An adaptive key selection method for the multilevel index model for effective service management in the cloud

The growing number of services processed and stored in the cloud has led to difficulties in managing and discovering the required services efficiently. Multilevel index model is an efficient method to manage and retrieve services in service repositories. When adding a new service to a multilevel index model, a key needs to be selected for the service, but existing key selection methods cannot adapt to the situation that hot services change over time. To address this problem, this article proposes an adaptive key selection method to improve the efficiency of service retrieval. However, the service addition operation of the adaptive key selection method is inefficient in the multilevel index model. For this reason, this article improves the multilevel index model by introducing local equivalence partition. This indexing model improves the service addition efficiency of the adaptive key selection method without affecting the service retrieval efficiency. It is experimentally demonstrated that the retrieval and addition efficiencies of the adaptive key selection method are close to the ideal state optimum under the multilevel index model with local equivalence partitioning.

but also improves the efficiency of services add and retrieve operations.In Reference 9, the problem of retrieval efficiency is analyzed in detail, and an expectation formula for the number of services to be traversed by a retrieval operation is derived.The works of Reference 10 scrutinized the expectation formula for retrieval operations and highlighted that retrieval efficiency is independent of the number of keys, and proposed a random key selection method to improve the efficiency of service addition.Based on this random key selection, Gu et al. 11 proposed the designated key selection method to further improve the efficiency of service addition for intermediate and full indexes.
The above works only studied the efficiency of service addition and retrieval under the condition of services being invoked evenly.However, in real environments, the frequency of service invocations is unequal.Some services are "hot" and are invoked more frequently.Some services are "cold" and are rarely invoked.Gu et al. 12 studied the case of uneven service invocation and proposed a least-using key selection method to deal with this situation.It has been theoretically proven to be correct and experimentally validated.However, the least-used key selection method achieves maximum retrieval efficiency only under an ideal condition that every invocation frequency of each service is known and does not change, which is unrealistic in the actual environment.When service invocation frequencies are unknown or changed, its efficiency would decrease.Focusing on this problem, this article proposes a local equivalence partition based multilevel index model (LPMIM) to maintain high efficiency of service addition and proposes an adaptive key selection method to maintain high efficiency of service retrieval.The key innovations of this article are listed as follows: 1.A LPMIM is proposed in the article.Compared with existing multilevel index models, the proposed model improves the efficiency of service addition operation without affecting retrieval efficiency.Since it uses a local equivalence partition instead of a global equivalence partition, the proposed model is suitable for distributed deployment.
2. An adaptive key selection method is proposed to solve the service hotspot drift problem to improve service retrieval efficiency in a practical environment.Synergize with LPMIM, the proposed adaptive key selection method approaches maximum retrieval efficiency obtained only in ideal conditions before.
The rest of this article is organized as follows: Section 2 reviews existing service discovery, composition and retrieval.Section 3 introduces the novel multilevel index model called LPMIM and compares it with the previous multilevel index model to discover the advantages of the newly proposed model.Section 4 presents our proposed adaptive key selection method to accommodate service retrieval methods when service hotspots drift.Section 5 presents and discusses our experimental results.Section 6 concludes the article along with outlining our future research directions.

