Distributed wireless sensor network key node identification method and device and medium

Abstract

The invention discloses a distributed wireless sensor network key node identification method and device and a medium. The method comprises the following steps: modeling a distributed wireless sensor network topology into an undirected graph G; a maximum independent set MIS is obtained on the basis of a Reduction-Peeling framework in combination with a constraint rule; obtaining a K-order adjacent matrix of the graph G according to the topological structure; for all nodes in the maximum independent set, if a common adjacent node c exists between every two nodes, c is a key node influencing the connectivity of the distributed wireless sensor network; if the common adjacent nodes do not exist among the nodes in the maximum independent set, expanding to a higher-order adjacent matrix for re-judgment until the adjacent nodes exist; and if the adjacent nodes are unique, taking the nodes as key nodes of the distributed wireless sensor network. The distributed wireless sensor network key node identification method solves the problems that an existing key node identification method is not suitable for a distributed wireless sensor network and the calculation complexity is too high, and accurate and efficient distributed wireless sensor network key node identification is achieved.

Description

Technical Field

[0001] The present invention relates to the field of distributed wireless sensor network situation awareness, and particularly to a method, device and medium for identifying key nodes in a distributed wireless sensor network. Background Art

[0002] Distributed wireless sensor networks have the characteristics of being distributed and self-organizing, large scale and high density, dynamic topology, resource constraints, data-centric, high redundancy and fault tolerance, and multi-hop communication. These characteristics make it have broad application prospects in the fields of military, environmental monitoring, medical care, and industrial and commercial industries. With the development of wireless communication technology, the application scale of distributed wireless sensor networks (WSNs) is increasing day by day. At the same time, the nodes in the network need to undertake more onerous data exchange tasks. Once a certain node fails, it may cause more serious losses to the entire network. Therefore, there is an urgent need for an accurate and efficient key node identification method to identify as many nodes as possible in the network whose failures will cause serious losses, so as to facilitate the subsequent maintenance of network stability.

[0003] Key nodes usually refer to the core components in the network, which have an important impact on aspects such as network connectivity, data transmission, and information processing. By identifying these nodes, the overall structure and operation rules of the network can be better grasped, providing strong support for network optimization and upgrade. Therefore, key node identification technology plays a crucial role in enhancing network stability, data transmission efficiency, resource allocation rationality, maintaining the overall performance of the network, and extending network life. However, the current key node identification methods for distributed wireless sensor networks have defects such as high computational complexity, high energy consumption, and insufficient adaptability in different network topologies and dynamic environments. Therefore, there is an urgent need for an accurate and efficient key node identification method to address the challenges in distributed wireless sensor networks. This method should be able to accurately locate the key nodes in the network while ensuring the efficiency and feasibility of operations, thus providing a solid foundation for network optimization, management, and security protection.

[0004] In the prior art, there are methods to construct a comprehensive node importance evaluation index through information such as the number of nodes, node degree values, and paths; after evaluating the importance of each node and sorting, the key nodes are obtained. There are also methods to obtain node information including quantity, location, survival status, protection cost, and connection relationship, and based on this, construct a network protection objective function set and perform multi-objective optimization to solve for the node importance ranking. There are also methods to allocate initial votes to each node according to the shortest cycle paths formed between nodes, and the nodes on the cycle paths will selectively vote according to the voting ratio between them and adjacent nodes to obtain the key nodes. However, the above methods face some challenges in practical applications, especially in the distributed wireless sensor network environment. Due to the characteristics of self-organization and dynamic changes of wireless sensor networks, the above key node identification methods have certain limitations. In addition, considering the limited energy consumption and limited resources of nodes in wireless sensor networks, the above methods may be difficult to implement due to high computational complexity. In actual deployment, high computational requirements may lead to a rapid increase in node energy consumption, thereby affecting the continuous operation and overall performance of the network. Summary of the Invention

[0005] Object of the Invention: Aiming at the deficiencies in the prior art, the present invention aims to provide a method, device, and medium for identifying key nodes in a distributed wireless sensor network to solve the problems that the existing key node identification methods are not applicable to distributed wireless sensor networks and have too high computational complexity, and to achieve accurate and efficient identification of key nodes in a distributed wireless sensor network.

