# Research on the Revolution of Multidimensional Learning Space in the Big Data Environment

Authors: Weihua Huang
Journal: Complexity
 (2021)

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## Abstract

Multiuser fair sharing of clusters is a classic problem in cluster construction. However, the cluster computing system for hybrid big data applications has the characteristics of heterogeneous requirements, which makes more and more cluster resource managers support fine-grained multidimensional learning resource management. In this context, it is oriented to multiusers of multidimensional learning resources. Shared clusters have become a new topic. A single consideration of a fair-shared cluster will result in a huge waste of resources in the context of discrete and dynamic resource allocation. Fairness and efficiency of cluster resource sharing for multidimensional learning resources are equally important. This paper studies big data processing technology and representative systems and analyzes multidimensional analysis and performance optimization technology. This article discusses the importance of discrete multidimensional learning resource allocation optimization in dynamic scenarios. At the same time, in view of the fact that most of the resources of the big data application cluster system are supplied to large jobs that account for a small proportion of job submissions, while the small jobs that account for a large proportion only use the characteristics of a small part of the system’s resources, the expected residual multidimensionality of large-scale work is proposed. The server with the least learning resources is allocated first, and only fair strategies are considered for small assignments. The topic index is distributed and stored on the system to realize the parallel processing of search to improve the efficiency of search processing. The effectiveness of RDIBT is verified through experimental simulation. The results show that RDIBT has higher performance than LSII index technology in index creation speed and search response speed. In addition, RDIBT can also ensure the scalability of the index system.


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## Body

## 1. Introduction

For multidimensional analysis of big data, sometimes the timeliness of analysis tasks is the most critical indicator [1]. Analysts are required to quickly dig out commercial value or useful information from massive data and provide the analysis results to decision-makers in a timely manner to support decision-making. There are many difficulties in how to quickly discover valuable information from massive amounts of data. Due to the large amount of data and high dimensionality, it is difficult to analyze big data in a multidimensional manner. And, when multidimensional analysis of massive data is usually accompanied by a large number of complex operations (such as aggregate query), the efficiency of the analysis task is low [2]. At the same time, despite the rapid development of the computer industry, the level of computer hardware has also been greatly improved. Dedicated high-performance hardware devices are expensive, and support for complex calculations of massive data is still limited. Analysts are facing a severe test of how to quickly discover hidden value from massive amounts of data [3].The results of multidimensional data analysis provide data support for decision makers and help transform the multidimensional learning space. In addition to operation management, user viscosity also requires forward-looking strategic planning. If the multidimensional learning space is to survive in the complex and changeable environment and win in the increasingly fierce competition, managers need to quickly and accurately dig out valuable information from the complex product operation data and grasp it according to the development trend of the data [4]. The OLAP system satisfies the demand side to explore data from all possible dimensions because they do not know the final data they want from the beginning. It is impossible to rely on fixed reports to meet the demand; at the same time, it prevents developers from being affected by temporary access. The suffering is of great significance to improving work efficiency and optimizing data construction [5].In real multidimensional analysis tasks, sometimes calculating completely accurate results will cause a lot of time overhead. In order to pursue the timeliness of query response, appropriate errors can be tolerated. Approximate query processing technology has been widely used in data warehouses for a long time. Its basic idea is to quickly return an approximate accurate query result by querying a small amount of data that can represent the characteristics of the overall data. Therefore, approximate query processing technology can be applied to the multidimensional analysis of big data to improve the time-consuming calculation of aggregate functions such as count, sum, and avg, and the main purpose is to be within an acceptable error range. Approximate query processing technology is used in the multidimensional analysis of big data; without increasing hardware costs, it can significantly improve the efficiency of multidimensional analysis tasks, significantly shorten the cycle of analysis tasks, can quickly discover hidden knowledge from massive data, and make decisions quickly.Big data processing technology is the basis for big data analysis. This article introduces the big data processing technology and processing model, analyzes their typical application systems using open source systems as examples, then studies the multidimensional analysis technology, and analyzes the performance optimization technology of the multidimensional analysis; followed by the multidimensional analysis, approximate query processing technology in performance optimization technology is discussed. Efficient and fair sharing of cluster resources is an effective way to improve system resource utilization. In the context of multidimensional learning resource management in a hybrid big data application cluster system, shared clusters not only need to consider fairness but also the efficiency of sharing is equally important. Based on these considerations, this research proposes a dynamic allocation method of multidimensional learning resources that is aware of resource allocation efficiency. This approach takes into account the following characteristics: providing most of the resources of the clustering system of the big data analysis application to large jobs with a small percentage of submissions and proposing an approach for resource requests for large job tasks, with the expectation that the least remaining resources take priority over the server and exclude small resources. The impact of job resource requests on resource allocation efficiency. We use the dataset to verify the effectiveness of the indexing technique. The results show that the index structure can quickly index the learning content and has high query processing efficiency.