Service discovery and composition
Given in cloud computing, the cloud subscriber makes a service request and the cloud provider is required to discover services to meet the subscriber's requirements based on the subscriber's request and, where necessary, to perform a composition of services to achieve the functionality required by the subscriber, research focusing on service discovery modes has gained attention in recent years.Service discovery models can efficiently discover, compose and verify the services in a service resource pool by matching the user's application requirements against the functional description of services, with the intention of providing required services to the users. 5Rambold et al. 13 investigated the classification of service discovery methods into centralized registry-based service discovery methods, distributed service registry-based service discovery methods and decentralized service registry-based service discovery methods based on service registries, and while it helps to understand the different types of service discovery methods, it does not provide any specific methods to improve service discovery accuracy.Wang et al. 14 investigated the mining of common topic groups from the service-topic distribution matrix generated by the topic model, and further used the extracted common topic groups to match user queries with relevant web services.This work has claimed to achieve a better trade-off between the accuracy of service discovery and the number of candidate web services, but may not be suitable for complex service discovery requirements.
In order to improve the accuracy and efficiency of service discovery, Sha et al. 15 proposed a Petri net-based user-demand oriented web service discovery approach, but it may not be able to handle a large number of web services.Yang et al. 16 proposed a Petri net approach for service composition and monitoring services, but it requires a large amount of computational resources.Zhang et al. 17 proposed a novel approach named Q2C (query of quality correlation) to systematically model quality correlations, thereby utilizing efficient queries of quality correlations for service discovery.However, this approach utilizes only one module of the combined approach and does not take into account the degree of support for service discovery and ease of use for service management and maintenance, and is not applicable to all service discovery scenarios.In the latest research, Li et al. 18 proposed to construct knowledge graph-oriented service discovery models, and transformed the service discovery mechanism into a knowledge graph query to discover the required services.However, constructing and maintaining the knowledge graph may require significant effort.Due to the diversity of service types, Zhao et al. 19 proposed a new service discovery approach to retrieve target services by combining extreme learning machines (ELM) and differential evolution algorithms (DE).However, it is worth noting that any approach that relies on machine learning algorithms or evolutionary algorithms requires a large amount of data and computational resources to obtain accurate and efficient results.Therefore, the method proposed by Zhao et al. may have a high computational complexity, which may limit its scalability and practicality.
Recently, a novel privacy-aware cloud service composition approach, called SFLA-GA, has been proposed for optimizing the offered service compositions for enhancing the Quality of Service (QoS) in IoT environments. 20Moreover, Chen et al. 21proposed a novel two-stage GA-based approach to offer a robust web service composition based on adaptive evolutionary control and efficient robustness measurement.However, it is important to note that genetic algorithms (GAs) are computationally intensive and may require a large amount of time and resources to Moreover, the two-stage approach proposed by Chen et al. may require extensive manual intervention in the second stage, which may be time-consuming and may limit the scalability of the approach to larger and more complex service combinations.
Overall, the research on service discovery and composition is still evolving, and there is no one-size-fits-all solution for all scenarios.Each approach has its strengths and limitations, and further research is required to develop more efficient and effective methods for service discovery and composition in cloud computing.

Indexing methods
An efficient indexing model should improve the efficiency of service retrieval in service repositories.Several different indexing structures for service repositories, such as sequential index, inverted index, and multilevel index model have been proposed.Sequential index 7 stores all services in a sequential structure, such as a list.For a retrieval request, all the stored services are traversed and checked against a given request.The inverted index 22 is used in service retrieval, which finds corresponding services in the service repository according to the service parameters given by users.
Since services are formed by combining input and output parameters, the representation of a service can be simplified to s: {inputs → outputs}.
Figure 1 shows the operational mechanism of the inverted index in the service retrieval process, where the parameters a, b, and c represent a set of corresponding functions in the service repository.However, this approach results in a large number of identical services being retrieved multiple times, and the redundancy of services reduces the efficiency of the retrieval.
The multilevel index model 7 can reduce the service redundancy incurred by the inverted index model.The multilevel index model encompasses four layers of index structure, where each layer of index eliminates the redundancy caused by different aspects of the service, thus improving the efficiency of service retrieval.As shown in Figure 2, the first layer eliminates the service redundancy caused by the same service input and output parameters, while the second layer further eliminates the service redundancy caused by the same service input parameters based on the new set of services obtained in the first layer.In the third layer, all the input parameters are combined into a set of keys so that appropriate and unique keys can be selected for service retrieval in the fourth layer.
Service retrieval with the multilevel index model on a distributed environment to manage and maintain large-scale service repositories.Miao et al. 24 proposed an index model on the fog layer to improve the efficiency of service discovery.The authors used the DM-index model to insert a newly generated service into a matching fog node to determine whether the service exists in the fog node or not.In addition, Wu et al. 9 further studied the performance of the multilevel index model.
When a service is added to a multilevel index model, an input parameter is selected as the key for that service.The key selection method is usually not known to affect retrieval efficiency.Kuang et al. 10 researched key selection methods in the multilevel index model and proposed three different key selection methods, including the minimum key count selection method, the maximum key count selection method and the random key selection method, respectively.The minimum key count selection method tries to keep the number of keys as small as possible.Therefore, it aims to keep the average size of the key class as large as possible.In contrast, the maximum key count selection method attempts to keep the number of keys as large as possible.It, therefore, intends to keep the average size of the key class as small as possible.The random key selection method randomly selects any parameter in the service input as the key for the newly added service.Experiments have shown that the random key selection method improves service addition operations.Gu et al. 11 proposed a new key selection method called the designated key selection method to further improve the service addition efficiency of the partial index model and the full index model without affecting the service retrieval efficiency.
However, the designated key selection method is designed based on an equal probability distribution of service parameters in the multilevel index model, which does not match the actual service parameter distribution, and therefore the service retrieval efficiency cannot be optimized in practical applications.