[0006] Technical Solution: A method for identifying key nodes in a distributed wireless sensor network according to the present invention specifically includes the following steps:

[0007] S1, model the topology of the distributed wireless sensor network as an undirected graph G;

[0008] S2, obtain the maximum independent set MIS based on the Reduction-Peeling framework combined with constraint rules;

[0009] S3, obtain the K-order adjacency matrix of the graph G according to the topological structure;

[0010] S4, for all nodes in the maximum independent set, if there is a common adjacent node c between any two of them, then c is the key node affecting the connectivity of the distributed wireless sensor network; if there is no common adjacent node between the nodes in the maximum independent set, then expand to a higher-order adjacency matrix to re-judge until there is an adjacent node; if the adjacent node is unique, it is used as the key node of the distributed wireless sensor network.

[0011] Further, the undirected graph G in step S1 is a set composed of pairwise non-adjacent vertices, that is, an independent set.

[0012] Furthermore, the maximum independent set described in step S2 is the independent set with the largest size, that is, the independent set containing the largest number of vertices.

[0013] Furthermore, the implementation process of step S2 is as follows:

[0014] S21: Initialization and preprocessing: Initialize an empty MIS set Record all the vertex contraction operations that need to be restored in the graph;

[0015] S22: Degree-1 reduction: Find the unique neighbor v of the node u with degree 1; Delete node v and all its incident edges, exclude v from the candidate MIS; Add u to I, and update the graph G = G\{v};

[0016] S23: Degree-2 reduction: There exists a node u with degree 2, whose neighbors are v and w; If v and w are connected, that is, the edge (v, w) ∈ E: Delete v and w and all their incident edges, and update the graph G = G\{v, w}; If v and w are not connected, that is, the edge (v, w) ∈ / E, contract u, v, and w into a new node c, denoted as G′ = G / {u, v, w}; Recursively solve the MIS I′ of G′, if c ∈ I′, then restore at least one of v or w and add it to the MIS, and at the same time u is not selectable; Update the graph G = G′;

[0017] S24: Extended reduction rules: Introduce degree-2 path reduction, if there exists a path composed of degree-2 nodes Contract it into a single node and restore it after simplification; Introduce domination reduction, if the neighbor set of node u is a subset of the neighbor set of node v, then delete u;

[0018] S25: Main loop of the Reduction-Peeling framework, loop and execute the following operations:

[0019] Give priority to applying degree-1 reduction; If there are no degree-1 nodes, apply degree-2 reduction; If still unable to reduce, apply the extended reduction rules; If all reduction rules are not applicable, perform peeling; Delete the node v with the largest degree and its edges in the current graph; Update the graph G = G\{v}; Terminate when the graph G only has isolated points left;

[0020] S26: Restore vertex contraction and construct the final MIS: Process all vertex contraction operations in reverse. If the contracted node c is added to the MIS, restore it to one of v or w in the original graph; If the contracted node is not added to the MIS, restore it to u or other unselected nodes in the original graph; Add the isolated points directly to the MIS set I.

[0021] Furthermore, the implementation process of step S3 is as follows:

[0022] S31: Determine the graph type, the number of nodes, and the edge information;

[0023] S32: Initialize the adjacency matrix: Create an n×n zero matrix with all elements initialized to 0. For a graph with n nodes, its adjacency matrix is an n×n square matrix, denoted as A. In a directed graph, if there is an edge from node i to node j, then Aij = 1, otherwise it is 0. Define using boolean operations. By taking the boolean power of the adjacency matrix, that is, taking the non-zero elements of Ak as 1 to obtain a binary matrix. The boolean high-order matrix is used to determine whether nodes are reachable within k steps.

[0024] S33: Fill the matrix elements: For each edge (u, v) in an undirected graph, set Auv = 1 and Avu = 1. For each edge u→v in a directed graph, only set Auv = 1. If self-loops are allowed, set Auu = 1, otherwise keep the diagonal as 0.

[0025] Furthermore, the implementation process of step S4 is as follows:

[0026] S41: Determine the target node pair: Select any two non-adjacent nodes s and t from the maximum independent set MIS. Calculate their first-order neighborhood sets Us and Ut respectively.