### 1.1. Related Work

With the development of cloud computing technology and Internet technology, big data exists in all aspects of human life [6]. Users of big data application systems still require the system to respond quickly to operational requests. In order to meet the needs of users, the system cannot only adapt to the analysis and processing needs of big data by optimizing the data processing program but also provide a good data platform for the upper-level analysis and processing by optimizing the bottom-level data organization structure. Because in a distributed environment, the data processing mode of the big data system has been transformed into “computing close to the data,” and the location of the data block has a direct impact on the system load, which can directly affect the performance of analysis and processing [7].Relevant scholars, respectively, pointed out that, in the data management system under the Share Nothing (SN) structure and the Decouple Storage (DS) structure, when the load of each node is uneven, data blocks are migrated without affecting the normal operation of the system [8]. The researchers put forward a data distribution and migration strategy based on market rules for the uneven load of the system under the massive data management system. This method can also dynamically migrate data without affecting the normal operation of the system. The biggest advantage of these two methods is that they do not affect the normal operation of the system, try to make the system performance jitter as small as possible, and can make the system load in a relatively balanced state after the data migration is completed [9].When traditional relational data management technology deals with very large datasets, it mainly improves the computing power of a single node through vertical expansion (improving the computer hardware environment, such as increasing CPU and increasing memory). This method has high requirements for hardware equipment, high cost, and poor scalability of the multidimensional learning space, which is not enough to meet the requirements of big data analysis [10]. Therefore, the industry proposes to process and manage big data based on large-scale clusters. That is, through horizontal expansion, computing nodes are added as needed to realize and support big data analysis.In the initial big data application system, a single-dimensional resource management mode is usually adopted [11]. For example, the MapReduce cluster system divides server resources into several blocks of fixed size. In this period, in order to improve the resource utilization of the system, the main reliance on optimizing the division of jobs and designing more flexible “slots” did not consider the differences in job requirements for different types of resources, and there was a large waste of resources [12]. With the development of the big data application cluster system, the Hadoop 2.0 Yarn system has supported the cluster system for multidimensional learning resource management, and the resource request of a task is defined as a resource container of multiple dimensions [13]. The multidimensional learning resource management method greatly improves the utilization of system resources, but also poses higher optimization challenges to the optimization management of cluster system resources [14].In order to improve the scalability of the SN distributed database, related scholars proposed a graph-based data partitioning method, Schism, based on the characteristics of the operation [15]. This method uses a graph to represent the operation of the database (tuples or groups of tuples represent the vertices of the graph). The operation represents the edge of the graph, and the two vertices connecting the operation edge represent the tuples involved in the operation. They use the graph partition algorithm to divide the operation graph, and in the division process, the division result is required to have a minimum cut to minimize the operation across blocks. In the end, the goal of improving the efficiency of operation and processing is achieved. Researchers have proposed a new partitioning technology for the performance problems caused by the existing partitioning strategy in the application of very large databases without considering the access mode of the operation [16]. This technology mainly aims at newly added data and divides them by considering the affinity between these data and the query, so as to improve the performance of operation processing. Relevant scholars have proposed a dynamic data partition strategy for the part of the data involved in the query in response to the problem of large-scale distributed processing that will bring a large amount of data transmission [17]. This strategy has been applied in the Microsoft SCOPE system. Relevant scholars proposed to dynamically distribute data blocks according to the changes in the access frequency of data blocks and proposed a threshold algorithm based on access frequency to dynamically distribute data [18]. This method mainly focuses on the appropriate migration and distribution of data blocks according to load changes under the change of the data query mode. Researchers are comprehensively considering changes in data block access frequency and data movement costs to decide whether to redistribute data blocks [19–25].


