CN114679728A - Network bug fixing method, device and storage medium - Google Patents
Network bug fixing method, device and storage medium Download PDFInfo
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Abstract
The invention provides a method, a device and a storage medium for repairing a network bug, which are used for calculating the minimum moving distance required by a neighbor node for repairing the bug; calculating the redundancy of the node based on the common overlapping area of the node and the neighbor of the node; selecting a node with the maximum residual energy as an optimal coverage vulnerability repair node; calculating the bug fixing coverage rate of the fixing position based on a fixing algorithm; and calculating the global optimal value of the target function of the vulnerability repair coverage rate by adopting a coverage enhancement algorithm, so that the coverage effect is optimal, and the network performance is optimal.
Description
Technical Field
The invention relates to the technical field of network bug fixing, in particular to a network bug fixing method, a network bug fixing device and a storage medium.
Background
The wireless sensor network is a distributed sensor network, and the tail end of the wireless sensor network is provided with a plurality of miniature sensors which can monitor and sense the external environment. The nodes in the wireless sensor network communicate in a wireless mode, so that the network deployment is more flexible, and the nodes can also be set to have mobility and are connected with the Internet.
The system of the wireless Sensor network generally comprises a Sensor node (Sensor node), a Sink node (Sink node) and a management node, wherein the Sensor node is a basic function unit in the wireless Sensor network and is a micro embedded device, the Sensor mainly comprises a processor unit, a data processing unit, a communication transmission unit and an energy management unit, is a collection and conversion device with the characteristic of monitoring data, and has the functions of data management, processing, transmission, node control and the like. The sink node is equivalent to a bridge which is connected with an external network in the sensor network, can receive a task request from the external network, and can also transmit information obtained by monitoring in the wireless sensor network to the Internet. The network management node has the function of managing the whole network system in real time, and the terminal acquires all data in the monitored area through the management node.
The communication quality and integrity of data in the wireless sensor network are closely related to the coverage rate of the sensor nodes, and the coverage refers to that the nodes distributed in the network sense the external environment and detect the target through certain configuration in a target area, so that the wireless sensor network is a sensing and monitoring capability to the external world and is also a problem to be considered when the wireless sensor network is designed and deployed and planned. Because most of the energy of the sensor comes from a limited battery supply, the sensor is weak in the aspects of processing, long-term storage and communication of a large amount of concurrent data, and meanwhile, each sensor node in the network needs to collect and process local data and information and also needs to forward information resources obtained from other nodes in order to meet the requirement of a distributed network, the capacity of a single sensor node in the sensor network is limited by factors such as the cost and the structure of the sensor node, so that the reasonable optimization of the deployment and the distribution structure of the nodes in the network plays a very important role in better sensing the outside world of the whole network. And because the resources of the network system are limited, the energy of the nodes is also limited, and various resources in the area can be utilized to the maximum extent through network coverage deployment optimization.
The wireless sensor network monitors specific events and information by sensing the outside world, and the wireless sensor network is applied to a plurality of different fields due to the great convenience, but coverage holes appear in a monitoring area due to the failure of sensor nodes. Most of the existing vulnerability repairing methods are realized by adding nodes outside, the method only needs to know coordinates of vulnerabilities and move the repairing nodes according to an algorithm for repairing, and the method is easy to realize, but more resources are needed by adding the nodes, and the delay is larger.
Disclosure of Invention
The invention provides a network bug fixing method, which comprises the following steps:
step 1, calculating the minimum moving distance required by the neighbor node to repair the vulnerability;
step 2, calculating the redundancy of the node based on the common overlapping area of the node and the neighbor of the node;
step 3, selecting the node with the maximum residual energy as an optimal coverage vulnerability repair node;
step 4, calculating the bug fixing coverage rate of the fixing position based on a fixing algorithm;
and 5, calculating the global optimal value of the target function of the vulnerability repair coverage rate by adopting a coverage enhancement algorithm.
