CN115270008A - Maximum influence owner searching method and system, storage medium and terminal - Google Patents

Maximum influence owner searching method and system, storage medium and terminal Download PDF

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CN115270008A
CN115270008A CN202211196398.1A CN202211196398A CN115270008A CN 115270008 A CN115270008 A CN 115270008A CN 202211196398 A CN202211196398 A CN 202211196398A CN 115270008 A CN115270008 A CN 115270008A
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张九龙
寇纲
章宇
肖辉
肖峰
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Southwestern University Of Finance And Economics
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Abstract

The invention discloses a method and a system for searching a maximum influence blogger, a storage medium and a terminal, which are characterized by comprising the following steps: s1, microblog social network data are obtained, wherein the microblog social network data have bloggers, propagation weights among the bloggers and propagation thresholds among the bloggers; s2, abstracting the microblog social network into a directed acyclic graph
Figure 687740DEST_PATH_IMAGE002
The method includes the steps that information of the directed acyclic graph is obtained, V represents a set of nodes, each node corresponds to one individual in the microblog social network, the uncertainty of propagation weight in the social network is discussed to be more consistent with the reality background by combining a robust optimization theory, and meanwhile, a C is designed based on a proposed integer programming model&And (3) CG algorithm solution, and generalization capability on a large-scale social network is improved.

Description

Maximum influence owner searching method and system, storage medium and terminal
Technical Field
The invention belongs to the technical field of network propagation and dynamics, relates to a social network influence maximization problem solving technology, and particularly relates to a maximum influence blogger searching method and system, a storage medium and a terminal.
Background
The development of mobile internet in the past decade has brought various online social platforms to the rise, which has greatly promoted the daily communication and information dissemination of the public. Meanwhile, users of the system form a huge social network. How to screen out the least seed users, through the public praise effect, make it can influence more users, it is a problem with theoretical and economic value in the social network analysis-the influence maximization problem, select limited node as the seed set from the social network initially, entity such as the information is passed outward from the seed node along the edge that is connected in the network. Based on a given propagation model, the most individuals in the network receive entities at the end of the propagation process. The total number of individuals subsequently affected by the seed set (including the seed set) is defined as the impact propagation range of the seed set.
Taking virus-type marketing as an example, suppose that a manufacturer develops a new product, and intends to spread publicity in the form of issuing product promos, coupons and the like, and consumers who purchase the product are expected to publicize among friends and relatives of the consumers. Due to the limited popularization cost of manufacturers, a part of consumers need to be screened for targeted marketing in the early stage. At present, the proportion of internet advertisement delivery in all marketing channels rises sharply. Taking the microblog as an example, a manufacturer can select a blogger corresponding to the product category of the manufacturer, put advertisements (characters, pictures, videos and the like) on the homepage of the manufacturer, attach information and purchasing links of the product and pay certain cost. The field experiment shows that compared with vermicelli of a comprehensive bouquet owner (not concentrated on a single product), the vermicelli of a professional bouquet owner is fewer in number, but has higher tweet attention on the bouquet owner and stronger purchasing conversion power. How to effectively screen bloggers and improve the value of advertisement promotion is a marketing problem which is very worthy of research.
Due to the randomness of the propagation path of the entity in the network, the influence propagation range of the seed node is too complex to calculate. Even if only a seed set containing one node is considered to propagate on a directed acyclic graph, it is extremely difficult to accurately calculate the impact propagation range. In fact, it is difficult to accurately calculate the influence propagation range as a # P problem, and to find the optimal seed set as an NP problem.
The prior art has two categories: one is a greedy approximation algorithm of Monte Carlo method using submodel and monotonicity of influence propagation function and its improvement; another is a heuristic algorithm that takes advantage of the specific characteristics of the model.
The prior art has the defects that:
(1) The greedy approximation algorithm of the Monte Carlo method can theoretically obtain an approximation ratio guarantee lower limit of an optimal influence propagation range, but the Monte Carlo method needs to repeatedly simulate a certain candidate node to propagate in a network, count the total number of activated nodes at the end of each propagation process, calculate an average value and approximate the optimal influence propagation range. To obtain a higher quality solution, the method requires running thousands of simulations, resulting in long computation time and high cost.
(2) Although various heuristic algorithms replace Monte Carlo simulation, the solving speed is improved, and the global optimal seed set cannot be obtained. Meanwhile, in order to ensure the precision of the solution, taking a method based on reverse influence sampling as an example, the number of reverse reachable sets which is large enough needs to be sampled, so as to achieve the approximate ratio guarantee which is the same as the greedy approximation algorithm of the Monte Carlo method.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a method for searching a blogger with the maximum influence.
In order to achieve the purpose, the invention adopts the technical scheme that:
the method for searching the blogger with the maximum influence is characterized by comprising the following steps of:
s1, microblog social network data are obtained, wherein the microblog social network data have bloggers, propagation weights among the bloggers and propagation thresholds among the bloggers;
s2, abstracting the microblog social network into a directed acyclic graph
Figure 871472DEST_PATH_IMAGE001
Obtaining a directed acyclicInformation of the graph, V represents a set of nodes, each node corresponding to an individual in the microblog social network,
Figure 523033DEST_PATH_IMAGE002
the directed edge set representing the paired nodes, the number of the nodes in the network is
Figure 270147DEST_PATH_IMAGE003
The number of sides is
Figure 134197DEST_PATH_IMAGE004
；
S3, establishing a two-stage robust optimization model;
step S4, the directed acyclic graph is processed
Figure 682990DEST_PATH_IMAGE005
Inputting the information into a two-stage robust optimization model for calculation;
and S5, returning result data by the two-stage robust optimization model.
Preferably, in step S2,
directed acyclic graph
Figure 974295DEST_PATH_IMAGE006
The information of (2) includes nodes, corresponding propagation weights on each edge, activation thresholds of the nodes, and connection relationships of the edges.