Service hotspot drifting
Service hotspot drift refers to the phenomenon in which the popularity of a particular service in a cloud computing environment changes over time.
This can occur due to a variety of factors such as changes in user demand, the emergence of new services, changes in pricing or service quality, and other market or technological factors.As a result of service hotspot drift, some services may become less popular while others may become more popular, which can impact the overall performance and efficiency of the cloud system.Service providers need to be aware of service hotspot drift and take steps to manage it in order to ensure that their services continue to meet the changing needs of users.
In order to predict changes in users' interests and service hotspot drift, the framework proposed by Qi et al. 25 proposed framework uses a matrix factorization method to generate user preferences, and considers user privacy preferences to provide personalized recommendations while protecting user privacy.Liu et al. 26 proposed an interaction-enhanced and time-aware graph convolution network (ITGCN) for successive point-of-interest (POI) recommendation.Liu et al. 27 established a cloud-based greenhouse climate prediction model using long short-term memory (LSTM) neural network, which can help greenhouse managers make informed decisions.Liu et al. 28 calculated user interest using an ontology-based vector space model, where the vector terms are ontologies or concepts about user interest.Zhang et al. 29 proposed a recommendation system based on fuzzy user interest drift detection to mitigate the changes in user's interest drift, and claimed to have improved the prediction accuracy by adapting to user interest drift.In order to address the problem of predicting user interest drift, Sun et al. 30 used clustering and a matrix of temporal influence factors to monitor the extent of user interest drift in a class, where an improved prediction of event rating was achieved.While the references mentioned have made significant contributions to their respective fields, there are some potential drawbacks or limitations to be aware of.For example, the incompleteness of the data leads to compromised accuracy, a large number of calculations leads to computational overload, the use of clustering algorithms may affect the performance and robustness of the algorithms and so on.
Gu et al. 12 studied the case of unequal invocation frequency of services, proposed a key selection strategy for fixed service invocation frequency to improve service retrieval efficiency, and verified the effectiveness of the least-used key selection method.However, Reference 12 does not address the problem of hot services changing over time, which can degrade the retrieval efficiency.In a multilevel index model, the distribution of service invocation parameters is based on how often the user invokes the service, which is usually determined by the user's interests.In the process of service retrieval, the drift of user interest may cause the invocation frequency of service parameters to be unequal.Therefore, a new adaptive key selection method is proposed in this article to solve the problem of decreasing retrieval efficiency caused by service hotspot shift, and a new multilevel index model based on local partition is proposed to improve the efficiency of service addition.

Framework and basic definition of the multilevel index model
The architecture of the multilevel index model, as shown in Figure 3, allows for efficient retrieval, addition, deletion or replacement of services which was introduced in our previous study. 7The main goal of the indexing is to speed up the retrieval of services from the service repositories, whereby accelerating the speed of service discovery and service composition.During this process, ontologies are used to resolve service parameters into unique identifiers.After ontology transformation, only the matching of service parameters is considered at the service retrieval level, and there is no need to consider the semantics of the parameters.
Before describing the improved indexing model, several basic definitions and theories around the characteristics of mass storage services are introduced using Definitions 1, 2, and 3.