## 1.1. Related Work

With the development of cloud computing technology and Internet technology, big data exists in all aspects of human life [6]. Users of big data application systems still require the system to respond quickly to operational requests. In order to meet the needs of users, the system cannot only adapt to the analysis and processing needs of big data by optimizing the data processing program but also provide a good data platform for the upper-level analysis and processing by optimizing the bottom-level data organization structure. Because in a distributed environment, the data processing mode of the big data system has been transformed into “computing close to the data,” and the location of the data block has a direct impact on the system load, which can directly affect the performance of analysis and processing [7].Relevant scholars, respectively, pointed out that, in the data management system under the Share Nothing (SN) structure and the Decouple Storage (DS) structure, when the load of each node is uneven, data blocks are migrated without affecting the normal operation of the system [8]. The researchers put forward a data distribution and migration strategy based on market rules for the uneven load of the system under the massive data management system. This method can also dynamically migrate data without affecting the normal operation of the system. The biggest advantage of these two methods is that they do not affect the normal operation of the system, try to make the system performance jitter as small as possible, and can make the system load in a relatively balanced state after the data migration is completed [9].When traditional relational data management technology deals with very large datasets, it mainly improves the computing power of a single node through vertical expansion (improving the computer hardware environment, such as increasing CPU and increasing memory). This method has high requirements for hardware equipment, high cost, and poor scalability of the multidimensional learning space, which is not enough to meet the requirements of big data analysis [10]. Therefore, the industry proposes to process and manage big data based on large-scale clusters. That is, through horizontal expansion, computing nodes are added as needed to realize and support big data analysis.In the initial big data application system, a single-dimensional resource management mode is usually adopted [11]. For example, the MapReduce cluster system divides server resources into several blocks of fixed size. In this period, in order to improve the resource utilization of the system, the main reliance on optimizing the division of jobs and designing more flexible “slots” did not consider the differences in job requirements for different types of resources, and there was a large waste of resources [12]. With the development of the big data application cluster system, the Hadoop 2.0 Yarn system has supported the cluster system for multidimensional learning resource management, and the resource request of a task is defined as a resource container of multiple dimensions [13]. The multidimensional learning resource management method greatly improves the utilization of system resources, but also poses higher optimization challenges to the optimization management of cluster system resources [14].In order to improve the scalability of the SN distributed database, related scholars proposed a graph-based data partitioning method, Schism, based on the characteristics of the operation [15]. This method uses a graph to represent the operation of the database (tuples or groups of tuples represent the vertices of the graph). The operation represents the edge of the graph, and the two vertices connecting the operation edge represent the tuples involved in the operation. They use the graph partition algorithm to divide the operation graph, and in the division process, the division result is required to have a minimum cut to minimize the operation across blocks. In the end, the goal of improving the efficiency of operation and processing is achieved. Researchers have proposed a new partitioning technology for the performance problems caused by the existing partitioning strategy in the application of very large databases without considering the access mode of the operation [16]. This technology mainly aims at newly added data and divides them by considering the affinity between these data and the query, so as to improve the performance of operation processing. Relevant scholars have proposed a dynamic data partition strategy for the part of the data involved in the query in response to the problem of large-scale distributed processing that will bring a large amount of data transmission [17]. This strategy has been applied in the Microsoft SCOPE system. Relevant scholars proposed to dynamically distribute data blocks according to the changes in the access frequency of data blocks and proposed a threshold algorithm based on access frequency to dynamically distribute data [18]. This method mainly focuses on the appropriate migration and distribution of data blocks according to load changes under the change of the data query mode. Researchers are comprehensively considering changes in data block access frequency and data movement costs to decide whether to redistribute data blocks [19–25].