[0027] S42: Analyze the intersection situation of neighborhoods: Judge the intersection type of Us and Ut. When Us∩Ut = {c}, consider the unique intersection point c as the cut vertex, that is, the key point. When Us∩Ut = {c1, c2, …, ck}, k≥2, determine that there is no cut vertex between s and t. When Proceed to step S43 and extend the neighborhood to a higher order.

[0028] S43: When there is no intersection in the first-order neighborhood, gradually expand the neighborhood range: Define the k-order neighborhood Uv(k) of node v, which contains all nodes reachable in k steps. Expand the neighborhoods of s and t and calculate the second-order neighborhoods Us(2) and Ut(2). If the intersection is still empty, continue to expand to the third-order neighborhoods Us(3) and Ut(3), and so on. Until after a certain order of expansion, Us(k)∩Ut(k) = {c}, then mark c as the cut vertex. If there is still no unique intersection after expanding to the maximum order, determine that there is no cut vertex between s and t.

[0029] S44: Comprehensive verification and result output: Repeat steps S41~S43 for all node pairs in the MIS to generate a set of candidate key nodes. Remove the candidate node c and check whether the connectivity of graph G is destroyed. If the graph becomes disconnected after removing c, then confirm c as the cut vertex. Output the final list of key nodes and the node pairs they affect.

[0030] An apparatus and device according to the present invention includes a memory and a processor, wherein:

[0031] A memory for storing a computer program that can run on a processor;

[0032] A processor for, when running the computer program, executing the steps of a method for identifying key nodes in a distributed wireless sensor network as described above.

[0033] A storage medium according to the present invention, on which a computer program is stored, and when the computer program is executed by at least one processor, the steps of a method for identifying key nodes in a distributed wireless sensor network as described above are implemented.

[0034] Advantageous effects: Compared with the prior art, the advantageous effects of the present invention are as follows: Traditional methods evaluate the importance of nodes according to centrality metrics, but they cannot accurately represent whether the network will become disconnected directly after a node fails. The present invention can accurately and efficiently identify the key nodes in a distributed wireless sensor network that will cause the entire network to lose connectivity once they fail, which is of crucial significance for ensuring the stable operation of the network and improving the overall performance. Description of the Drawings

[0035] Figure 1 is a flowchart of a method for identifying key nodes in a distributed wireless sensor network;

[0036] Figure 2 is a schematic diagram of the topology of a small-scale distributed wireless sensor network;

[0037] Figure 3 is a schematic diagram of the topology of a BA scale-free network with 100 nodes;

[0038] Figure 4 is a schematic diagram for validating the effectiveness of a method for identifying key nodes based on the maximum independent set in terms of algebraic connectivity;

[0039] Figure 5 is a schematic diagram for validating the effectiveness of a method for identifying key nodes based on the maximum independent set in terms of the number of the largest connected components in the network; where (a) is the number of the largest connected components in a small-scale distributed wireless sensor network after deleting key nodes proportionally; (b) is the number of the largest connected components in a BA scale-free network with 100 nodes after deleting key nodes proportionally. Detailed Embodiments

[0040] The present invention will be further described in detail below with reference to the drawings.

[0041] As Figure 1 shown, the present invention proposes a method for identifying key nodes in a distributed wireless sensor network, including the following steps:

[0042] S1, modeling the topology of the distributed wireless sensor network as an undirected graph.

[0043] In an undirected graph G, a set of vertices that are pairwise non-adjacent is called an independent set. That is, for any two vertices u and v in the independent set, the edge (u, v) is not an edge of graph G. And an independent set with the largest size (i.e., containing the largest number of vertices) is called a maximum independent set. In an undirected connected graph, if removing a certain vertex makes the graph no longer connected (i.e., any two points cannot reach each other), then that vertex is called a cut vertex. In other words, a cut vertex is a vertex whose incident edges are bridges connecting different parts of the graph. Once this vertex is removed, the graph will be split into multiple unconnected parts. Therefore, cut vertices are nodes that affect network connectivity. From the perspective of maintaining network functions, identifying the key nodes in the network is to identify cut vertices. The Reduction-Peeling framework is a technique for solving graph theory problems, especially when finding the maximum independent set. The maximum independent set refers to a set of vertices in a graph where any two vertices in the selected vertex set are non-adjacent (i.e., there is no direct edge connecting them). The Reduction-Peeling framework can assist in finding such an independent set by coloring the vertices of the graph with different colors.