Further, the step 2 specifically includes the following steps:
Step2.1, acquiring position coordinate information of nodes in the network, calculating coordinates to obtain all neighbor nodes of a target node, and sensing range overlapping between the target node and the neighbor nodes;
step2.2, respectively calculating the overlapping area of the target node and all the neighbor nodes, and calculating the overlapping area S of the two circlesTWO：
Wherein, the first and the second end of the pipe are connected with each other,
(xi,yi),(xj,yj) Two points in a plane space, d is the minimum moving distance required by the neighbor node to repair the leak, and r is the radius of a circle;
step2.3, calculating the overlapping area of the three circles, calculating the coordinates of two intersection points of the target node and each neighbor node, and comparing whether the two intersection points fall in the third circle or not to judge the overlapping condition;
if neither intersection falls within the third circle, STHREE＝0；
If only one or both of the two intersection points fall within the third circle, STHREECalculated according to the following formula:
wherein, a, b and c are the side lengths of the circular triangles in the overlapped area, and s is half of the perimeter of the triangles;
step2.4 overlap area S of all two circles and three circles based on target nodei TWOAnd Sj THREEAnd calculating the redundancy R:
further, in step 3, the redundancy and the moving distance are normalized into residual energy, a node with the largest residual energy is selected as an optimal coverage hole repairing node, and the residual energy E of the node is:
Wherein E is0To initial residual energy, kvEnergy consumed for moving every meter, R is redundancy, d is minimum moving distance required by neighbor nodes to repair the loophole, ksThe energy consumed by the node every hour of operation is E, the initial residual energy of the node is E, and t is the working time of the node.
Further, in the step 4, if the node siResidual energy E ofsiLess than a set energy threshold EthThen the node will execute the repair algorithm:
node siPeripheral quilt node sjAt an angle [ pi-alpha, pi + alpha]Covering, gradually increasing alpha angle to make the covering angle finally reach [0, 2 pi ]]Candidate points sj(xj，yj) Constrained to line segment sisjS ofj(xj，yj) At a certain step length along sisjThe moving, adaptive step size epsilon is controlled as follows:
in the formula: phi is the relative increment of the angle d after the movement; k is equal to [0, 1 ]]Is a dynamic balance factor; t ismaxThe maximum number of movements; t is the current moving times;
and converting the maximum vulnerability repair coverage rate into a global optimal value for calculating the objective function, wherein the objective function F is as follows:
further, in the step5, the enhancement algorithm specifically includes the following steps:
step5.1: initializing algorithm coefficients, randomly generating an initial algorithm coefficient sequence A ═ beta 1, beta 2, beta 3 … beta n, and calculating an objective function F (e);
Step5.2: iterative optimization is carried out, and a more optimal solution is continuously iterated;
step5.3: judging whether the parameter is the optimal value in the set or not, if so, entering the next step, otherwise, returning to Step5.2, and calculating the next parameter;
step5.4: judging whether the coverage rate of the nodes of the current generation is superior to that of the current node, and if so, replacing the coverage rate of the nodes of the current generation with the coverage rate of the current optimal node; otherwise, keeping the coverage rate of the current optimal node;
step5.5, judging whether an iteration termination condition is reached, if so, ending the loop process; otherwise, return to Step5.3.
The invention also provides a network bug fixing device which is used for realizing the network bug fixing method.
The present invention further provides a storage medium having a computer program stored thereon, where the computer program is executed by a processor to implement the steps of the network bug fixing method.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive labor.
FIG. 1 is a flow chart of a method for repairing a network vulnerability according to the present invention;
FIG. 2 is a schematic diagram of the moving distance of a neighbor node according to the present invention;
FIG. 3 is a flow chart of redundancy calculation and processing of the present invention;
FIG. 4 is a flow chart of the enhancement algorithm of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
In the drawings of the embodiments of the present invention, in order to better and more clearly describe the working principle of each element in the system, the connection relationship of each part in the apparatus is shown, only the relative position relationship between each element is clearly distinguished, and the restriction on the signal transmission direction, the connection sequence, and the size, the dimension, and the shape of each part structure in the element or structure cannot be formed.