## 2. Key Technologies of Multidimensional Analysis in Big Data Environment

### 2.1. Big Data Processing Technology

#### 2.1.1. Big Data Batch Processing Technology

Compared with processing all data at once, big data batch processing divides a large batch of data into several small blocks, processes only one of the small blocks at a time, and executes them in batches in sequence. The data must be stored in the hard disk, and once the user submits the processing command, the task can no longer be intervened during the entire execution process, and the result can be output only when all tasks are executed. Therefore, in big data analysis, if you need to access all datasets to get the analysis results, you must use batch processing for business processing. The big data batch processing model is shown in Figure1.Figure 1
Big data batch processing model.Hadoop is a typical big data batch processing architecture. When using Hadoop for data processing, if the problem has been clearly analyzed, you can write a MapReduce program to process the data. The big data warehouse Hive system based on this framework can realize multidimensional analysis of massive data. Hive stores massive amounts of static data in the distributed file system HDFS and then distributes computing tasks to each data node through the MapReduce parallel computing framework, thereby realizing parallel computing and value discovery of massive data. Its advantage is that it can analyze the complete set of data and does not require expensive computer hardware.The intermediate results generated by Hive execution of the query need to be continuously written back to the HDFS distributed file system, so each task needs to read and write to the disk multiple times, so it is usually time-consuming, even the simplest query may take several minutes. And, after the task is submitted, the user is not allowed to control the execution of the task, so when the result is seriously wrong, more time will be wasted, which is also a common problem of all batch processing systems. Therefore, batch data processing is suitable for large-scale data processing jobs that do not require high response time and are relatively mature in business.


#### 2.1.2. Big Data Interactive Processing Technology

Compared with the batch processing mode, big data interactive processing emphasizes the timeliness of data processing. In the process of data processing, the user submits tasks to the system through human-computer interaction, and the processing results can be quickly returned. The user then gradually completes the operation according to the acquired information and finally completes the analysis task. Big data interactive processing is mainly used for query and analysis type calculations, such as interactive ad hoc query and analysis. Once a user submits a query, it needs to respond in a very short time; during the execution of the analysis, the user is allowed to modify the operation appropriately. Typical systems are Facebook Presto and Apache Drill.Presto adopts the Master-Slave architecture, including one Presto coordinator node and multiple worker nodes. The query is submitted from the client (such as Presto CLI) to the coordinator, and then, the coordinator parses the query, then generates the corresponding execution plan, and assigns the execution task to the worker node; the worker node is responsible for executing the actual query task and is responsible for interacting with HDFS to read data. Presto also provides pluggable connectors for querying data and supports accessing data from multiple data sources. If Hive connector is configured, a Hive MetaStore service needs to be configured to provide Hive meta-information for Presto. Presto abandoned the MapReduce computing architecture. All calculations are completely based on memory, which may cause memory overflow and has no fault tolerance measures. If a task fails, the entire query will fail. The processing of Presto data is shown in Figure2.Figure 2
Processing of Presto data.


#### 2.1.3. Big Data Streaming Technology

Samza’s stream unit is neither a tuple nor a Dstream, but a series of divided, reproducible, multicast, and stateless message sequences. When processing the data stream, the data stream will be divided into several partitions. Each partition consists of an ordered sequence of read-only messages. Each message has a unique ID (amount of bias) and is ordered separately. Samza also supports batch processing, such as processing multiple messages successively from the same stream partition. Figure3 shows the principle diagram of Samza streaming.Figure 3
Schematic diagram of Samza streaming processing.


### 2.2. Multidimensional Analysis Technology

Multidimensional data analysis refers to a data analysis process that summarizes data across multiple dimensions and displays query results to users. The definition of dimension is very important for multidimensional analysis. It is a collection of several attributes, which represents a specific angle of observation data, such as time and place. Online analysis and processing is a specific solution for realizing multidimensional data analysis. The data is combined in a multidimensional form to form a data cube structure, allowing users to access and process online data for a specific topic. OLAP technology has become the preferred solution for multidimensional data analysis. The core of OLAP technology is to build a data cube, which is composed of dimensions and measures.