Preferably, in step S3,
in directed acyclic graphs
Figure 975749DEST_PATH_IMAGE007
A virtual node s is introduced to obtain a new augmented graph
Figure 643490DEST_PATH_IMAGE008
New, new
Figure 46790DEST_PATH_IMAGE009
New, new
Figure 774574DEST_PATH_IMAGE010
J is a node;
hypothetical edge
Figure 263325DEST_PATH_IMAGE011
Is located in the interval
Figure 734757DEST_PATH_IMAGE012
Introduction of external excitation
Figure 726984DEST_PATH_IMAGE013
Establishing a two-stage robust optimization model;
Figure 891249DEST_PATH_IMAGE015
Figure 100251DEST_PATH_IMAGE016
（1）
wherein,
Figure 844216DEST_PATH_IMAGE017
representing a first stage decision as a cost of screening the seed set;
wherein,
Figure 222108DEST_PATH_IMAGE018
representing the unit cost of the node j entering the selected seed set;
wherein,
Figure 291695DEST_PATH_IMAGE019
the variables are 0 and 1, and the variables are,
Figure 755038DEST_PATH_IMAGE020
a value equal to 1 indicates that node j is selected as the seed set,
Figure 302694DEST_PATH_IMAGE021
a value of 0 indicates that node j has not been selected as the seed set;
wherein, B represents the number of seed sets;
wherein,
Figure 535092DEST_PATH_IMAGE022
a decision in the second stage is shown,
Figure 775580DEST_PATH_IMAGE023
representing the difference between the external incentive cost and the node activation profit;
wherein,
Figure 460640DEST_PATH_IMAGE024
a state variable representing a node is represented by,
Figure 77566DEST_PATH_IMAGE025
the state variable representing the edge is represented by,
Figure 898891DEST_PATH_IMAGE026
represents an external stimulus;
wherein,
Figure 74395DEST_PATH_IMAGE027
representing the external stimulus introduced by node j,
Figure 981171DEST_PATH_IMAGE028
representing the unit cost of node j introducing an external stimulus,
Figure 136209DEST_PATH_IMAGE029
representing the unit profit of the activated node j in the propagation process;
wherein,
Figure 343200DEST_PATH_IMAGE030
a state variable representing the node j is shown,
Figure 191070DEST_PATH_IMAGE031
a value equal to 1 indicates that node j is activated,
Figure 585142DEST_PATH_IMAGE032
equal to 0 indicates that node j is not activated;
wherein the edge
Figure 543871DEST_PATH_IMAGE033
Representing the outgoing edge of the node i and the incoming edge of the node j;
wherein,
Figure 74209DEST_PATH_IMAGE034
a set of budget uncertainties is represented,
Figure 92981DEST_PATH_IMAGE035
representing an allowable perturbation upper limit of the propagation weight;
wherein,
Figure 239929DEST_PATH_IMAGE036
representing edges
Figure 2348DEST_PATH_IMAGE037
A corresponding propagation weight;
wherein,
Figure 918352DEST_PATH_IMAGE038
is a threshold value for the node(s),
Figure 92979DEST_PATH_IMAGE039
represents a number greater than 10;
wherein,
Figure 727223DEST_PATH_IMAGE040
representing the disturbance propagation weight.
Preferably, in step S4,
the resulting data has an optimal seed set, total number of activated nodes, total cost and external stimuli.
Preferably, the first and second liquid crystal materials are,
with the C & CG algorithm, the algorithm,
wherein the C & CG algorithm framework has an outer layer C & CG algorithm and an inner layer C & CG algorithm;
wherein the outer layer C&CG algorithm for determining optimal seed set
Figure 27754DEST_PATH_IMAGE041
；
Wherein the inner layer C&CG Algorithm for calculating worst scenarios
Figure 798264DEST_PATH_IMAGE042
。
Preferably, the outer C & CG algorithm comprises,
the main problem of the outer layer is that,
Figure 893259DEST_PATH_IMAGE043
（2）
wherein,
Figure 749220DEST_PATH_IMAGE044
is an intermediate variable, l represents the outer layer C&The iteration number of the CG algorithm, L represents the outer layer C&The upper limit of the iteration times of the CG algorithm;
wherein,
Figure 853442DEST_PATH_IMAGE045
representing the external stimulus introduced by node j at the ith iteration,
Figure 478458DEST_PATH_IMAGE046
representing the state variable of node j at the ith iteration,
Figure 744355DEST_PATH_IMAGE047
representing edges
Figure 822032DEST_PATH_IMAGE048
The state variables at the time of the l-th iteration,
Figure 729945DEST_PATH_IMAGE049
representing an uncertain parameter at the first iteration;
the problem of the outer layer is that,
Figure 475047DEST_PATH_IMAGE050
Figure 410380DEST_PATH_IMAGE051
（3）。
preferably, the outer layer C & CG algorithm comprises the steps of,
step S3a1, initialization: upper boundary of problem (1)
Figure 975354DEST_PATH_IMAGE052
Lower boundary of problem (1)
Figure 421378DEST_PATH_IMAGE053
The number of iterations is
Figure 755408DEST_PATH_IMAGE054
The convergence criterion is
Figure 628686DEST_PATH_IMAGE055
；
S3a2, solving an outer layer main problem (2);
step S3a3, judging whether the outer layer main question (2) has a solution or not,
if not, the original problem (1) has no robust feasible solution, and returns a result, and if the original problem has the solution, the next step is carried out;
step S3a4, obtaining an optimal solution
Figure 946535DEST_PATH_IMAGE056
The upper bound of the update problem (1) is
Figure 665092DEST_PATH_IMAGE057
；
Step S3a5, fixing decision variables of the first stage
Figure 384786DEST_PATH_IMAGE058
Solving an outer layer sub-problem (3);
step S3a6, obtaining a worst scene
Figure 428966DEST_PATH_IMAGE059
And corresponding sub-problem objective function
Figure 234111DEST_PATH_IMAGE060
Update
Figure 756359DEST_PATH_IMAGE061
；
Step S3a7, judging whether the requirements are met
Figure 563516DEST_PATH_IMAGE062
，
If the condition is not met, adding a variable
Figure 778596DEST_PATH_IMAGE063
And the constraint conditions (2 c) - (2 h) are met, then the step S3a2 is skipped, and if the conditions are met, the next step is carried out;
step S3a8, returning the optimal seed set
Figure 805458DEST_PATH_IMAGE064
。
Preferably, the inner layer C & CG algorithm includes,
for the outer sub-problem (3), go through
Figure 396976DEST_PATH_IMAGE065
And the equivalence problem (4) is obtained,
Figure 560105DEST_PATH_IMAGE066
（4）
wherein,
Figure 680507DEST_PATH_IMAGE067
denotes an intermediate variable, k denotes an inner layer C&The iteration number of CG algorithm, K represents the inner layer C&The upper limit of the iteration times of the CG algorithm;
wherein,
Figure 460244DEST_PATH_IMAGE068
representing the external stimulus introduced by node j at the kth iteration,
Figure 324295DEST_PATH_IMAGE069
representing the state variable of node j at the kth iteration,
Figure 607509DEST_PATH_IMAGE070
representing edges
Figure 429972DEST_PATH_IMAGE071
The state variable at the k-th iteration,
Figure 431426DEST_PATH_IMAGE072
a derived deterministic parameter representing an outer-layer main question;
the equivalence problem (5) is obtained by utilizing a strong dual theorem,
Figure 364747DEST_PATH_IMAGE073
（5）
wherein,
Figure 735423DEST_PATH_IMAGE074
are newly added variables.