[0044] S2. Obtain the maximum independent set based on the Reduction-Peeling framework combined with constraint rules.

[0045] S21: Initialization and preprocessing: Input the undirected graph G(V, E), and initialize an empty MIS set Record all the reduction operations of vertices that need to be restored in the graph (for subsequent restoration).

[0046] S22: Degree-One Reduction:

[0047] When there exists a node u with degree 1. Find the only neighbor v of u; delete node v and all its incident edges, and exclude v from the candidate MIS (because retaining v will prevent u from being added to the MIS); add u to I (because u is the only optional node to maximize the independent set); update the graph G = G\{v}. This operation does not change the size of the original graph's MIS.

[0048] S23: Degree-Two Reduction:

[0049] When there is a node u with degree 2, whose neighbors are v and w. If v and w are connected (i.e., the edge (v, w) ∈ E), delete v and w and all their connected edges (because retaining one of them will prevent the other from being added to the MIS); update the graph G = G\{v, w}. If v and w are not connected (i.e., the edge (v, w) ∉ E), contract u, v, and w into a new node c, denoted as G′ = G / {u, v, w}. Recursively solve the MIS I′ of G′. If c ∈ I′, then restore at least one of v or w to be added to the MIS, and at the same time u is not selectable (the size of the independent set increases by 1). Update the graph G = G′.

[0050] S24: Extended Reduction Rules (Optional Optimization):

[0051] To improve efficiency, the following additional reduction rules can be introduced: ① Degree-Two Path Reduction: If there is a path consisting of nodes with degree 2 Contract it into a single node and restore it after simplification. ② Dominance Reduction: If the neighbor set of node u is a subset of the neighbor set of node v, then delete u (because choosing v is better than u).

[0052] S25: Main loop of the Reduction-Peeling framework, perform the following operations in a loop:

[0053] Give priority to applying degree-one reduction; if there are no degree-one nodes, apply degree-two reduction; if still unable to reduce, apply the extended reduction rules; if all reduction rules are not applicable, perform Peeling, delete the node v with the highest degree and its edges in the current graph; update the graph G = G\{v}. Terminate when the graph G only has isolated points (nodes without edge connections).

[0054] S26: Restore the contracted nodes and construct the final MIS:

[0055] Process all contracted nodes in reverse; if the contracted node c is added to the MIS, restore it to one of v or w in the original graph (select the optimal solution according to the contraction rule); if the contracted node is not added to the MIS, restore it to u or other unselected nodes in the original graph. Add the isolated points directly to the MIS set I.

[0056] S3. Obtain the K-order adjacency matrix of graph G according to the topological structure.

[0057] S31: Determine the basic properties of the graph: Type: undirected graph or directed graph. Number of nodes: denoted as n. Edge information: given in the form of an edge list (such as E = {(u, v)}) or an adjacency list (such as 1: [2, 3]).

[0058] S32: Initialize the adjacency matrix: Create an n×n zero matrix and initialize all elements to 0. The first-order adjacency matrix is the most basic matrix representation in graph theory, used to describe the direct connection relationships between nodes in a graph. For a graph with n nodes, its adjacency matrix is an n×n square matrix, denoted as A. In a directed graph, if there is an edge from node i to node j, then Aij = 1; otherwise, it is 0. Higher-order adjacency matrices are used to describe the indirect relationships between nodes through multi-step paths (non-direct connections). In this method, it is defined using boolean operations, and a binary matrix is obtained through the boolean power of the adjacency matrix (i.e., taking non-zero elements of Ak as 1). The boolean-type higher-order matrix can be used to determine whether nodes are reachable within k steps.

[0059] S33: Fill the matrix elements. Undirected graph: For each edge (u, v), set Auv = 1 and Avu = 1. Directed graph: For each edge u→v, only set Auv = 1. Self-loop handling: If self-loops are allowed (such as the edge (u, u)), then set Auu = 1; otherwise, keep the diagonal as 0.