Global partition based multilevel index model
Wu et al. proposed the multilevel index model, 7,8 which is constructed by equivalence relations and quotient set theory, referred as the global partition based multilevel index model (GPMIM) in this article.GPMIM is a four-layer indexing structure, as shown in Figure 4.In the first layer, the set of all services S is divided into multiple disjoint subsets, where each subset contains services with the same input and output parameters, and each subset is called as a similar-class C s and the set of all similar-classes is called  1 .In the second layer, the set of all similar-classes  1 is further divided into multiple disjoint subsets, each of which contains services with the same input parameters, and each subset is referred as an input-similar class  is .The set of all input-similar service classes is called ℜ 2 .Moreover, in order to further reduce the search space in the third and fourth-layer indexes, the concept of "keys" is introduced.In the third layer index, a selected service input parameter is specified as a key in each input-similar class  is .
The set of all input-similar classes ℜ 2 is further divided into multiple disjoint subsets.Each subset containing services with the same key is called as a key class ℭ k .The set of all key classes is called R 3 .Finally, in the fourth layer, each key class ℭ k is mapped into a unique key, and the set of all keys is called K .
To facilitate a more comprehensive understanding of the process for partitioning services in a multilevel index model, Figure 5 presents a specific example to explicate the method.Figure 5 depicts a multilevel service index containing five services, namely, s 1 -s 5 , in the service repository.
The services s 1 and s 2 form a similar class as they share the same inputs and outputs.The remaining services form distinct similar classes.Furthermore, the first and second similar classes comprise an input-similar class due to identical inputs, while the remaining similar classes form separate input-similar classes.Lastly, the second and third input-similar classes form a key class since they share the same key.The remaining input-similar class forms a standalone key class.

Local partition based multilevel index model
In GPMIM, equivalence partitions are defined globally at each level.For example, in L 2 I of GPMIM, an equivalence partition is defined over all input-similar classes.In the proposed LPMIM, a method to define equivalence partitions over each subset locally in each level without losing any information for service retrieval has been found.For example, in L 2 I of LPMIM, an equivalence partition can be defined in every input-similar class.Since the scale of a class in a level is smaller than one of all classes, LPMIM with suitable key class methods can be more efficient than GPMIM.
LPMIM also has a four-layer index structure like GPMIM.In the fourth layer, all keys and all key classes form a bijection function, as shown in Figure 6.
The fourth layer of LPMIM The third layer of LPMIM However, the partition of the index model differs from the third layer index.The key of the input-similar class  is , denoted as ( is ).
The third layer index can be partitioned equivalently for each key class ℭ k using the binary relation R 3, as defined in Definition 4.
Figure 7 shows the division according to the improved equivalence relations described above, where all  is contains the same key in any one ℭ k , which is consistent with GPMIM.The difference is that in LGMIM, ℜ 2 may have • isi = • isj and i ≠ j, whereas this situation does not exist in GPMIM.
The second layer index can be equivalently divided for each input-similar class  is based on relation R 2 .
The second layer of LPMIM The first layer of LPMIM After the partition by local equivalence, as shown in Figure 8, similarly to GPMIM, each  is set contains similar service classes C s with the same input and output parameters.The difference in LPMIM is that  1 may exist where The first layer index can be equivalently divided for each similar class C s based on relation R 1 .

Definition 6.
A relation R 1 is a binary relation on a defined set C s .
After the partition by local equivalence, as shown in From the comparison between Figures 10 and 11, it can be seen that Figure 10 follows the principle of global equivalence division in GPMIM, where each  is cannot be the same among each other and each C s cannot be the same among each other.However, Figure 11 uses the principle of equivalence partition within each class as only in the case of LPMIM, so that the same subset can exist in the set ℜ 2 of all input similar classes  is , as in the cases Similarly, the same C s can exist in the set ℜ 1 of all similar classes C s , as in the case of In the service set S, services with the same input and output parameters are not necessarily placed in the same C s .
For instance, services s 1 , s 2 , s 3 with the same input and output parameters can be divided into two different similar classes C s1 and C s4 , respectively in Figure 11.The advantage of LPMIM is that when adding services, only the input similar classes  is within a key class ℭ k need to be retrieved to ensure the uniqueness of • is within that key class.However, in GPMIM all input similar classes need to be retrieved to prove the uniqueness of • is globally.Thus, our proposed LPMIM effectively reduces the search space and reduces the complexity of service addition operations, that is, it effectively improves service addition time without affecting the efficiency of service retrieval.In addition, LPMIM only retrieves within a key class when a service is added, so it is more adaptable to distributed application scenarios.