Preferably, the inner layer C & CG algorithm includes,
the main problem of the inner layer is that,
Figure 728787DEST_PATH_IMAGE075
（6）
wherein k = q represents the inner layer C&The CG algorithm converges at the qth iteration,
Figure 951958DEST_PATH_IMAGE076
is a newly added variable;
the problem of the inner layer is solved,
Figure 157811DEST_PATH_IMAGE077
（7）
wherein,
Figure 150038DEST_PATH_IMAGE078
are uncertain parameters.
Preferably, the inner layer C & CG algorithm comprises the steps of,
step S3b1, initializing decision variables of the first stage
Figure 314303DEST_PATH_IMAGE079
Let the upper bound of problem (3) be
Figure 24770DEST_PATH_IMAGE080
Let the lower boundary of problem (3) be
Figure 299893DEST_PATH_IMAGE081
The iteration number is k =0 and the convergence criterion is
Figure 412206DEST_PATH_IMAGE082
；
S3b2, solving an inner layer main problem (6);
step S3b3, obtaining the worst scene
Figure 481793DEST_PATH_IMAGE083
And its corresponding objective function value
Figure 945135DEST_PATH_IMAGE084
Update
Figure 997186DEST_PATH_IMAGE085
；
Step S3b4, fixing uncertain parameters
Figure 229584DEST_PATH_IMAGE086
Solving an inner layer sub-problem (7);
step S3b5, obtaining an optimal solution
Figure 470073DEST_PATH_IMAGE087
Updating the upper boundary of the question (7)
Figure 155132DEST_PATH_IMAGE088
；
Step S3b6, judging whether the condition is satisfied
Figure 772058DEST_PATH_IMAGE089
If not, adding new variable
Figure 593383DEST_PATH_IMAGE090
And the constraint conditions (6 c) - (6 h) are set, the step S3b2 is skipped, and if the constraint conditions are met, the next step is carried out;
step S3b7, returning uncertain parameters
Figure 270352DEST_PATH_IMAGE091
。
A searching system for the most influential blogger is characterized by comprising,
the maximum influence blogger searching method can be executed.
A read storage medium characterized in that,
for storing a specific computer program, the execution of which can implement the maximum influence blogger finding method.
A terminal, comprising:
a memory for storing executable program code;
a processor;
wherein the processor is coupled with the memory;
the processor calls the executable program code stored in the memory to execute the maximum influence blogger searching method.
Provides a method and a system for searching for the maximum influence blogger, a storage medium and a terminal, and has the advantages that,
(1) In the problem of maximization of the influence of the social network, the method is based on a classical linear threshold model, and the propagation weight is assumed to be located in an uncertain set of a certain interval, so that uncertainty is introduced, and the method is more consistent with the current situation that parameters cannot be accurately estimated in a real scene;
(2) The invention designs a double-layer optimization framework and constructs an integer programming model. Based on a Nested Column and Constraint Generation algorithm, the optimal seed set can be accurately solved, and due to the fact that iteration times needed by the algorithm are reduced, the expandability is still achieved on a large-scale social network;
(3) According to the invention, because uncertainty is introduced into parameters in the network, the seed nodes obtained by solving are more robust. Therefore, the advertisement putting effect on the social platform can be effectively simulated, and pricing guidance is provided.
Drawings
FIG. 1 illustrates an outer C & CG flow diagram of the two-stage robust optimization model of the present invention;
FIG. 2 illustrates an inner C & CG flow diagram of the two-stage robust optimization model of the present invention;
FIG. 3 illustrates an overall flow diagram of the two-stage robust optimization model of the present invention;
FIG. 4 shows a social network propagation diagram of 9 nodes.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the 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 invention.
Referring to fig. 1-4, the embodiments of the present invention are as follows:
example 1:
the method for searching for the maximum influence blogger is characterized by comprising the following steps of:
s1, microblog social network data are obtained, wherein the microblog social network data have bloggers, propagation weights among the bloggers and propagation thresholds among the bloggers;
s2, abstracting the microblog social network into a directed acyclic graph
Figure 442708DEST_PATH_IMAGE092
Obtaining information of a directed acyclic graph, wherein V represents a set of nodes, and each node corresponds to one node in a microblog social networkThe number of the individuals is increased,
Figure 332166DEST_PATH_IMAGE093
the directed edge set representing the paired nodes, the number of the nodes in the network is
Figure 539157DEST_PATH_IMAGE094
The number of sides is
Figure 855869DEST_PATH_IMAGE095
；
S3, establishing a two-stage robust optimization model;
step S4, the directed acyclic graph is processed
Figure 14055DEST_PATH_IMAGE096
Inputting the information into a two-stage robust optimization model for calculation;
and S5, returning result data by the two-stage robust optimization model.
In this embodiment, the microblog social network is abstracted as a directed acyclic graph
Figure 972784DEST_PATH_IMAGE097
Acquiring information of a directed acyclic graph, wherein V represents a set of nodes, each node corresponds to one individual in a microblog social network, and each node has two possible states: active and inactive. The active state represents that the node receives the propagated entity (information, product, technology and the like), and the inactive state represents that the node does not receive the entity;
Figure 768702DEST_PATH_IMAGE098
the method comprises the steps that a directed edge set representing paired nodes is obtained, each directed edge represents that the influence between the paired nodes is directional, the influence of a node i on a node j is different from the influence of the node j on the node i, and each edge corresponds to a propagation weight
Figure 787473DEST_PATH_IMAGE099
The propagation weight can be expressed as the last node in the propagation processThe strength of the impact on the next node. The number of nodes in the network is
Figure 668842DEST_PATH_IMAGE003
The number of sides is
Figure 165682DEST_PATH_IMAGE100
(ii) a For each node j in V define its in-neighbor as
Figure 81685DEST_PATH_IMAGE101
All the nodes at the upper level pointing to j are represented.
Initialization definition
Figure 5779DEST_PATH_IMAGE102
Denotes the set of active nodes at time t, where
Figure 640023DEST_PATH_IMAGE103
Is the initial seed set. The seed nodes are used to influence other nodes in the diffusion process so that the entity propagates through the social network. If from any time t to the next time (t + 1), the set of active nodes does not change, i.e. there is no change
Figure 674975DEST_PATH_IMAGE104
The propagation ends. The invention is based on a linear threshold propagation model and aims at all nodes
Figure 445485DEST_PATH_IMAGE105
Assuming the sum of its propagation weights into neighbors, threshold
Figure 39015DEST_PATH_IMAGE106
Respectively, do not exceed 1, respectively,
Figure 160555DEST_PATH_IMAGE107
at random
Figure 733618DEST_PATH_IMAGE108
At a time, for all inactive nodes, if all of its active-to-neighbor propagation weights are activeThe minimum sum of weights is
Figure 624214DEST_PATH_IMAGE109
I.e. by
Figure 890110DEST_PATH_IMAGE110
Then it indicates that node j was successfully activated.