A vulnerability refers to a defect of a system in hardware, software, a specific implementation of a protocol, or a security policy, which will be discovered during the use of the system. For example, the system may have an error or the like while performing an operation. Since the system generates error information when an error occurs, the system can collect the generated error information and transmit the collected error information to the server through the terminal, and a developer develops a patch according to the error information. The patch can repair the bugs existing in the system during installation. Generally, one patch can fix at least one vulnerability.
Before bug fixing, detection is needed for bugs. Specifically, there are many methods for detecting a vulnerability, for example, information of all files and processes in the system may be acquired, the acquired information is matched with a scanning rule provided by a local vulnerability policy repository, and if a matching condition is satisfied, it is determined that a vulnerability exists, that is, a vulnerability is detected. The vulnerability policy base is used for storing scanning rules of vulnerabilities, the scanning rules are corresponding matching rules formed by analysis of system security vulnerabilities and hacker attack cases by security experts and experience of system administrators about system security configuration, and the vulnerability scanning policy base can support application programs to automatically perform scanning analysis of the system vulnerabilities. Because vulnerabilities are discovered continuously during the use of the system, the scanning rules need to be updated frequently to ensure that the vulnerability policy repository can scan out newly discovered vulnerabilities.
As shown in fig. 1, a schematic flow chart of the network bug fixing method of the present invention is shown, and the specific flow chart is as follows:
step 1, calculating the minimum moving distance required by the neighbor node to repair the vulnerability.
In order to repair the coverage hole, the repair node needs to find the optimal moving distance and the target position. Each neighbor node will calculate the distance it needs to move and this distance will be used to select the best-fit repairing node.
Specifically, each node calculates an intersection point between itself and each neighboring node, and as can be seen from fig. 2, each two neighboring nodes have at least two intersection points, and the intersection point closer to the coverage hole area is reserved for calculation of the movement distance, while the other intersection point is discarded. The minimum moving distance required by the neighboring node to repair the vulnerability is shown as a dashed line segment d in fig. 2, and d can be obtained by the distance formula (1). By calculating the intersection point of each neighbor node, an intersection point list for defining the coverage hole can be obtained, and an approximation can be made to the coverage hole through the intersection point list.
The moving distance in the algorithm refers to the straight-line distance from one point to another point in a two-dimensional plane space. The moving distance is an important index in the coverage hole repairing algorithm and can pass through two points (x) in a plane space i，yi)，(xj，yj) The distance between the two is obtained by the formula (1):
and 2, calculating the redundancy of the node based on the common overlapping area of the node and the neighbor of the node.
In the present invention, each node Si，SiE.g. S, all have the self residual energy information, and the redundant area overlapped with the neighbor intersection point can be calculated from the position coordinate information. And considering the redundant coverage of the overlapping area, wherein the redundancy actually shows the utilization efficiency of the nodes in the monitoring target area. The higher the redundancy is, the larger the overlapping area between the nodes is, and the lower the utilization efficiency is.
In order to calculate the redundancy of a node, the area of the overlap region common to a given node and its neighbors must be calculated. For the condition that the coverage areas of two nodes are overlapped, the redundant area can be obtained by using the area formula (3) of the intersection of two circles. However, when there is an overlap of three nodes, only the overlap area S of two circles is calculatedTWOThe area that would result in the overlap of the three circles is calculated twice. Therefore, the three-circle overlap area S must also be calculatedTHREEAnd the three-circle overlap area needs to be subtracted when calculating the sum of the redundant areas, so as to obtain the accurate total node overlap area.
Finally, the redundancy R can be calculated by equation (2):
wherein n is the overlapping times of two circles, m is the overlapping times of three circles, and the overlapping area S of all the two circles of the target node is calculated i TWOOverlap area S with three circlesj THREEAnd performing subtraction to obtain an effective overlapping area, and then calculating the ratio of the effective overlapping area to the sensing area of the target node to obtain the size of the redundancy.
As shown in fig. 3, the redundancy calculation and processing flow for any target node in the network is summarized as follows:
step2.1, acquiring position coordinate information of nodes in the network, calculating coordinates to obtain all neighbor nodes of the target node, sensing range overlapping between the target node and the neighbor nodes, and communicating and exchanging information mutually.