AN ADAPTIVE KEY SELECTION METHOD
In our previous paper, 12 the unequal frequency of service invocations in GPMIM was studied.One of its key contributions is that it provides a guideline for key selection under the condition of unequal frequency of service invocations.The guideline is that frequently invoked services should be placed in small key classes.Then they can be retrieved quickly within less time.The guideline has been proved theoretically and validated experimentally.Based on the guideline, a least-used key selection method was proposed. 12However, it only works under an ideal condition that the frequency of service invocations is fixed and known.Therefore, it does not solve the problem of retrieval efficiency degradation caused by drift of "hot" services.In order to deal with this situation, this article proposes an adaptive key selection method to adaptively select keys according to variations of service invocation frequencies.The adaptive key selection method is integrated into LPMIM to improve service retrieval efficiency further.
Figure 12 illustrates the application architecture of the proposed adaptive key selection method.A watchtower is established in our method to observe frequency changes of service parameter invocations.The watchtower maintains a table of invocation frequencies of service parameters.When a user invokes a service retrieval operation, the watchtower collects the parameter information in the service retrieval and updates the invocation frequency table of service parameters at a certain time interval.When a new service is added to LPMIM, the service addition operation invokes the adaptive key selection method to select an appropriate key for the service according to the service parameter invocation frequency table.After that, the service can be added to LPMIM.
The dynamic weight formula (DWF) 31 is used to update invocation frequencies of all service parameters.DWF proposed by Wu et al. 31 was originally used to calculate service reputation, which can reflect the recent changes in service quality.Its basic idea is that the last rating score is assigned the highest weight in order to change the service reputation quickly.Here, DWF is introduced to calculate the invocation frequencies of service parameters to reflect the recent changes of invocation frequencies of service parameters, which can provide accurate references for the adaptive key selection method to select suitable keys.The recursive formula for DWF is shown in Equation ( 1), where xn represents the service reputation value calculated after receiving n reviews.
Since xn is the value used to calculate service reputation and cannot be used directly to calculate service invocation frequency, this article makes some transformations based on the idea of DWF.As shown in Figure 13, time is divided into a number of consecutive time intervals, and when time reaches t i , the sentinel post counts the number of invocations of each parameter within the nearest time interval from t i−1 to t i .Using y j i to denote the number of invocations of parameter p j within the ith time interval and x j i to denote the value of the frequency of invocations of parameter p j resulting from the update calculation at time t i , we calculate x j i using the DWF, as shown below. ( In formula (2), q represents the weight of the invocation times of service parameters in a given time interval.The above time slicing method converts the number of invocations values on the spatial domain into invocation frequency values on the temporal domain.A larger q value implies that the frequency value of the most recent time period is weighted more heavily, which allows an easy reflection of the changes in popular services.
However, a very large value of q is easily influenced by occasional high and low frequency noise.Based on the recommendations of Reference 31, the q value is taken as 0.5.
Formula (2) presents the calculation of the frequency of invocation of only one parameter.Therefore, the frequency of invocations for all parameters at time t i can be expressed as a column vector X i , as shown in formula (3).
The number of invocations of all parameters in the time interval t i−1 to t i can be expressed in formula (4) as a column vector Y i .
Therefore, the frequency of invocation of all parameters can be calculated using the following formula (5).
The list of service parameter invocations is updated at the end of each time interval using formula (5) to maintain the changes in invocation frequency up-to-date.Second, when a new service is added, the add operation first invokes the key selection method to select a key for that service, which is then inserted into the LPMIM.The adaptive key selection method proposed in this article is shown in Algorithm 1.