Example 2:
in the step S2, the process is carried out,
directed acyclic graph
Figure 967788DEST_PATH_IMAGE111
The information of (2) includes nodes, corresponding propagation weights on each edge, activation thresholds of the nodes, and connection relationships of the edges.
In the step S3, the process is carried out,
in directed acyclic graphs
Figure 610122DEST_PATH_IMAGE112
Introducing virtual node s to obtain augmented graph
Figure 355224DEST_PATH_IMAGE113
，
Figure 57601DEST_PATH_IMAGE114
，
Figure 622574DEST_PATH_IMAGE115
J is a node;
hypothetical edge
Figure 803020DEST_PATH_IMAGE116
Is located in the interval
Figure 901164DEST_PATH_IMAGE117
Introduction of external excitation
Figure 774442DEST_PATH_IMAGE118
Establishing a two-stage robust optimization model;
Figure 826711DEST_PATH_IMAGE119
Figure 545269DEST_PATH_IMAGE120
（1）
wherein,
Figure 999384DEST_PATH_IMAGE121
representing a first stage decision as a cost of screening the seed set;
wherein,
Figure 43563DEST_PATH_IMAGE122
representing the unit cost of the node j entering the selected seed set;
wherein,
Figure 848708DEST_PATH_IMAGE123
the variables are 0 and 1, and the variables are,
Figure 636535DEST_PATH_IMAGE124
a value equal to 1 indicates that node j is selected as the seed set,
Figure 210736DEST_PATH_IMAGE125
a value of 0 indicates that node j is not selected as the seed set;
wherein, B represents the number of seed sets;
wherein,
Figure 425817DEST_PATH_IMAGE126
the decision in the second stage is shown,
Figure 187100DEST_PATH_IMAGE127
representing the difference between the external incentive cost and the node activation profit;
wherein,
Figure 271294DEST_PATH_IMAGE128
a state variable representing a node is represented by,
Figure 434422DEST_PATH_IMAGE129
a state variable representing the edge is represented by,
Figure 820404DEST_PATH_IMAGE130
represents an external stimulus;
wherein,
Figure 600141DEST_PATH_IMAGE131
representing the external stimulus introduced by node j,
Figure 464192DEST_PATH_IMAGE132
representing the unit cost of node j introducing an external stimulus,
Figure 481826DEST_PATH_IMAGE133
representing the unit profit of the activated node j in the propagation process;
wherein,
Figure 304289DEST_PATH_IMAGE134
a state variable representing the node j is shown,
Figure 305743DEST_PATH_IMAGE135
a value equal to 1 indicates that node j is activated,
Figure 707905DEST_PATH_IMAGE136
equal to 0 indicates that node j is not activated;
wherein the edge
Figure 111205DEST_PATH_IMAGE137
Representing the outgoing edge of the node i and the incoming edge of the node j;
wherein,
Figure 104569DEST_PATH_IMAGE138
a set of budget uncertainties is represented,
Figure 327740DEST_PATH_IMAGE139
representing an allowable perturbation upper limit of the propagation weight;
wherein,
Figure 297707DEST_PATH_IMAGE140
representing edges
Figure 555513DEST_PATH_IMAGE037
A corresponding propagation weight;
wherein,
Figure 454199DEST_PATH_IMAGE141
is a threshold value for the node(s),
Figure 430245DEST_PATH_IMAGE142
represents a number greater than 10;
wherein,
Figure 439790DEST_PATH_IMAGE143
representing the disturbance propagation weight.
In the internet era, the rise of social platforms accelerates the spread of entities such as information. Social networks formed between individuals are beneficial to the development of commercial activities such as viral marketing, and also enable rumors to be spread more easily, leading to social turbulence. Therefore, it is very urgent to find key influence nodes from the social network, and in fact, researchers usually assume that parameters of an influence propagation model are determined, and in the case of a linear threshold propagation model, key parameter propagation weights and thresholds are estimated from data in the social network by a specific method, and the estimated propagation weights and thresholds in the social network are inaccurate. And the propagation weight and the threshold value in the social network are input data for finding the optimal blogger model, the two data have estimation deviation at the beginning, and the accuracy of the optimal solution solved by the model has no great reference value.
Researchers usually ignore the inaccuracy problem, and use the deterministic propagation weight and threshold value input model, so that the model is also a deterministic model, the deterministic model simplifies the complexity of the problem to a certain extent, but supposing that the background is extremely strong, the difference between the calculation result in the real social network and the actual effect is large, most of the prior art are approximate solutions, the total number of nodes activated by the seed set obtained by the approximate algorithm is greater than or equal to 0.63 multiplied by the total number of nodes activated by the optimal seed set, and obviously, the "optimal solution" of the approximate algorithm is not the optimal solution in the true sense.
Taking an example of marketing a new perfume by a cosmetic manufacturer, the manufacturer hopes that most customers see the new perfume, and because uncertainty of real data is not considered, the perfume is popularized by finding an optimal blogger through an approximate method, and the optimal solution found by the method has great errors. There is a high probability that this situation will occur, and although the influence spread of the blogger is maximized, the blogger is a general class blogger, the conversion rate of the bought of the perfume after the advertisement is placed is low, the cost of the boulder invested by the merchant cannot be returned, and the conversion power is still not available after a period of time, and the merchant has invested a large amount of funds in the boulder, which is undoubtedly a very large loss to the merchant. Particularly, many small and medium-sized enterprises, the advertisement of the blogger cannot be profitable, and the company faces the risk of direct closing. In real life, over 70% of merchants cannot bear high risk with low probability, and therefore, it is necessary to improve the solution accuracy of the model.
In this embodiment, the model introduces the weight of the propagation of the disturbance and the external excitation
Figure 552102DEST_PATH_IMAGE144
Assuming edges, taking into account the uncertainty of the input data
Figure 887269DEST_PATH_IMAGE145
Is located at
Figure 85032DEST_PATH_IMAGE146
And (3) establishing a two-stage robust optimization model, and enabling the fluctuation range of the finally found optimal solution to be smaller through calculation of the model, so that the model is more stable. The final optimal solution returned by the model is robust, and the objective function value corresponding to the solution represents the net gain that can be achieved in the worst case.