Step2.2 calculating the overlapping area of the target node and all the neighbor nodes respectively because only two circles overlap between the two nodes, namely calculating the overlapping area S of the two circles by using a formula (3)TWO。
Wherein (x)i,yi),(xj,yj) Two points in a plane space, d is the minimum moving distance required by the neighbor node to repair the vulnerability, and r is the radius of a circle.
And Step2.3, continuously calculating the overlapping area of the three circles, solving the coordinates of two intersection points of the target node and each neighbor node, and judging the type of the overlapping condition at the moment which belongs to the three-circle intersection by comparing whether the two intersection points fall into the third circle or not.
If neither intersection point falls within the third circle, the situation that three circles are overlapped does not exist at this time, namely S THREE＝0。
If only one or both of the two intersection points fall within the third circle, S is calculated using equation (4)THREE。
Where a, b, c are the side lengths (i.e., the distances between the intersections, which can be derived using the distance formula) of the circular triangles in the overlap region, forming a triangle of the calculated area, s is half the perimeter of the triangle, aiFor the intersection point, the area of the triangle can be calculated by using a Helen formula, and the area of the three circular areas is added, so that the overlapping area of the three circles is obtained.
And Step2.4, obtaining the overlapping area of all two circles and three circles of the target node, and calculating the redundancy R by using a formula (2).
And 3, selecting the node with the maximum residual energy as the optimal coverage hole repairing node.
The optimal repair node is selected comprehensively according to the three conditions of the redundancy, the residual energy and the moving distance of each node, because the three-dimensional variables are adopted, the redundancy and the moving distance are normalized into the residual energy for explanation, and finally the node with the maximum residual energy is selected as the optimal coverage vulnerability repair node.
First consider the node movement distance, for an initial residual energy of E0The node moves to the position of the vulnerability in the vulnerability repairing process, the longer the moving distance is, the larger the energy consumption is, the residual energy is reduced, and the residual energy E is when the moving distance is d dIt can be derived from equation (5):
Ed＝EO-kvd (5)；
wherein k isvThe energy consumed for every meter of movement. Considering the redundancy of the nodes again, combining the static working time of the nodes, after the deployment of the network model is completed, the nodes do not move, but need to monitor the occurrence of events and perform data statistics and processing, the process also needs to consume energy, the consumed energy is increased along with the increase of the working time of the nodes, and the residual energy E of the nodes in each working time t istThe following can be obtained by equation (6):
wherein k issFor the energy consumed by the node every hour of operation, combining the formula (5) and the formula (6), the total residual energy E of the node can be obtained as the formula (7):
and (4) the total residual energy E is obtained through the moving distance, the redundancy and the residual energy of each vulnerability neighbor node, the sizes of all neighbor nodes E are compared, and the neighbor node with the maximum E value is selected as the optimal node for vulnerability repair.
Therefore, the selected nodes need smaller moving distance, larger node redundancy and larger node residual energy in comprehensive consideration. The energy loss of the nodes in the moving process can be reduced by selecting the nodes with smaller moving distance; the selection of the node with higher redundancy means that the node has the most overlapping area and the movement of the node has the least influence on the monitored area; and the node with larger total residual energy is selected, so that the node can be ensured to maintain longer working time after completing vulnerability repair, and the reliability is ensured. Once a repair node is selected, the node is moved by a distance d in the moving direction in step 1, and the repair location is reached.
And 4, calculating the bug fixing coverage rate of the fixing position based on the fixing algorithm.
When the position of the loophole is detected, a plurality of candidate nodes can be obtained, and the appropriate candidate nodes are moved to the appropriate position, so that the coverage rate of the network can be improved, the moving distance of the nodes can be reduced, and the problem of repairing the whole network is solved.
If node siResidual energy E ofsiLess than a set energy threshold EthThen it is expected that its node will die and cause a coverage hole, then the node will execute the repair algorithm.