Algorithm 1. Adaptive key selection method
Input: s.
Output: key of s.
1. Select the first input parameter of s as its k; 2. Find the k.invokingfrequency from the service parameter invocation frequency table ; 3. For each input parameter p of s.

4.
Find the p. invokingfrequency from the service parameter invocation frequency table ; 5.
7. Select k as the key of s and return k.
In Algorithm 1, the first input parameter in the service is first selected as the key and the invoking frequency of that key is denoted as k.invokingfrequency, which is obtained from the service parameter invoking frequency table.Next, the invoking frequency of each input parameter p in the service denote as p. invokingfrequency, which is obtained through a loop of line 3, and if p. invokingfrequency is less than k.invokingfrequency in line 5, then the key k of service s is updated to p in line 6.Through the loop of lines 3-6, the smallest invoking frequency parameter can be selected as the key of service s.Since the invoking frequency table of parameters is maintained up to date by formula (5), our proposed adaptive key selection algorithm can improve the efficiency of service retrieval by automatically selecting the appropriate key to mitigate changes in the invocation frequency of popular services.

EXPERIMENTS AND ANALYSIS
Wu et al. have proved that the efficiency of service retrieval in the multilevel index model is much higher than ones in other indices. 7,8Therefore, only the multilevel index model is tested in our experiments.Five key selection methods are evaluated under GPMIM and LPMIM.They are the original key selection method that is the first key selection method for the multilevel index proposed by Wu et al., 7 the random key selection method that is a base line proposed by Kuang et al., 10 the designated key selection method 11 which is the first key selection method to optimize service addition, the least-used key selection method 12 which is the first key selection method to deal with uneven invocations of services, and the proposed latest adaptive key selection method which aims to deal with the situation that invocation frequencies of services dynamically change.The original key selection method makes |ℭ k | as close as possible to √ | ℜ 2 | in a multilevel index model, thereby assigning the input similar classes to the key classes using an equal probability.The random key selection method randomly selects any parameter in the service input as the key for a newly added service to reduce the time overhead in the system resulting from the computation around the service parameter assignment.The random key selection method can be used as a benchmark for testing.The designated key selection method gives each parameter a unique ID and finds the only specified service input parameter that can be used as a key through a recursive formula in the linear congruence method, which is characterized by high efficiency of service addition without affecting the efficiency of service retrieval.The least-used key selection method can improve the efficiency of service retrieval under a known unequal distribution probability of the service invocation frequency.The proposed adaptive key selection method is designed to improve the efficiency of service retrieval when the service invocation frequency characterizes an unequal distribution frequency and the probability distribution is dynamically changing.
In order to evaluate the effectiveness of the proposed key selection methods in the indexing models, a set of experiments was conducted on a test platform developed in C#.The configurations of the experiments are consistent with the previous works 12 for the purpose of fair comparisons.
Configuration details are as follows.The experiment used 20 different datasets, each consisting of 50,000 services and 1000 retrieval requests.
The datasets were designed to simulate real-world scenarios where the frequency of service parameter invocations is not evenly distributed.This allows for a more comprehensive evaluation of the effectiveness of the proposed key selection methods under varying conditions.The size of the input parameter set is set to 1000.Each service includes 10 input parameters.Each retrieval request contains 32 parameters.For each dataset a comparative test is performed with the aforementioned five key selection methods under GPMIM and LPMIM to verify the effectiveness of the adaptive key selection method for service retrieval under the conditions of unequal probability distribution of service invocation frequency and unknown distribution probability, as well as the effectiveness of service addition in LPMIM.

