicast routing protocols, such as AODV, DSR, and TORA[7]. Compared with vehicular ad hoc networks (VANETs) and mobile sensor networks, UAV networks have some unique characteristics. First, UAV networks often undergo topology changes, which makes it challenging for topology-aware methods to maintain real-time topology information. Second, UAV networks have poor link quality due to link interruptions. Therefore, the protocols designed for traditional MANETs are not applicable to UAV networks.

[0006] This patent proposes an efficient arbitrary multicast routing protocol suitable for UAV networks. Arbitrary multicast is an extension of unicast and multicast, which can support more UAV applications. Inspired by the path planning algorithm, this patent proposes a topology perception strategy based on predicted trajectories. This strategy is simpler and more efficient than traditional detection mechanisms and mobility prediction models.

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[0008] [2] Oubbati OS, Lakas A, Zhou F, et al. A survey on position-based routing protocols for Flying Ad hoc Networks (FANETs) [J]. Vehicular Communications, 2017, 10: 29-56.

[0009] [3]Lakew DS, Sa'ad U, Dao NN, et al.Routing in flying ad hoc networks: A comprehensive survey[J].IEEE Communications Surveys&Tutorials, 2020, 22(2):1071-1120.

[0010] [4]Hussen HR, Choi SC, Park JH, et al.Predictive geographic multicastrouting protocol in flying ad hoc networks[J].International Journal ofDistributed Sensor Networks, 2019, 15(7):1550147719843879.

[0011] [5]Gupta AK, Mandal JK, Bhattacharya I, et al.CTMR-collaborative time-stamp based multicast routing for delay tolerant networks in post disasterscenario[J].Peer-to-Peer Networking and Applications, 2018, 11: 162-180.

[0012] [6]Bai Y, Chen L.Extended multicast optimized link state routing protocol in manets with asymmetric links[C] / / IEEE GLOBECOM 2007-IEEE GlobalTelecommunications Conference.IEEE, 2007: 1312-1317.

[0013] [7] El-Sayed HH, Younes A, Alghamdi F A. Multi-objective multicast DSR algorithm for routing in mobile networks with cost, delay, and hop count[J]. Complexity, 2021, 2021: 1-8. Summary of the invention

[0014] The present invention aims to solve the following technical problems:

[0015] Anycast is an important communication paradigm in UAV networks, where a source node communicates with one potential destination in the anycast region. However, anycast was proposed to efficiently route data from a source node to any k destinations (e.g., storage nodes or base stations). Currently, anycast is still in a relatively early stage and much less work has been done in UAV networks. In this patent, we propose an efficient anycast routing scheme. Our research can well support scenarios of distributed applications and multiple base stations, where this patent outperforms traditional routing schemes in terms of resource utilization, robustness, and efficiency. Our goal is to ensure a high transmission ratio to reduce latency and cost.

[0016] The present invention adopts the following technical solutions to solve the technical problems:

[0017] This invention patent proposes an arbitrary multicast algorithm for UAV networks based on route perception, which includes three steps:

[0018] (1) Modeling of UAV route information. Given any starting time, with the help of known trajectory information, we can calculate the position of each UAV over time. However, in the present invention, we are not concerned with the specific location, but rather with when they meet and leave, i.e., the encounter event. In this case, a new connection may be established when they meet and disappear when they separate. An encounter event can be represented as a tuple. It contains the two UAVs that meet and the time and duration of the encounter between the two UAVs. Specifically, when the distance between the two UAVs is within the transmission radius, they are in an encounter state and can establish a connection to transmit data. When the distance between them exceeds the transmission radius, data cannot be transmitted. With the trajectory information known in advance, the encounter event of any node can be easily calculated. During the routing process, each UAV stores this information in memory.

[0019] (2) Constructing a spatiotemporal topology graph. The routing protocol in the present invention utilizes predetermined drone trajectory information to record when the drone leaves a point and how long it takes to reach the next target. At any starting time, with the help of known trajectory information, we can calculate the position of each drone over time. However, in the present invention, we are not concerned with the specific locations, but rather with when they meet and separate. In this scenario, new connections may be established when they meet and disappear when they separate. In the present invention, we propose and implement a data structure called an encounter record tree, which is a well-designed structure to efficiently store the spatiotemporal characteristics of drone flight trajectories.