[0060] S4. For all nodes in the maximum independent set, if there is a unique common neighbor node c between any two of them, then c is the key node affecting network connectivity; if there are no common adjacent nodes between the nodes in the maximum independent set, then extend to a higher-order adjacency matrix and re-judge until there are adjacent nodes; if the adjacent node is unique, then it is the key node of the distributed wireless sensor network.

[0061] S41: Determine the target node pairs:

[0062] Select any two non-adjacent nodes s and t from the MIS (since nodes in the MIS are not connected to each other). Calculate their first-order neighborhood sets Us (nodes directly connected to s) and Ut (nodes directly connected to t) respectively. If MIS = {s, t, u}, then it is necessary to traverse all node pairs (s, t), (s, u), (t, u) and calculate the neighborhood intersection of each pair of nodes.

[0063] S42: Analyze the neighborhood intersection situation:

[0064] Judge the intersection type of Us and Ut: ① Unique intersection (Us ∩ Ut = {c}): Directly mark c as the cut vertex (key node); ② Multiple intersections (Us ∩ Ut = {c1, c2,..., ck}, k≥2): Determine that there is no cut vertex between s and t (because there are redundant paths); ③ No intersection Proceed to step S43 and extend the neighborhood to a higher order.

[0065] For example, if the neighbors of s are {a, b} and the neighbors of t are {b, c}, then the intersection is {b}, and mark b as the key node. If the neighbors of s are {a, b} and the neighbors of t are {c, d}, then the intersection is empty, and the neighborhood needs to be extended.

[0066] S43: Expand the neighborhood to a higher-order path:

[0067] When the first-order neighborhoods have no intersection, gradually expand the neighborhood range: ① Define the k-order neighborhood Uv(k) of node v: It contains all nodes reachable in k steps (excluding v itself and nodes on shorter paths). ② Expand the neighborhoods of s and t and calculate: the second-order neighborhoods Us(2) (neighbors of neighbors) and Ut(2). If the intersection is still empty, continue to expand to the third-order neighborhoods Us(3) and Ut(3), and so on.

[0068] Termination conditions: ① After a certain order of expansion, if Us(k) ∩ Ut(k) = {c}, then mark c as a cut vertex. ② If there is still no unique intersection after expanding to the maximum order, it is determined that there is no cut vertex between s and t.

[0069] For example, if the second-order neighborhood of s is {c, d} and the second-order neighborhood of t is {c, e}, then the intersection is {c}, and mark c as a key node.

[0070] S44: Comprehensive verification and result output:

[0071] Repeat steps S41 - S43 for all node pairs in all MISs to generate a set of candidate key nodes. Remove candidate node c and check whether the connectivity of graph G is destroyed (such as using DFS / BFS). If the graph becomes disconnected after removing c, then confirm that c is a cut vertex; the final list of key nodes and the node pairs they affect. Take the identified cut vertices as the key nodes affecting network connectivity.

[0072] For example, if node c is marked by the algorithm and the graph splits into two subgraphs after removing c, then confirm that c is a key node.

[0073] The present invention also provides a device, including a memory and a processor, wherein: the memory is used to store a computer program that can run on the processor; the processor is used to execute the steps of a method for identifying key nodes in a distributed wireless sensor network as described above when running the computer program.

[0074] The present invention also provides a storage medium, on which a computer program is stored, and the computer program, when executed by at least one processor, implements the steps of a method for identifying key nodes in a distributed wireless sensor network as described above.

[0075] In such as Figure 2In the small-scale distributed wireless sensor network shown, the node numbers of the maximum independent set obtained through the Reduction-Peeling framework are: [1, 3, 5, 7, 10, 11, 14, 17, 20]. And there is a unique common adjacent node 6 between node 5 and node 7. Therefore, node 6 serves as a cut vertex, and when it fails, the network will be divided into two unconnected parts. Thus, node 6 can be identified as a critical node. There are common adjacent nodes 2 and 4 between node 3 and node 5. Therefore, when one of the nodes 2 and 4 fails, it will not affect the connectivity of the network. Among the independent set nodes 9 and 14, although there are no direct common neighbor nodes, when extended to the second-order neighborhood, there is a common neighbor node 12. Therefore, node 12 is also a critical node. Among them, if the first-order neighborhood refers to the points or sets directly adjacent to a certain point, then the second-order neighborhood can be understood as the points or sets adjacent to these directly adjacent points again.