#### 2.2.1. ROLAP Technology

ROLAP uses relational or expanded relational DBMS to store and manage the data that needs to be analyzed and divides the multidimensional structure into a number of two-dimensional fact tables and dimensional table structures for storage. The fact table contains a large number of records, which are used to store specific business data, specifically to store the measures at the intersection of dimensions and the key values of each dimension; the dimension table is used to store the dimension information of the observation data, and it only contains the attributes recorded in the fact table details.In practical applications, in order to improve the analysis efficiency of ROLAP, a batch of physical views can be selectively defined according to specific needs, and these views can be stored in the database. For example, for queries with a high query frequency and a large amount of calculation, the query results are stored on the hard disk. When the OLAP server receives the query request, the stored and calculated query results are first used to execute the query, thereby improving the query performance. At the same time, the RDBMS can be optimized accordingly, such as parallel storage, parallel query, parallel data management, query optimization based on cost estimation, bitmap index, and SQL OLAP extension. Accessing relational databases through multidimensional logic model DMR for multidimensional analysis belongs to ROLAP.


#### 2.2.2. MOLAP Technology

MOLAP physically stores the multidimensional data used in OLAP analysis in the form of a multidimensional array, forming a “cube” structure. The attribute value of the dimension is mapped to the subscript value or the range of the subscript of the multidimensional array, and the summary data is stored in the unit of the array as the value of the multidimensional array. Because MOLAP adopts a new storage structure, starting from the physical layer, it is also called physical OLAP, while ROLAP is mainly implemented through some software tools or intermediate software, and the physical layer still uses the storage structure of a relational database, so it is called virtual OLAP.


#### 2.2.3. HOLAP Technology

There are advantages and disadvantages to using ROLAP and MOLAP. ROLAP’s multidimensional learning space has better scalability, can handle large-scale datasets, and has higher flexibility and higher adaptability to data changes, but the query efficiency is relatively low, and the multidimensional computing capability is weak; MOLAP has higher query efficiency and supports complex calculations between dimensions, but the dataset that can be processed is limited and requires higher computer hardware.The design principles and system architectures of ROLAP and MOLAP are obviously different, and they have their own usage scenarios. In order to support more OLAP applications, the industry has proposed a hybrid OLAP. HOLAP organically combines ROLAP and MOLAP and, at the same time, has the advantages of both, which can satisfy more complex analysis requests.


## 2.1. Big Data Processing Technology

### 2.1.1. Big Data Batch Processing Technology

Compared with processing all data at once, big data batch processing divides a large batch of data into several small blocks, processes only one of the small blocks at a time, and executes them in batches in sequence. The data must be stored in the hard disk, and once the user submits the processing command, the task can no longer be intervened during the entire execution process, and the result can be output only when all tasks are executed. Therefore, in big data analysis, if you need to access all datasets to get the analysis results, you must use batch processing for business processing. The big data batch processing model is shown in Figure1.Figure 1
Big data batch processing model.Hadoop is a typical big data batch processing architecture. When using Hadoop for data processing, if the problem has been clearly analyzed, you can write a MapReduce program to process the data. The big data warehouse Hive system based on this framework can realize multidimensional analysis of massive data. Hive stores massive amounts of static data in the distributed file system HDFS and then distributes computing tasks to each data node through the MapReduce parallel computing framework, thereby realizing parallel computing and value discovery of massive data. Its advantage is that it can analyze the complete set of data and does not require expensive computer hardware.The intermediate results generated by Hive execution of the query need to be continuously written back to the HDFS distributed file system, so each task needs to read and write to the disk multiple times, so it is usually time-consuming, even the simplest query may take several minutes. And, after the task is submitted, the user is not allowed to control the execution of the task, so when the result is seriously wrong, more time will be wasted, which is also a common problem of all batch processing systems. Therefore, batch data processing is suitable for large-scale data processing jobs that do not require high response time and are relatively mature in business.


### 2.1.2. Big Data Interactive Processing Technology

Compared with the batch processing mode, big data interactive processing emphasizes the timeliness of data processing. In the process of data processing, the user submits tasks to the system through human-computer interaction, and the processing results can be quickly returned. The user then gradually completes the operation according to the acquired information and finally completes the analysis task. Big data interactive processing is mainly used for query and analysis type calculations, such as interactive ad hoc query and analysis. Once a user submits a query, it needs to respond in a very short time; during the execution of the analysis, the user is allowed to modify the operation appropriately. Typical systems are Facebook Presto and Apache Drill.Presto adopts the Master-Slave architecture, including one Presto coordinator node and multiple worker nodes. The query is submitted from the client (such as Presto CLI) to the coordinator, and then, the coordinator parses the query, then generates the corresponding execution plan, and assigns the execution task to the worker node; the worker node is responsible for executing the actual query task and is responsible for interacting with HDFS to read data. Presto also provides pluggable connectors for querying data and supports accessing data from multiple data sources. If Hive connector is configured, a Hive MetaStore service needs to be configured to provide Hive meta-information for Presto. Presto abandoned the MapReduce computing architecture. All calculations are completely based on memory, which may cause memory overflow and has no fault tolerance measures. If a task fails, the entire query will fail. The processing of Presto data is shown in Figure2.Figure 2
Processing of Presto data.