[0020] (3) Routing path search. The encounter record tree represents all possible paths from the source node to all possible targets within any multicast group within a specified time range. The goal of any multicast is to send data to any multiple of a specified threshold number of destinations at the lowest transmission cost. Based on the construction of the encounter record tree, the goal is to find the minimum subtree connecting the source node and any threshold number of targets. As mentioned above, the arbitrary multicast problem is a generalization of the Steiner tree problem, which is known to be NP-hard. Specifically, when the network scale is large, the search space will grow exponentially. Therefore, in this patent, we propose an efficient routing search algorithm. The algorithm is based on iterative search of trees with low density, where lower density means a lower average transmission cost to reach the target. Each tree covers only a subset of the targets, and the final solution is obtained by combining them together.

[0021] Compared with the prior art, the present invention adopts the above technical solution and has the following beneficial effects:

[0022] (1) Compared with the traditional UAV network routing protocol, this patent proposes a new routing scenario and an arbitrary multicast algorithm. The arbitrary multicast algorithm can better support distributed applications and multi-base station scenarios, and is superior to traditional routing solutions in terms of resource utilization, robustness and efficiency.

[0023] (2) Traditional routing algorithms mainly rely on a posteriori methods and require real-time collection of network information. However, in dynamic drone networks, these methods consume a lot of resources to maintain topology and find routes. This patent proposes a strategy based on a priori and topology awareness. This strategy is simpler and more efficient than traditional post hoc methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is an example of any-multicast.

[0025] Figure 2 It is a system module diagram.

[0026] Figure 3 It is the encounter record tree construction process.

[0027] Figure 4 It is the path search algorithm process. DETAILED DESCRIPTION

[0028] like Figure 1 As shown, any multicast is different from traditional unicast and multicast routing, and there is no predefined routing target. Implementing any multicast in a highly dynamic UAV network will face many challenges. The present invention is further described in detail below in conjunction with the accompanying drawings, and the symbols involved are referenced in Table 1.

[0029] Table 1 Explanation of symbols

[0030]

[0031] The overall workflow of the present invention is as follows Figure 2 As shown, it includes path planning information collection, construction of encounter record tree to record spatiotemporal topology and path search. Based on the route information of the drone, the present invention patent proposes a data structure called encounter record tree, and its construction process is as follows:

[0032] Assume that the encounter event EC is stored on each node, EC = {ec i To generate the child nodes of node v, v = (n, {ec i}, t, TTL), we must find a candidate set from the set EC. The following is the encounter event ec i =(ux ,u y , t s , t d ), the conditions added to the candidate set: (1) event ec i Related to vn (u x =n or u y =n); (2) Event ec i Satisfy the time overlap principle. The time overlap principle requires that the start time t of the candidate event s One of the following two conditions is met: (a) t s <t, t s +t d >t; (b)t s >t,t s <TTL.

[0033] Condition (1) means that there is a neighboring drone within the transmission radius of drone n. In other words, this neighbor can establish a connection with n, connecting the source to n. Principle (a) in the temporal overlap principle indicates that the start time of the candidate event is earlier than t. However, the end time is later. Principle (b) indicates that the start time of the candidate event is later than t, but earlier than the expiration time of the data packet. For a candidate encounter event ec that satisfies all conditions candi =(n,u y , t s , t d ), the child nodes of node v can be represented as (u y , {ec 1 ,...,ec n ,ec candi}, t s , TTL). Then, the same logic is used to find and create the remaining child nodes until there are no candidate encounter events that meet these conditions. When implementing the algorithm, we can add more information to the tree nodes, depending on the routing constraints. For example, we can estimate its value based on the link quality. Depending on the duration of the encounter event, each node is attached with an event duration. In addition, we can also consider more factors such as energy, capacity, and overhead. Figure 3 As shown in Figure 2, this figure introduces the construction process of the encounter record tree. Given a drone u 0 , root node v 0 Expressed as (u 0 ,{(u 0 ,u 0 , t 0 ,0)},t 0 , TTL). 0 is the source drone, which is at time t 0Generate a message. The message will expire at TTL. There are several candidate encounter events in the encounter event set at the bottom of the legend. Among them, the encounter event ec 1 =(u 0 ,u 1 , t 1 , t 2 ) indicates that at time t 1 ,u 0 and u 1 Met and lasted for 2 ; Encounter event ec 2 =(u 1 ,u 2 , t 3 , t 4 ) indicates that at time t 3 ,u 1 and u 2 Met and lasted for 4 The next step is to select candidate events that meet the above conditions and assign them to the root node v 0 Generates child nodes.