The disturbance propagation weight may be adjusted according to social network data, such as the authenticity of the social network data, the range of true propagation weights, and so forth. In one embodimentIn the step S3, in the step S,
Figure 898267DEST_PATH_IMAGE147
and
Figure 130665DEST_PATH_IMAGE148
the proportion relation is that,
Figure 105574DEST_PATH_IMAGE149
g is a proportionality coefficient, and the value range of G is in the interval [0,1]。
The invention obtains better solution under the condition of adding less calculation time compared with the heuristic algorithm, the optimal seed set can reduce the sinking cost, and the solving precision is improved under the condition of ensuring that the solving time does not fluctuate greatly.
Example 3:
in step S4, the resulting data has the optimal seed set, total number of activated nodes, total cost and external stimuli.
In this embodiment, for example, a cosmetic manufacturer promotes a new perfume, the optimal seed set may be used to help the manufacturer screen bloggers from a social network constructed on a microblog platform, and advertise on the blogger's homepage, including video, text, voice, etc., so that fans of the bloggers see advertisements, and most fans purchase, and hope that the purchase conversion efficiency of advertising is improved.
The introduction of the external incentive can reduce the node threshold, the introduction of the external incentive in the practical case can reduce the psychological expectation of the fans and increase the purchasing power, the external incentive can be discount coupons, preferential activities and the like, for example, a manufacturer places an order for a special discount link coupon, and fans unwilling to buy at the original price can be motivated, so that the number of purchasers is increased. If no external incentive is introduced, although the promotion issued by the blogger is seen, the customer is still not willing to buy at the original price, which means that the manufacturer loses the customer, but a discount ticket is issued to the customer, the probability of buying the product by the customer is greatly increased, the customer buys the product, then promotes the product in his blog, and then his fan goes to buy again, thereby achieving the maximization of the propagation influence, and the final accumulated profit is far higher than the cost of issuing the discount ticket.
In this embodiment, the data returned by the two-stage robust optimization model includes the optimal seed set, the total number of activated nodes, the total cost and the external stimulus. The disturbance propagation weight, the disturbance quantity and the output of the external excitation regulation model can be regulated according to the needs of merchants.
Example 4:
with the C & CG algorithm, the algorithm,
wherein the C & CG algorithm framework has an outer layer C & CG algorithm and an inner layer C & CG algorithm;
wherein the outer layer C&CG algorithm for determining optimal seed set
Figure 56213DEST_PATH_IMAGE150
；
Wherein the inner layer C&CG Algorithm for calculating worst scenarios
Figure 171674DEST_PATH_IMAGE151
。
The outer layer C & CG algorithm includes,
the main problem of the outer layer is that,
Figure 993000DEST_PATH_IMAGE043
（2）
wherein,
Figure 404390DEST_PATH_IMAGE152
is an intermediate variable, l represents the outer layer C&The iteration number of the CG algorithm, L represents the outer layer C&The upper limit of the iteration times of the CG algorithm;
wherein,
Figure 311166DEST_PATH_IMAGE153
representing the external stimulus introduced by node j at the ith iteration,
Figure 731783DEST_PATH_IMAGE154
representing the state variable of node j at the ith iteration,
Figure 673194DEST_PATH_IMAGE155
representing edges
Figure 521064DEST_PATH_IMAGE156
The state variables at the time of the l-th iteration,
Figure 180716DEST_PATH_IMAGE049
representing an uncertain parameter at the first iteration;
the problem of the outer layer is that,
Figure 873865DEST_PATH_IMAGE157
Figure 669783DEST_PATH_IMAGE158
（3）。
the outer layer C & CG algorithm comprises the following steps,
step S3a1, initialization: upper boundary of problem (1)
Figure 688554DEST_PATH_IMAGE159
Lower boundary of problem (1)
Figure 802879DEST_PATH_IMAGE160
The number of iterations is
Figure 565298DEST_PATH_IMAGE161
The convergence criterion is
Figure 481302DEST_PATH_IMAGE162
；
S3a2, solving an outer layer main problem (2);
step S3a3, judging whether the outer layer main question (2) has a solution or not,
if not, the original problem (1) has no robust feasible solution, and returns a result, and if the original problem has the solution, the next step is carried out;
step S3a4, obtaining an optimal solution
Figure 405395DEST_PATH_IMAGE163
The upper bound of the update problem (1) is
Figure 39639DEST_PATH_IMAGE164
；
Step S3a5, fixing decision variables of the first stage
Figure 340170DEST_PATH_IMAGE165
Solving an outer layer sub-problem (3);
step S3a6, obtaining a worst scene
Figure 110680DEST_PATH_IMAGE166
And corresponding sub-problem objective function
Figure 205675DEST_PATH_IMAGE167
Update
Figure 61636DEST_PATH_IMAGE168
；
Step S3a7, judging whether the requirements are met
Figure 165858DEST_PATH_IMAGE169
，
If the condition is not met, adding a variable
Figure 56454DEST_PATH_IMAGE170
And the constraint conditions (2 c) - (2 h) are met, then the step S3a2 is skipped, and if the conditions are met, the next step is carried out;
step S3a8, returning the optimal seed set
Figure 322350DEST_PATH_IMAGE171
。
The outer C & CG flow chart of the two-stage robust optimization model of the invention is shown in FIG. 1.
The inner layer C & CG algorithm includes,
for external diseasesLayer problem (3), by traversing
Figure 665607DEST_PATH_IMAGE172
And the equivalence problem (4) is obtained,
Figure 546756DEST_PATH_IMAGE173
（4）
wherein,
Figure 26279DEST_PATH_IMAGE174
denotes an intermediate variable, k denotes an inner layer C&The iteration number of CG algorithm, K represents the inner layer C&The upper limit of the iteration times of the CG algorithm;
wherein,
Figure 728655DEST_PATH_IMAGE175
representing the external stimulus introduced by node j at the kth iteration,
Figure 559208DEST_PATH_IMAGE176
representing the state variable of node j at the kth iteration,
Figure 739654DEST_PATH_IMAGE177
representing edges
Figure 604842DEST_PATH_IMAGE178
The state variable at the k-th iteration,
Figure 478120DEST_PATH_IMAGE179
a derived deterministic parameter representing an outer layer main question;
the equivalence problem (5) is obtained by utilizing the strong dual theorem,
Figure 530389DEST_PATH_IMAGE073
（5）
wherein,
Figure 514526DEST_PATH_IMAGE074
are newly added variables.