Impact of the five key selection methods on retrieval performance in GPMIM and LPMIM
The two different indexing models, GPMIM and LPMIM, are both constructed from service add operations, and the service addition algorithms can be chosen from the five proposed key selection methods.Therefore, the primary objective of this experiment is to test the impact of these five key selection methods on the service retrieval performance of GPMIM and LPMIM under conditions of varying frequency of service invocations.
Figure 14 shows the impact of the five key selection methods in GPMIM on the service retrieval time.It can be observed that the least used key selection method characterizes the shortest service repository retrieval time.Since the least used key selection method has the service parameters invocation frequency distributed in an ideal way in the experimental condition setting, the least-used key selection method can be used in the optimal way for key selection according to the theory proposed by Reference 12.The performance of the adaptive key selection method is very close to that of the best-performing least-used key selection method.However, its retrieval time in the initial phase is essentially the same as the retrieval performance of the service repository corresponding to the random key selection method.This is because in the initial stage, the adaptive algorithm cannot obtain information on the invocation frequency of service parameters, and thus the key selection method cannot optimize the service retrieval efficiency, making its key selection strategy no different from the random key selection method, so the retrieval efficiency of both remain basically the same in the initial stage.However, after a short period of statistical learning, the adaptive key selection method can be optimized according to the service invocation frequency information, so its retrieval efficiency is immediately improved.The other algorithms cannot handle the case of unequal frequency of dynamic service invocations, thus the retrieval speed of their corresponding service repository is much lower than these two algorithms.Therefore, our proposed adaptive key selection method significantly improves the efficiency of service retrieval under GPMIM with non-average distribution of service invocation frequency and unknown distribution probability.The reason for the change in its retrieval performance in the initial phase is the same as that under GPMIM, that is, in the initial stage, the adaptive algorithm does not have access to information on the frequency of invocation of service parameters, so the key selection method cannot optimize the efficiency of service retrieval in the initial stage.
It can be seen from Figures 14 and 15 that the proposed adaptive key selection method can significantly improve the service retrieval efficiency in both GPMIM and LPMIM under the conditions of non-average distribution of service invocation frequency and unknown distribution probabilities.

Performance of the five key selection methods for service addition in GPMIM and LPMIM
The purpose of this experiment is to test the effect of the five key selection methods on the efficiency of service addition in GPMIM and LPMIM under the condition of unequal frequency of service invocations.When the frequency of service invocation is not evenly distributed and the distribution changes dynamically, the adaptive key selection method proposed in this article can effectively improve service retrieval efficiency.However, as shown in Figure 16, the service addition efficiency of the adaptive key selection method is low under GPMIM.Herein, LPMIM is proposed to improve the service addition efficiency of the adaptive key selection method.for multiple key classes.On the contrary, in LPMIM, the service addition algorithms corresponding to all the key selection methods do not need to search for multiple key classes, but only for a selected key class.Thus, the service addition operations for these three key selection algorithms can save a significant amount of time.The efficiency of their service addition operations is improved by 45%, 55% and 80%, respectively.

CONCLUSION AND FUTURE RESEARCH
This article proposes LPMIM, in which local equivalence partition is introduced into the multilevel index model to replace the global equivalence partition.LPMIM improves the efficiency of service addition because the search space is reduced when the service is added.Based on LPMIM, this article further proposes the adaptive key selection method to address the issue that the least-used key selection method cannot adapt to the change of service invocation frequency over time.In the adaptive key selection method, DWF is introduced to track the change of service invocation frequency, which can reflect the change of recent service invocation frequency and provide an important reference for the service key selection.It is experimentally verified that the efficiencies of service retrieval and addition operations are close to the theoretical optimum using the adaptive key selection method in LPMIM.
Our experiments use simulated data to verify the correctness and effectiveness of the proposed method.In the future, we plan to study the deploying of the system in cloud environment to validate the effectiveness of the proposed method for the purpose of improving the efficiency of service management.

CONFLICT OF INTEREST STATEMENT
The author declares no conflict of interest.
The multilevel index model proposed byWu et al. not only improves the service retrieval efficiency but also facilitates the management of service repositories, such as the addition and deletion of services.The efficiency of the multilevel index model has made it widely used.Xu et al. 23 used a distributed hash table-based Chord algorithm to adapt service storage in a distributed environment, and proposed a multilevel index model based F I G U R E 1 Service retrieval with the inverted index