[0034] Consider encounter event ec 1 ,u 1 Meet u 0 , time t 0 <t 1 <TTL meets condition (b). Creates a child node c(v 0 )=(u 1 ,{u 0 ,u 1}, t 1 , TTL), indicating u 1 and u 0 In t 1 Consider the event ec 2 ,u 2 Meet u 1 , time t 3 <t 1 , t 3 +t 4 >t 1 Satisfies rule (a). Creates a child node c(c(v 0 ))=(u 2 ,{u 0 ,u 1 ,u 2}, t 3 , TTL), which means that in u 0 to u 1 After sending the message, u 1 In t 3 Time and u 2A connection has been established. So far, 0 The created message has formed a possible routing path P = u 0 -u 1 =u 2 . Repeat the above operations to create a complete encounter record tree for all leaf nodes in the encounter record tree for the subsequent algorithm to find the best arbitrary multicast path. In order to control the size of the encounter record tree, we must ensure that the tree we build is valid. To avoid building a bad tree, we add some additional constraints during the construction process. A bad tree contains many meaningless and redundant branches. These branches not only increase the cost of building the tree, but also affect the subsequent process of finding multicast paths, increase the computational cost and improve the accuracy of the results.

[0035] Based on the encounter record tree, this invention proposes a path search algorithm. The entire algorithm flow is described as follows:

[0036] First, we will introduce some important concepts. For any node v in the encounter record tree i =(n,p,t,TTL), if p contains u i , then we say that node v i Covered drone u i Here, we will introduce the concept of node groups. Assuming that a communication target is given, the path search algorithm will generate a node group for each target. In addition, if a tree contains any node in a group, then the tree is called a covering tree of the group, denoted by T[g i The goal of the path search algorithm is to find a subtree from T that covers the set {g i}. And, we need the weight of this subtree to be as small as possible.

[0037] It is worth noting that this paper aims to find any k destinations from all potential destinations to achieve arbitrary multicast routing. If the tree covers the set {g i}, then we call it T k [g i ]. Ultimately, the goal of the path search algorithm is to find a tree covering k groups from the encounter record tree, covering exactly k groups, with the smallest possible weight.

[0038] By definition, it can be concluded that the path search algorithm attempts to solve the classic group Steiner tree problem. This is a derivative of the Steiner tree problem and is considered NP-hard.

[0039] As mentioned earlier, any node v i There is a parent node, denoted as p(v i ), and a child node, denoted as c(vi ). i The subtree with root is denoted as T(v i ). In the encounter record tree, an edge can be represented as (p(v), v). The weight of the subtree T(v) is represented as w(T(v)). The cover number of the subtree is represented as n(T(v)). We define a metric called energy density to evaluate the routing path. The energy density of the subtree T(v) can be expressed as:

[0040]

[0041] The smaller the energy density, the more groups it can cover at a lower cost. From a routing perspective, it can complete any multicast task with lower latency. The energy density indicator will be used as a criterion for path search to evaluate the quality of routing.

[0042] like Figure 4 As shown, there is an encounter record tree T = (V, E) and a series of node groups G = {g i}, where g i ∈V. The routing destination of the message can be expressed as Targets = {u 1 ,u 3 ,u 5}. It can be concluded that for the routing destination u 1 , and its corresponding g 1 = {N 1 , N 5}; For routing destination u 3 , and its corresponding g 2 = {N 3 , N 6}; For routing destination u 5 , and its corresponding g 3 = {N 4}. The optimization goal of this algorithm is to find the subtree T with R as the root sub Given a coverage threshold k, 0<k≤3, T sub It needs to satisfy the condition of covering exactly k groups in G and have the minimum weight.

[0043] In order to solve the above NP-hard problem, this invention patent designs an efficient path search algorithm for optimal subtree discovery. The basic implementation of the path search algorithm will be described in detail below. The input of the algorithm includes the encounter record tree T = (V, E), with v 0 is the root node. The node group to be covered and the given coverage threshold k. The algorithm returns a k-covering tree T k [g i ] and its energy density. Next, the basic implementation of the path search algorithm will be introduced.

[0044] In each recursive round of the algorithm, according to the given coverage threshold k need , the function will try to find a node with the current node v i is the subtree of the new root. This subtree can cover k 0 groups, where 1≤k 0 <k need Once all such subtrees are returned, the algorithm selects the one with the lowest energy density.