[0076] The BA scale-free network is a complex network model with growth and preferential attachment characteristics, which can well describe and simulate the network structures of many complex systems in the real world. Therefore, take the BA scale-free network in Figure 3 as an example for further verification.

[0077] Compared with the traditional method, the critical node identification method based on the maximum independent set can additionally identify nodes [12, 25, 46, 59, 87]. To further verify the effectiveness of the method, it is necessary to measure the impact on the network connectivity when these additionally identified nodes fail. Therefore, the concept of algebraic connectivity is introduced, as Figure 4 shown. Algebraic connectivity is usually closely related to the eigenvalues of the Laplacian Matrix of a network or graph. For a given graph G, its algebraic connectivity can be measured by the second smallest eigenvalue of its Laplacian Matrix (usually called λ2 or algebraic connectivity degree). This eigenvalue reflects the degree of the graph from "separated" to "connected". As can be seen from Figure 4 , when the critical nodes identified by the algorithm fail, the algebraic connectivity of the network drops sharply, proving the effectiveness of the critical node identification method based on the maximum independent set.

[0078] In addition, the Giant Connected Component (GCC) is a core concept in graph theory and complex network analysis, used to describe the most important connected structure in a network. Its definition is as follows: in an undirected graph, if there exists a subgraph where any two nodes are connected by a path, and the node scale of this subgraph is much larger than that of other connected components, then this subgraph is called the giant connected component of the network. The existence and scale change of the giant connected component not only reflect the internal topological characteristics of the network but also provide a theoretical basis for optimization design (such as enhancing robustness) or intervention strategies (such as precisely targeting key nodes). Therefore, further verify the effectiveness of the key nodes identified by the algorithm through the change in the number of the network's largest connected components. As Figure 5 shown, where Figure 5 (a) in [figure] shows the number of the largest connected components of a small-scale distributed wireless sensor network after proportionally deleting key nodes; Figure 5 (b) in [figure] shows the number of the largest connected components of a BA scale-free network with 100 nodes after proportionally deleting key nodes. Whether in a small-scale distributed wireless sensor network or a BA scale-free network with 100 nodes, the failure of the key nodes identified by this algorithm will lead to a decrease in the number of the largest connected components of the network. Therefore, it is considered that the key nodes identified by this algorithm are effective.

[0079] The above embodiments are only used to illustrate the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the present invention.

Claims

1. A method for identifying key nodes in a distributed wireless sensor network, characterized in that, It includes the following steps: S1. Model the topology of the distributed wireless sensor network as an undirected graph G; S2. Obtain the maximum independent set MIS based on the Reduction-Peeling framework combined with constraint rules; S3. Obtain the K-order adjacency matrix of graph G according to the topological structure; S4. For all the nodes in the maximum independent set, if there is a common adjacent node c between any two of them, then c is the key node affecting the connectivity of the distributed wireless sensor network; If there is no common adjacent node between the nodes in the maximum independent set, then extend to a higher-order adjacency matrix for re-judgment until there is an adjacent node; If the adjacent node is unique, it is used as the key node of the distributed wireless sensor network.

2. The key node identification method for a distributed wireless sensor network according to claim 1, wherein The undirected graph G described in step S1 is a set composed of pairwise non-adjacent vertices, that is, an independent set.

3. A method for identifying key nodes in a distributed wireless sensor network according to claim 1, characterized in that, The maximum independent set described in step S2 is an independent set with the largest size, that is, the independent set containing the most vertices.