The inner layer C & CG algorithm includes,
the main problem of the inner layer is that,
Figure 234220DEST_PATH_IMAGE180
（6）
wherein k = q represents the inner layer C&The CG algorithm converges at the qth iteration,
Figure 278400DEST_PATH_IMAGE181
is a newly added variable;
the problem of the inner layer is solved,
Figure 50921DEST_PATH_IMAGE182
（7）
wherein,
Figure 838749DEST_PATH_IMAGE183
are uncertain parameters.
The inner layer C & CG algorithm comprises the following steps,
step S3b1, initializing decision variables of the first stage
Figure 147370DEST_PATH_IMAGE184
Let the upper bound of problem (3) be
Figure 362451DEST_PATH_IMAGE185
Let the lower boundary of problem (3) be
Figure 389313DEST_PATH_IMAGE186
The iteration number is k =0 and the convergence criterion is
Figure 449673DEST_PATH_IMAGE187
；
S3b2, solving an inner layer main problem (6);
step S3b3, obtaining a worst scene
Figure 143959DEST_PATH_IMAGE188
And its corresponding targetFunction value
Figure 529941DEST_PATH_IMAGE189
Update
Figure 44099DEST_PATH_IMAGE190
；
Step S3b4, fixing uncertain parameters
Figure 908150DEST_PATH_IMAGE191
Solving an inner layer sub-problem (7);
step S3b5, obtaining an optimal solution
Figure 456943DEST_PATH_IMAGE192
Updating the upper boundary of the question (7)
Figure 13826DEST_PATH_IMAGE193
；
Step S3b6, judging whether the condition is satisfied
Figure 248236DEST_PATH_IMAGE194
If not, adding new variable
Figure 915978DEST_PATH_IMAGE195
And the constraint conditions (6 c) - (6 h) are set, the step S3b2 is skipped, and if the constraint conditions are met, the next step is carried out;
step S3b7, returning uncertain parameters
Figure 319277DEST_PATH_IMAGE196
。
Inner layer C of two-stage robust optimization model of the invention&CG flow diagram is shown in FIG. 2, and the overall flow diagram of the two-stage robust optimization model of the present invention is shown in FIG. 3, wherein the inner dotted frame is the inner layer C&CG flow, wherein an outer layer C is arranged between an inner dotted line frame and an outer dotted line frame&And (5) CG flow. One embodiment of social network propagation of 9 nodes is shown in FIG. 4, where each ellipse represents a node in the social network, where the first row of numbers in the ellipse represents a different node number and the second row of numbers in each ellipse is the node numberA node threshold of the network node; the social network of 9 nodes in the figure, wherein,
Figure 47062DEST_PATH_IMAGE197
，
Figure 535812DEST_PATH_IMAGE198
introducing a virtual node s to obtain an augmented graph, wherein a solid line with an arrow indicates a directed edge of a matched node, a number beside each edge indicates a propagation weight of the edge, a numerical value of a font with a minimum size beside each node in the graph indicates a threshold value of the node, a dotted line with an arrow indicates a directed edge from the virtual node s to 9 nodes, and the propagation weight of the directed edge is fixed to be fixed
Figure 7245DEST_PATH_IMAGE199
. In numerical experiments, the unit cost of the fixed selection seed set is
Figure 265051DEST_PATH_IMAGE200
External excitation
Figure 898157DEST_PATH_IMAGE201
Unit cost of
Figure 608625DEST_PATH_IMAGE202
Due to the fact that
Figure 883748DEST_PATH_IMAGE203
Is a value ratio of
Figure 996061DEST_PATH_IMAGE204
The method is one order of magnitude lower, the cost of reducing the node threshold by introducing external excitation is great, and the unit yield of the activated node is
Figure 564183DEST_PATH_IMAGE205
The magnitude of the propagation weight perturbation is
Figure 761946DEST_PATH_IMAGE206
。
Table 1 shows a community of 9 nodesAnd (4) propagating the experimental result in the two-stage robust optimization model by using the network. And (3) carrying out sensitivity analysis on the experiment, wherein in the experiment, the solving results of the model under different parameter combinations are compared. Wherein
Figure 840760DEST_PATH_IMAGE207
Indicating the total number of active nodes,
Figure 807579DEST_PATH_IMAGE208
representing the external stimulus introduced and TC representing the corresponding minimum total cost under the model. Allowable perturbation ceiling at different propagation weights
Figure 48068DEST_PATH_IMAGE209
Next, as the size B of the seed set increases, TC tends to stabilize gradually, the requirement for external excitation decreases to 0, and when all nodes have been activated, it does not make sense to increase the size of the seed set any more. Meanwhile, under the same seed set size B, the total number of the activated nodes is reduced and the TC is increased along with the increase of the allowable disturbance upper limit of the propagation weight.
As the propagation weight perturbation upper bound increases, the uncertainty increases and node activation becomes more difficult. The purpose of increasing the seed set size B is to make more nodes active, the smaller the total net negative benefit TC should be. However, the relationship between TC and B is not monotonous, and as B increases, TC decreases but gradually stabilizes, and external stimuli (reduced dependence on discount and other preferential activities) decrease from greater than 0 to equal to 0, i.e., the minimum TC can be reached without introducing external stimuli. And as the propagation weight allows the disturbance upper limit to increase, the total number of the activated nodes does not decrease to a certain degree, which indicates that the total number of the activated nodes can achieve net benefits under the worst scenario for the model. The model of the invention can find out the maximum influence blogger under the worst condition and return the corresponding minimum total cost. The influence and the corresponding prediction cost under the worst condition can be predicted by the merchant, and the merchant can be helped to make budget so as to help the merchant make pricing guidance.
Figure 733127DEST_PATH_IMAGE210
In the problem of maximization of the influence of the social network, the method is based on a classical linear threshold model, and the propagation weight is assumed to be located in an uncertain set of a certain interval, so that uncertainty is introduced, and the fact that parameters cannot be accurately estimated in a real scene is better met; the invention designs a double-layer optimization framework and constructs an integer programming model. The method can accurately solve the optimal seed set based on the Tailored seed and constraint generation algorithm, still has popularization value on a large-scale social network due to the fact that iteration times needed by the algorithm are reduced, and the seed nodes obtained by solving are more robust due to the fact that uncertainty is introduced into parameters in the network. Therefore, the advertisement putting effect on the social platform can be effectively simulated, and pricing guidance is provided.
With the current researchers generally assuming that the parameters of the influence propagation model are determined, in the case of a linear threshold propagation model, the key parameter propagation weights thereof are estimated from data in the social network by a specific method, and thus, inaccurate parameters are obtained. Neglecting this problem, the deterministic model simplifies the complexity of the problem to some extent, but assumes a strong background and a general landing practice effect.