[0045] The recursive stop condition is, input tree T 0 Contains only one node, namely T(v 0 ) leaf node. At this point, the single-node tree T is returned directly 0 and its energy density (T 0 ). If the current node v i There are child nodes, and the coverage threshold has reached the required threshold k need , then the function will find i is the subtree of the new root. This subtree may cover k 0 groups, where 1≤k 0 ≤k need After returning all subtrees, the subtree with the lowest energy density is selected. The problem domain is then reduced to finding the subtree with the lowest energy density from the remaining nodes, which must cover k res groups, where k res =k need -k 0 . k res Indicates the number of groups that still need to be covered. If a node covers g i But i If the node has not been covered yet, it can be added to the current cover tree, and the cover number increases by 1. The T finally returned res is a tree with the lowest energy density and a cover number equal to the required k. The outer loop indicates that not every search can find a subtree that satisfies k. This is because the search space contains g i The number of itself is less than k, or some smaller cover T res has a lower energy density. Therefore, the operation of searching the subtree must be repeated until T res = 0. Each recursion has three stages: recursion, selection, and update.

[0046] Recursive phase: When the algorithm is in the recursive phase, subtrees are constructed with child nodes as their roots. Traverse all child nodes of node v, and for each child node c, select a subtree from the range [1, k res] to obtain the coverage number k″ and make a recursive call. For each call, the recursive input parameter is (T(v), k″). The calculated subtree is represented by T c，k″ ,.

[0047] Selection phase: When the algorithm is in the selection phase, multiple subtrees T generated in the recursive phase are connected c，k″ , to node v. The new tree rooted at node v is called a "boosted tree". Then, a boosted tree with the lowest energy density is selected.

[0048] Update phase: First, obtain the best boosted tree T from the selection phase aug . Secondly, coverSet(T aug ) Calculate T aug The result is recorded and combined with the current covered set. In subsequent processing, the groups in the covered set should be ignored. Finally, with T aug The relevant nodes have been removed from T res In the subsequent loop processing, the used nodes are inactive. The active nodes still participate in the calculation without considering the weight.

[0049] When the input encounter record tree is large, traversing [1, k res ] range is expensive. Therefore, we refer to the solution in the literature and change the selection range of k in the loop to [a*k res , k res ]. From the performance point of view of the algorithm, this change reduces the search space and reduces the execution time of the algorithm. From the operation results, this change avoids the generation of subtrees with small coverage.

[0050] In order to prevent the algorithm from generating a large-scale cover tree on a subtree, it is necessary to encourage the algorithm to try multiple subtree branches in each recursive exploration. When the cover number reaches the h threshold for the first time, the function returns immediately. This temporary result will be recorded. When the recursive termination condition is triggered, the result is compared with the temporary result, and the one with lower energy density is returned.

Claims

1. An arbitrary multicast algorithm for UAV networks based on route perception, characterized by The following steps: (1) Formalization process: Formalization of arbitrary multicast problem in UAV networks. (2) UAV route modeling: UAV route modeling and construction of space-time topology map. (3) Spatiotemporal data structure: A data structure of an encounter record tree is proposed to store spatiotemporal topological graphs. (4) Path search algorithm: An arbitrary multicast path search algorithm for UAV networks based on the encounter record tree.

2. The formalization process as claimed in claim 1, comprising the following: The UAV network can be defined as a weighted directed graph G = (V, E), where V = {u1, u2, ..., u i } is a set of nodes, each node represents a drone, E = {e1, e2, ..., e i } is a set of linked nodes. Edge e=(u i ,u j , t s , t d ) indicates drone u i At time t s With drone u j Meet, t d represents the link lifetime caused by topology changes. The transmission rate is represented by r (bytes per second) and the message size is represented by b (bytes). In addition, a cost function C is defined on E so that each edge e of E i There is an associated transmission cost C(e i ). An arbitrary multicast problem can be defined as: k any =[s→(D,k)] Where s is the source node of any multicast. It represents the set of all destination drones in any multicast group. k represents the number of drones to which the message needs to be delivered, i.e., the threshold of any multicast.