4. A method for identifying key nodes in a distributed wireless sensor network according to claim 1, characterized in that The implementation process of step S2 is as follows: S21: Initialization and preprocessing: Initialize an empty MIS set Record all the contracted node operations that need to be restored in the graph; S22: Degree-one reduction: Find the unique neighbor v of the node u with degree 1; Delete node v and all its connected edges, exclude v from the candidate MIS; Add u to I, and update graph G = G\{v}; S23: Degree-two reduction: There exists a node u with degree 2, and its neighbors are v and w; If v and w are connected, that is, edge (v, w) ∈ E: Delete v and w and all their connected edges, and update graph G = G\{v, w}; If v and w are not connected, that is, edge (v, w) ∉ E, contract u, v, and w into a new node c, denoted as G′ = G / {u, v, w}; Recursively solve the MIS I′ of G′, if c ∈ I′, then restore at least one of v or w to be added to MIS, and at the same time u is not selectable; Update graph G = G′; S24: Extended reduction rules: Introduce degree-two path reduction. If there is a path consisting of degree-2 nodes, contract it into a single node and restore after simplification; Introduce dominance reduction. If the neighbor set of node u is a subset of the neighbor set of node v, then delete u; S25: The main loop of the Reduction-Peeling framework, perform the following operations in a loop: Give priority to applying degree-one reduction; If there is no degree-one node, apply degree-two reduction; If still unable to reduce, apply the extension reduction rule; If all reduction rules are not applicable, perform peeling; Delete the node v with the largest degree and its edges in the current graph; Update graph G = G\{v}; Terminate when graph G only has isolated points left; S26: Restore the contracted points and construct the final MIS: Process all the contraction operations in reverse. If the contracted node c is added to MIS, restore it to one of v or w in the original graph; If the contracted node is not added to MIS, restore it to u or other unselected nodes in the original graph; Add the isolated points directly to the MIS set I.

5. A method for identifying key nodes in a distributed wireless sensor network according to claim 1, characterized in that, The implementation process of step S3 is as follows: S31: Determine the graph type, the number of nodes, and edge information; S32: Initialize the adjacency matrix: Create an n×n zero matrix, and initialize all elements to 0; For a graph containing n nodes, its adjacency matrix is an n×n square matrix, denoted as A; In a directed graph, if there is an edge from node i to node j, then Aij = 1, otherwise it is 0; Define using boolean operations, and obtain the binary matrix by taking the non-zero elements of Ak as 1 through the boolean power of the adjacency matrix; The boolean high-order matrix is used to judge whether nodes are reachable within k steps; S33: Fill matrix elements: For each edge (u, v) in the undirected graph, set Auv = 1 and Avu = 1; for each edge u → v in the directed graph, only set Auv = 1; if self-loops are allowed, set Auu = 1, otherwise keep the diagonal as 0.

6. A method for identifying key nodes in a distributed wireless sensor network according to claim 1, characterized in that, The implementation process of the step S4 is as follows: S41: Determine the target node pair: Select any two non-adjacent nodes s and t from the maximum independent set MIS; calculate their first-order neighborhood sets Us and Ut respectively; S42: Analyze the intersection of neighborhoods: Determine the intersection type of Us and Ut; when Us ∩ Ut = {c}, consider the unique intersection point c as the cutting vertex, that is, the key point; when Us ∩ Ut = {c1, c2, …, ck}, k ≥ 2, determine that there is no cutting vertex between s and t; when Proceed to step S43 to expand the neighborhood to a higher order; S43: When the first-order neighborhoods have no intersection, gradually expand the neighborhood range: Define the k-order neighborhood Uv(k) of node v, which includes all nodes reachable in k steps; expand the neighborhoods of s and t, and calculate the second-order neighborhoods Us(2), Ut(2); if the intersection is still empty, continue to expand to the third-order neighborhoods Us(3), Ut(3), and so on; until after a certain order of expansion, Us(k) ∩ Ut(k) = {c}, then mark c as the cut vertex; If there is still no unique intersection after expanding to the maximum order, it is determined that there is no cut vertex between s and t; S44: Comprehensive verification and result output Repeat steps S41 - S43 for all node pairs in the MIS to generate a candidate set of key nodes; Remove the candidate node c, check whether the connectivity of the graph G is destroyed. If the graph becomes disconnected after removing c, then confirm that c is the cut vertex; output the final list of key nodes and the node pairs they affect.

7. A device, characterized in that, Comprising a memory and a processor, where: The memory is used to store a computer program that can run on the processor; The processor is used to execute the steps of a method for identifying key nodes in a distributed wireless sensor network as described in any one of claims 1 to 6 when running the computer program.

8. A storage medium, characterized in that, A computer program is stored on the storage medium, and when the computer program is executed by at least one processor, it implements the steps of a method for identifying key nodes in a distributed wireless sensor network as described in any one of claims 1 to 6.

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