Therefore, the invention provides a method for solving the problem of uncertainty of social network parameters by introducing a robust optimization theory, and the uncertainty of propagation weight is mainly considered, so that the method is more consistent with the real influence diffusion range, and the greatest advantage of the method in the prior art is realized. Under the assumption, the model of the invention is more complex, and the classical algorithm is difficult to solve. Therefore, a Nested Column and Constraint Generation algorithm is proposed in a targeted manner, and the integer programming problem is solved accurately under the condition that the second-stage problem meets the Extended relative Complete recovery Property. Although the computational complexity of the method is related to the network scale, the method still has generalization capability on a large-scale network due to the fact that the iteration number of the computation is small.
A searching system for the most influential blogger is characterized by comprising,
the maximum influence blogger searching method can be executed.
A read storage medium characterized in that,
for storing a designated computer program, the execution of which may implement the maximum impact blogger finding method.
A terminal, comprising:
a memory for storing executable program code;
a processor;
wherein the processor is coupled with the memory;
the processor calls the executable program code stored in the memory to execute the maximum influence blogger searching method.
In the description of the embodiments of the present invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "center", "top", "bottom", "inner", "outer", and the like indicate orientations or positional relationships.
In the description of the embodiments of the present invention, it is to be understood that "-" and "-" denote ranges of two numerical values, and the ranges include endpoints. For example, "A-B" means a range greater than or equal to A and less than or equal to B. "A to B" represents a range of A or more and B or less.
In the description of the embodiments of the present invention, the term "and/or" herein is only one kind of association relationship describing an associated object, and means that there may be three kinds of relationships, for example, a and/or B, and may mean: a exists alone, A and B exist simultaneously, and B exists alone. In addition, the character "/" herein generally indicates that the former and latter related objects are in an "or" relationship.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (13)

1. The method for searching for the maximum influence blogger is characterized by comprising the following steps of:
s1, microblog social network data are obtained, wherein the microblog social network data have bloggers, propagation weights among the bloggers and propagation thresholds among the bloggers;
s2, abstracting the microblog social network into a directed acyclic graph
Figure 758663DEST_PATH_IMAGE001
Obtaining information of a directed acyclic graph, wherein V represents a set of nodes, each node corresponds to one individual in a microblog social network,
Figure 410225DEST_PATH_IMAGE002
the directed edge set representing the paired nodes, the number of the nodes in the network is
Figure 534169DEST_PATH_IMAGE003
The number of sides is
Figure 663800DEST_PATH_IMAGE004
；
S3, establishing a two-stage robust optimization model;
step S4, the directed acyclic graph is processed
Figure 71647DEST_PATH_IMAGE005
Inputting the information into a two-stage robust optimization model for calculation;
and S5, returning result data by the two-stage robust optimization model.
2. The method of claim 1, wherein in step S2,
directed acyclic graph
Figure 628530DEST_PATH_IMAGE006
The information of (2) includes nodes, corresponding propagation weights on each edge, activation thresholds of the nodes, and connection relationships of the edges.
3. The maximum influence blogger searching method according to claim 2, wherein in step S3,
in directed acyclic graphs
Figure 629984DEST_PATH_IMAGE007
A virtual node s is introduced to obtain a new augmented graph
Figure 563305DEST_PATH_IMAGE008
New, new
Figure 74927DEST_PATH_IMAGE009
New, new
Figure 802712DEST_PATH_IMAGE010
J is a node;
hypothetical edge
Figure 291462DEST_PATH_IMAGE011
Is located in the interval
Figure 887528DEST_PATH_IMAGE012
Introduction of external excitation
Figure 145334DEST_PATH_IMAGE013
Establishing a two-stage robust optimization model;
Figure 44020DEST_PATH_IMAGE014
Figure 895433DEST_PATH_IMAGE015
（1）
wherein,
Figure 639398DEST_PATH_IMAGE016
representing a first stage decision as a cost of screening the seed set;
wherein,
Figure 17289DEST_PATH_IMAGE017
representing the unit cost of the node j entering the selected seed set;
wherein,
Figure 211510DEST_PATH_IMAGE018
the variables are 0 and 1, and the variables are,
Figure 674853DEST_PATH_IMAGE019
a value equal to 1 indicates that node j is selected as the seed set,
Figure 222509DEST_PATH_IMAGE020
a value of 0 indicates that node j has not been selected as the seed set;
wherein, B represents the number of seed sets;
wherein,
Figure 828808DEST_PATH_IMAGE021
a decision in the second stage is shown,
Figure 334876DEST_PATH_IMAGE022
representing the difference between the external incentive cost and the node activation profit;
wherein,
Figure 19935DEST_PATH_IMAGE023
a state variable representing a node is represented by,
Figure 495916DEST_PATH_IMAGE024
the state variable representing the edge is represented by,
Figure 582821DEST_PATH_IMAGE025
represents an external stimulus;
wherein,
Figure 259790DEST_PATH_IMAGE026
representing the external stimulus introduced by node j,
Figure 41932DEST_PATH_IMAGE027
representing the unit cost of node j introducing an external stimulus,
Figure 196970DEST_PATH_IMAGE028
representing the unit profit of the activated node j in the propagation process;
wherein,
Figure 403960DEST_PATH_IMAGE029
a state variable representing the node j is shown,
Figure 251830DEST_PATH_IMAGE030
a value equal to 1 indicates that node j is activated,
Figure 770536DEST_PATH_IMAGE031
equal to 0 indicates that node j is not activated;
wherein the edge
Figure 729265DEST_PATH_IMAGE032
Representing the outgoing edge of the node i and the incoming edge of the node j;
wherein,
Figure 525183DEST_PATH_IMAGE033
a set of budget uncertainties is represented,
Figure 917856DEST_PATH_IMAGE034
representing an allowable perturbation upper limit of the propagation weight;
wherein,
Figure 64803DEST_PATH_IMAGE035
representing edges
Figure 561644DEST_PATH_IMAGE036
A corresponding propagation weight;
wherein,
Figure 602281DEST_PATH_IMAGE037
is a threshold value for the node(s),
Figure 526375DEST_PATH_IMAGE038
represents a number greater than 10;
wherein,
Figure 160618DEST_PATH_IMAGE039
representing the disturbance propagation weight.
4. The method of claim 3, wherein in step S4,
the resulting data has an optimal seed set, total number of activated nodes, total cost and external stimuli.