Due to node siPeripheral quilt node sjAt an angle [ pi-alpha, pi + alpha]Covering, gradually increasing the alpha angle toThe coverage angle finally reaches [0, 2 pi]. Candidate points sj(xj，yj) Constrained to line segment sisjS toj(xj，yj) At a certain step length along sisjAnd moving, thus ensuring that the vulnerability repair is completed by using the minimum moving step length, wherein the formula of the self-adaptive step length epsilon is as follows:
in the formula: phi is the relative increment after the alpha angle is moved; k is equal to [0,1 ]]Is a dynamic balance factor; t ismaxThe maximum number of movements; and T is the current moving times.
And converting the maximum vulnerability repair coverage rate into a global optimal value for calculating the objective function, wherein the objective function F is as follows:
the objective function F (epsilon) can be any optimization function known in the art.
And 5, calculating the global optimal value of the objective function of the vulnerability repair coverage rate by adopting a coverage enhancement algorithm.
Solutions meeting the threshold condition are retained in a high-quality solution cluster together with a high-quality solution, the high-quality solution cluster is provided with an upper limit, when the cluster reaches an online state, the network discards an individual with the minimum fitness in the high-quality solution cluster, and finally the optimal solution of the network is generated from the high-quality solution cluster, as shown in fig. 4, the flow of the enhanced algorithm is as follows:
step 5.1. initialize the algorithm coefficients, randomly generate the initial algorithm coefficient sequence a ═ β 1, β 2, β 3 … β n ], and calculate the objective function F (∈).
Step5.2, carrying out iterative optimization and continuously iterating to obtain a more optimal solution.
And 5.3, judging whether the parameter is the optimal value in the set, if so, entering the next step, otherwise, returning to the step5.2, and calculating the next parameter.
Step5.4, judging whether the coverage rate of the node of the current generation is superior to the coverage rate of the current node, and if so, replacing the coverage rate of the node of the current generation with the current optimal coverage rate of the node; otherwise, the current optimal node coverage rate is reserved.
Step5.5, judging whether an iteration termination condition is reached, if so, ending the loop process; otherwise, return to Step5.3.
Each iteration process of the algorithm approaches to the direction of increasing the optimization objective function, and the final purpose of the algorithm is to calculate the global optimum value of the objective function, so that the coverage effect is optimal, and the network performance is optimal. By utilizing the coverage enhancement algorithm, the coverage rate of the nodes initialized randomly is optimized, and the coverage range of the nodes is remarkably improved.
When the network bug fixing method is adopted, bugs are fixed when fixing instructions are received. The bug fixing method comprises the steps that a bug fixing instruction is sent by a background automatically, or a bug prompt and a bug fixing process are associated, a bug fixing button is added to the bug prompt, if a user selects the bug fixing at this time, the bug fixing button on the bug prompt can be clicked, when the system receives the instruction of clicking the bug fixing button by the user, the bug fixing process is triggered, and patches corresponding to bugs are downloaded and installed to finish the bug fixing. If the user chooses to fix the vulnerability the next time, the vulnerability prompt may be selected to be ignored or turned off.
Preferably, after the bug fixing process is triggered, the bug fixing process can be set to be background fixing, and the icon of the bug fixing process is displayed in a system tray at the lower right corner of the desktop, so that disturbance to a user is reduced. In addition, in order to enhance the perception of the user for repairing the bug, the bug prompt can be closed, and the system bubble prompts that bug repairing is being performed. The system bubble is a prompt popped up in a background repairing mode, and is usually triggered by a background and appears on an icon of a process to prompt the state of the process.
In the above embodiments, all or part of the implementation may be realized by software, hardware, firmware, or any combination thereof. When implemented in software, it may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When loaded and executed on a computer, cause the processes or functions described in accordance with the embodiments of the application to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in or transmitted over a computer-readable storage medium. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that incorporates one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
While the invention has been described with reference to specific embodiments, the scope of the invention is not limited thereto, and those skilled in the art can easily conceive various equivalent modifications or substitutions within the technical scope of the invention. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (7)
1. A network bug fixing method is characterized by comprising the following steps:
step 1, calculating the minimum moving distance required by the neighbor node to repair the bug;
step2, calculating the redundancy of the node based on the common overlapping area of the node and the neighbor of the node;
step 3, selecting the node with the maximum residual energy as an optimal coverage hole repairing node;
step 4, calculating the bug fixing coverage rate of the fixing position based on the fixing algorithm;
and 5, calculating the global optimal value of the objective function of the vulnerability repair coverage rate by adopting a coverage enhancement algorithm.