Definition 1 . 2 .
In a service repository, each service has an input parameter set, an output parameter set and a set of service attributes associated with it.Therefore, a service S can be defined as a collection of services containing an input parameter set and an output parameter set, that is, S = {•s, s•, O}, where •s is the set of input parameters, and s• is the set of output parameters.O is a set of service attributes, for example, QoS or description.F I G U R E 3The structure of the multilevel index modelF I G U R E 4The structure of GPMIM Definition Service retrieval is represented as a tuple Re (A, S) = {s| •s ⊆ A ∧ s∈ S}, where A is a given parameter set and S represents a service set.Service retrieval can be defined as the process of finding all the services whose input parameters are contained in A from the service set S, which eventually returns all the services that can be invoked under A. Definition 3. A user's request can be denoted as Q = {Q p , Q r }, where Q p is a parameter set provided by the user, and Q r is a parameter set required by the user.In addition, when the input parameter set of a service contains {a, b} and the output parameter set contains {c, d}, it can be expressed simply as s: {a, b → c, d}.

Figure 9 ,
similarly to GPMIM, each C s set contains services s with the same input and output parameters.The difference in LPMIM is that S may exist where •s i = •s j ∧ s i • = s j • and i ≠ j, but there are cases where s i and s j may belong to different similar service classes C s , respectively.In order to better understand and distinguish between the two partitions of the index structure, two specific examples of the service index structure are presented in Figures10 and 11, showing the index structure of 10 different services in GPMIM and LPMIM, respectively.Suppose a F I G U R E 10 An example of GPMIM F I G U R E 11 An example of LPMIM given set of services is: S = {s 1 : {a, b → e, f}, s 2 : {a, b → e, f}, s 3 : {a, b → e, f}, s 4 : {a, b → g, h}, s 5 : {a, b → g, l}, s 6 : {b, c → f, g}, s 7 : {b, c → f, g}, s 8 : {a, c → g, f}, s 9 : {a, c → g, f}, s 10 : {c, e → k, l}}.

F I G U R E 12
Application architecture for adaptive key selection methods F I G U R E 13 Number and frequency of invocations of the service parameter p j over time

Figure 15
Figure15presents the service retrieval time of LPMIM formed by the service addition operation corresponding to the five key selection methods.The performance is generally consistent with that of GPMIM, which indicates that LPMIM does not result in a loss of service retrieval performance.The retrieval performance of the service repository corresponding to the adaptive key selection method remains close to the retrieval

Figure 16
depicts the service addition times in GPMIM for the service addition algorithms corresponding to the five key selection methods.The linear congruence operation of the designated key selection method is simple and efficient, as its corresponding service addition algorithm does not need to search for multiple key classes, but only needs to select the unique key class according to the key selection method, thus exhibiting the highest efficiency of service addition.The service addition algorithm corresponding F I G U R E 16 Service addition time of five key selection methods under GPMIM with unequal distribution of retrieval parameters F I G U R E 17 Service addition time of five key selection methods under LPMIM with unequal distribution of retrieval parameters to the least-used key selection method does not need to search for multiple key classes, but only needs to search for the uniquely selected key class.However, it results in the formation of a sizable key class, causing the services belonging to that corresponding key class to consume a certain amount of time when inserted, thus its service addition consumes more time than the service addition algorithm corresponding to the designated key selection method.The proposed adaptive key selection method, the original key selection method and the random key selection method involve the search for multiple key classes, thus incurring a longer service addition time.

Figure 17
presents the service addition time of the five key selection methods under LPMIM.The random key selection method and the designated key selection method characterize the least incurred time to add services, because their key selection algorithms are the simplest with minimal computation.The original key selection method involves a certain amount of computation and therefore requires more time to add services than the random key selection method and the designated key selection method.Although the proposed adaptive key selection method and the least-used key selection method characterize simple arithmetic operations, their corresponding service addition operations may result in the formation of larger key classes.Thus, these two methods consume notable time when key class members are inserted, thereby characterizing longer service addition time.

Figure 18
Figure 18 compares the service addition time of the five key selection methods under GPMIM and LPMIM.In GPMIM, the service addition operations for the adaptive key selection algorithm, the original key selection algorithm and the random key selection algorithm all need to search