5. The method of claim 4 wherein the maximum influence blogger searches for the specific blogger,
with the C & CG algorithm, the algorithm,
wherein the C & CG algorithm framework has an outer layer C & CG algorithm and an inner layer C & CG algorithm;
wherein the outer layer C&CG algorithm for determining optimal seed set
Figure 461150DEST_PATH_IMAGE040
；
Wherein the inner layer C&CG Algorithm for calculating worst scenarios
Figure 107026DEST_PATH_IMAGE041
。
6. The method of claim 5, wherein the outer C & CG algorithm includes,
the main problem of the outer layer is that,
Figure 202021DEST_PATH_IMAGE042
（2）
wherein,
Figure 323561DEST_PATH_IMAGE043
is an intermediate variable, l represents the outer layer C&The iteration number of the CG algorithm, L represents the outer layer C&The upper limit of the number of iterations of the CG algorithm;
wherein,
Figure 286837DEST_PATH_IMAGE044
representing the external stimulus introduced by node j at the ith iteration,
Figure 911854DEST_PATH_IMAGE045
representing the state variable of node j at the ith iteration,
Figure 443329DEST_PATH_IMAGE046
representing edges
Figure 900767DEST_PATH_IMAGE047
The state variables at the time of the l-th iteration,
Figure 808681DEST_PATH_IMAGE048
representing an uncertain parameter at the first iteration;
the problem of the outer layer is that,
Figure 553783DEST_PATH_IMAGE049
Figure DEST_PATH_IMAGE051AA
（3）。
7. the method of claim 5 wherein the outer C & CG algorithm includes the steps of,
step S3a1, initialization: upper boundary of problem (1)
Figure 928263DEST_PATH_IMAGE052
Lower boundary of problem (1)
Figure 493237DEST_PATH_IMAGE053
The number of iterations is
Figure 63895DEST_PATH_IMAGE054
The convergence criterion is
Figure 663504DEST_PATH_IMAGE055
；
S3a2, solving an outer layer main problem (2);
step S3a3, judging whether the outer layer main question (2) has a solution or not,
if not, the original problem (1) has no robust feasible solution, and returns a result, and if the original problem has the solution, the next step is carried out;
step S3a4, obtaining an optimal solution
Figure 271203DEST_PATH_IMAGE056
The upper bound of the update problem (1) is
Figure 962953DEST_PATH_IMAGE057
；
Step S3a5, fixing decision variables of the first stage
Figure 947090DEST_PATH_IMAGE058
Solving an outer layer sub-problem (3);
step S3a6, obtaining a worst fieldLandscape
Figure 401205DEST_PATH_IMAGE059
And corresponding sub-problem objective function
Figure 570018DEST_PATH_IMAGE060
Update
Figure 109584DEST_PATH_IMAGE061
；
Step S3a7, judging whether the requirements are met
Figure 897411DEST_PATH_IMAGE062
，
If the condition is not met, adding a variable
Figure 346978DEST_PATH_IMAGE063
And the constraint conditions (2 c) - (2 h) are met, then the step S3a2 is skipped, and if the conditions are met, the next step is carried out;
step S3a8, returning to the optimal seed set
Figure 562059DEST_PATH_IMAGE064
。
8. The method of claim 5, wherein the inner C & CG algorithm includes,
for the outer sub-problem (3), go through
Figure 588921DEST_PATH_IMAGE065
And the equivalence problem (4) is obtained,
Figure DEST_PATH_IMAGE067A
（4）
wherein,
Figure 351078DEST_PATH_IMAGE068
denotes an intermediate variable, k denotes an inner layer C&The iteration number of CG algorithm, K represents the inner layer C&The upper limit of the iteration times of the CG algorithm;
wherein,
Figure 514206DEST_PATH_IMAGE069
representing the external stimulus introduced by node j at the kth iteration,
Figure 900188DEST_PATH_IMAGE070
representing the state variable of node j at the kth iteration,
Figure 804559DEST_PATH_IMAGE071
representing edges
Figure 934189DEST_PATH_IMAGE072
The state variable at the time of the kth iteration,
Figure 217403DEST_PATH_IMAGE073
a derived deterministic parameter representing an outer layer main question;
the equivalence problem (5) is obtained by utilizing the strong dual theorem,
Figure DEST_PATH_IMAGE075A
（5）
wherein,
Figure 711969DEST_PATH_IMAGE076
is a newly added variable.
9. The maximum influence blogger finding method according to claim 5, wherein the inner C & CG algorithm comprises,
the main problem of the inner layer is that,
Figure 713423DEST_PATH_IMAGE077
（6）
wherein k = q represents the inner layer C&The CG algorithm converges at the qth iteration,
Figure 381165DEST_PATH_IMAGE078
is a newly added variable;
the problem of the inner layer is solved,
Figure 892787DEST_PATH_IMAGE079
（7）
wherein,
Figure 620571DEST_PATH_IMAGE080
are uncertain parameters.
10. The method of claim 5 wherein the inner C & CG algorithm includes the steps of,
step S3b1, initializing decision variables of the first stage
Figure 109321DEST_PATH_IMAGE081
Let the upper boundary of the problem (3) be
Figure 705388DEST_PATH_IMAGE082
Let the lower boundary of problem (3) be
Figure 697615DEST_PATH_IMAGE083
The iteration number is k =0 and the convergence criterion is
Figure 861880DEST_PATH_IMAGE084
；
S3b2, solving an inner layer main problem (6);
step S3b3, obtaining a worst scene
Figure 447713DEST_PATH_IMAGE085
And its corresponding objective function value
Figure 722836DEST_PATH_IMAGE086
Update
Figure 835149DEST_PATH_IMAGE087
；
Step S3b4, fixing uncertain parameters
Figure 29370DEST_PATH_IMAGE088
Solving an inner layer sub-problem (7);
step S3b5, obtaining an optimal solution
Figure 492712DEST_PATH_IMAGE089
Update the upper boundary of the problem (7)
Figure 40368DEST_PATH_IMAGE090
；
Step S3b6, judging whether the condition is satisfied
Figure 398667DEST_PATH_IMAGE091
If not, adding new variable
Figure 639155DEST_PATH_IMAGE092
And the constraint conditions (6 c) - (6 h) are set, the step S3b2 is skipped, and if the constraint conditions are met, the next step is carried out;
step S3b7, returning uncertain parameters
Figure 448848DEST_PATH_IMAGE093
。
11. A searching system for the most influential blogger is characterized by comprising,
a method of searching for a maximum influence blogger according to any one of claims 1 to 10 may be performed.
12. A read storage medium characterized in that,
for storing a specific computer program, the execution of which can implement the maximum influence blogger finding method of any one of claims 1-10.
13. A terminal, comprising:
a memory for storing executable program code;
a processor;
wherein the processor is coupled with the memory;
the processor calls the executable program code stored in the memory to execute the maximum impact blogger finding method according to any one of claims 1-10.
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