3. The UAV route modeling as claimed in claim 1, comprising the following contents: As mentioned in the abstract, the routing algorithm in this paper relies on the UAV trajectory information generated by the path planning algorithm, recording when the UAV leaves a point and how long it takes to reach the next target. Given any starting time, with the known trajectory information, we can calculate the position of each UAV over time. However, in this invention, we are not concerned with the specific positions, but rather when they meet and leave, i.e., the encounter event. In this case, new connections may be established when they meet, and disappear when they separate. An encounter event can be represented as a tuple ec = (u x ,u y , t s , t d ). Among them, u x and u y Represents two drones that have met each other. x and u y is in order, y is called the visitor UAV. In this invention, we briefly describe it as ec and u x or y Related. Variable t s represents the start time t of the encounter between the two drones d , represents the duration of the encounter. Specifically, when the distance between two drones is within the transmission radius, they are in an encounter state and can establish a connection to transmit data. When the distance between them exceeds the transmission radius, data cannot be transmitted. Given two drones u1 and u2, an encounter event ec can be defined as (u1, u2, t1, t2), where t1 represents the time point when they enter the communication range of each other. Finally, the variable t2 represents the duration for which they remain connected. With the trajectory information known in advance, the encounter event of any node can be easily calculated. During the routing process, each drone stores this information in memory.

4. The spatiotemporal data structure according to claim 1, comprising the following contents: Each encounter record tree is spatiotemporally coupled. The tree created at a node at time t includes all encounter events after it. Therefore, the encounter record tree is rooted and can be defined as T = (V, E). Each node v in T represents an encounter event and can be defined as a four-dimensional vector (n, p, t, TTL). In the above four-tuple, n is a node that directly or indirectly encounters the source. p is the path that records all encounter events between the source and n, which can be represented as an ordered set ec of size N i For better understanding, p can also be expressed as {u i }, which is the path composed of drones. The variable t represents the timestamp when n meets the source. To prevent the tree from growing infinitely, TTL limits the upper limit of t. In this invention, we set the value of TTL to the expiration time of the data packet, because once the message is invalid, the encounter event becomes meaningless. In the encounter record tree, node v i The parent node is represented as p(v i ), v i The child nodes are represented as c(v i ). The expression w(e i ) represents p(v i ) and v i The edge weights between them. For p = {ec i }, where ec0 is the head of p, ec n is the tail of p. Given an encounter record tree, generate a subtree T with any node as the root node sub , the subtree is generated from T. If T sub The leaf nodes of are also the leaf nodes of T, then T sub is called closed. A closed subtree of T can be represented as T closed-sub .

5. The path search algorithm as claimed in claim 1, comprising the following contents: For any node v in the encounter record tree i =(n,p,t,TTL), if p contains u i , we call node v i Covered drone u i Here, we introduce the node group g i Given T = (V, E), if v x Covered by v y , it will be added to g y , where v x ∈V. Assume that all communication destinations are {u1, ..., u n }, then the set g i The size of is n. In addition, if T contains g i For any node in T, we say that T covers the group g. i , that is, T is g i The cover tree is represented by T[g i ]. The purpose of the path search algorithm in the present invention is to find a subtree of T, which must cover {g i }, and the weight of the subtree should be as small as possible. According to the definition, it can be concluded that this path search algorithm attempts to solve a classic group Steiner tree problem. This is a derivative problem of the Steiner tree problem and is NP-hard. It is worth noting that this paper aims to find any k destinations from all candidate destinations to achieve any k multicast routing. Therefore, if the tree covers {g i }, it is called a k-covering tree and is defined as T k [{g i }]. At this point, the goal of the path search algorithm is to find a subtree of the encounter record tree that covers {g i }, with the exact k groups in the set, and the weights are as small as possible. As mentioned above, for any node v, its parent node is represented as p(v), and one of its child nodes is represented as c(v). The subtree with node v as the root node is represented as T(v). In the encounter record tree, the edge e can be represented as (p(v), v). Suppose there is an encounter record tree T, T(v) is a subtree of T, and the weight of T(v) is represented as w(T(v)). n(T(v)) represents the number of covers of this subtree. We define the energy density of this subtree T(v) as: The lower the energy density of the tree, the more groups it can cover at a lower cost. From a routing perspective, it can complete any k multicast task with lower latency. The energy density measure will be used as a criterion for evaluating paths by the path search algorithm. Specifically, the routing target of the message is {u1, ..., u n }, with the group {g1, ..., g n In the encounter record tree that has been constructed, we need to find the best subtree starting from the root. This subtree must satisfy that any k nodes in different groups can be reached through the path on this subtree, where k≤n.

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