2. The method according to claim 1, wherein the step2 specifically comprises the following steps:
step2.1, acquiring position coordinate information of nodes in the network, calculating coordinates to obtain all neighbor nodes of a target node, and sensing range overlapping between the target node and the neighbor nodes;
step2.2, respectively calculating the overlapping area of the target node and all the neighbor nodes, and calculating the overlapping area S of the two circlesTWO：
Wherein, the first and the second end of the pipe are connected with each other,
(xi,yi),(xj,yj) Two points in a plane space are defined, d is the minimum moving distance required by the neighbor node to repair the vulnerability, and r is the radius of a circle;
step2.3, calculating the overlapping area of the three circles, calculating the coordinates of two intersection points of the target node and each neighbor node, and comparing whether the two intersection points fall into the third circle or not to judge the overlapping condition;
If neither intersection falls within the third circle, STHREE＝0；
If only one or both of the two points of intersection fall within the third circle, STHREECalculated according to the following formula:
wherein a, b and c are the side length of the circular triangle in the overlapping area, s is half of the perimeter of the triangle, aiIs a point of intersection, riIs the radius of the circle;
step2.4 overlap area S of all two circles and three circles based on target nodeiTWOAnd SjTHREEAnd calculating the redundancy R:
wherein n is the number of two circles overlapping and m is the number of three circles overlapping.
3. The method according to claim 1, wherein in step 3, the redundancy and the moving distance are normalized into residual energy, the node with the largest residual energy is selected as the optimal coverage vulnerability repair node, and the residual energy E of the node is:
wherein E is0To initial residual energy, kvEnergy consumed for moving every meter, R is redundancy, d is minimum moving distance required by neighbor nodes to repair the loophole, ksThe energy consumed by the node every hour of operation is E, the initial residual energy of the node is E, and t is the working time of the node.
4. The method according to claim 1, wherein in the step 4, if node s is located iResidual energy E ofsiLess than a set energy threshold EthThen the node will execute the repair algorithm:
node siPeripheral quilt node sjAt an angle [ pi-alpha, pi + alpha]Covering, gradually increasing alpha angle to make the covering angle finally reach [0, 2 pi ]]Candidate points sj(xj，yj) Constrained to line segment sisjS toj(xj，yj) At a certain step length along sisjThe moving, adaptive step size epsilon is controlled as follows:
in the formula: phi is the relative increment of the alpha angle after the movement; k is equal to [0,1 ]]Is a dynamic balance factor; t ismaxThe maximum number of movements; t is the current moving times;
and converting the maximum vulnerability repair coverage rate into a global optimal value for calculating the objective function, wherein the objective function F is as follows:
5. the method according to claim 1, wherein in the step5, the enhancement algorithm specifically includes the following steps:
initializing algorithm coefficients, randomly generating an initial algorithm coefficient sequence A ═ beta 1, beta 2, beta 3 … beta n, and calculating an objective function F (epsilon);
step5.2, performing iterative optimization, and continuously iterating a more optimal solution;
step5.3, judging whether the parameter is the optimal value in the set or not, if so, entering the next step, otherwise, returning to step5.2, and calculating the next parameter;
step5.4, judging whether the coverage rate of the node of the current generation is better than the coverage rate of the current node, and if so, replacing the coverage rate of the node of the current generation with the coverage rate of the current optimal node; otherwise, keeping the coverage rate of the current optimal node;
Step5.5, judging whether an iteration termination condition is reached, if so, ending the loop process; otherwise, return to Step5.3.
6. A network vulnerability fixing device, for implementing the network vulnerability fixing method of any one of claims 1 to 5.
7. A storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the network vulnerability repair method of any of claims 1 to 5.
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| CN115119215B (en) * | 2022-07-04 | 2023-09-22 | 河南科技大学 | Optimal path repairing method for fence coverage holes in natural protected area |
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