### 2.1.3. Big Data Streaming Technology

Samza’s stream unit is neither a tuple nor a Dstream, but a series of divided, reproducible, multicast, and stateless message sequences. When processing the data stream, the data stream will be divided into several partitions. Each partition consists of an ordered sequence of read-only messages. Each message has a unique ID (amount of bias) and is ordered separately. Samza also supports batch processing, such as processing multiple messages successively from the same stream partition. Figure3 shows the principle diagram of Samza streaming.Figure 3
Schematic diagram of Samza streaming processing.


## 2.1.1. Big Data Batch Processing Technology

Compared with processing all data at once, big data batch processing divides a large batch of data into several small blocks, processes only one of the small blocks at a time, and executes them in batches in sequence. The data must be stored in the hard disk, and once the user submits the processing command, the task can no longer be intervened during the entire execution process, and the result can be output only when all tasks are executed. Therefore, in big data analysis, if you need to access all datasets to get the analysis results, you must use batch processing for business processing. The big data batch processing model is shown in Figure1.Figure 1
Big data batch processing model.Hadoop is a typical big data batch processing architecture. When using Hadoop for data processing, if the problem has been clearly analyzed, you can write a MapReduce program to process the data. The big data warehouse Hive system based on this framework can realize multidimensional analysis of massive data. Hive stores massive amounts of static data in the distributed file system HDFS and then distributes computing tasks to each data node through the MapReduce parallel computing framework, thereby realizing parallel computing and value discovery of massive data. Its advantage is that it can analyze the complete set of data and does not require expensive computer hardware.The intermediate results generated by Hive execution of the query need to be continuously written back to the HDFS distributed file system, so each task needs to read and write to the disk multiple times, so it is usually time-consuming, even the simplest query may take several minutes. And, after the task is submitted, the user is not allowed to control the execution of the task, so when the result is seriously wrong, more time will be wasted, which is also a common problem of all batch processing systems. Therefore, batch data processing is suitable for large-scale data processing jobs that do not require high response time and are relatively mature in business.


## 2.1.2. Big Data Interactive Processing Technology

Compared with the batch processing mode, big data interactive processing emphasizes the timeliness of data processing. In the process of data processing, the user submits tasks to the system through human-computer interaction, and the processing results can be quickly returned. The user then gradually completes the operation according to the acquired information and finally completes the analysis task. Big data interactive processing is mainly used for query and analysis type calculations, such as interactive ad hoc query and analysis. Once a user submits a query, it needs to respond in a very short time; during the execution of the analysis, the user is allowed to modify the operation appropriately. Typical systems are Facebook Presto and Apache Drill.Presto adopts the Master-Slave architecture, including one Presto coordinator node and multiple worker nodes. The query is submitted from the client (such as Presto CLI) to the coordinator, and then, the coordinator parses the query, then generates the corresponding execution plan, and assigns the execution task to the worker node; the worker node is responsible for executing the actual query task and is responsible for interacting with HDFS to read data. Presto also provides pluggable connectors for querying data and supports accessing data from multiple data sources. If Hive connector is configured, a Hive MetaStore service needs to be configured to provide Hive meta-information for Presto. Presto abandoned the MapReduce computing architecture. All calculations are completely based on memory, which may cause memory overflow and has no fault tolerance measures. If a task fails, the entire query will fail. The processing of Presto data is shown in Figure2.Figure 2
Processing of Presto data.


## 2.1.3. Big Data Streaming Technology

Samza’s stream unit is neither a tuple nor a Dstream, but a series of divided, reproducible, multicast, and stateless message sequences. When processing the data stream, the data stream will be divided into several partitions. Each partition consists of an ordered sequence of read-only messages. Each message has a unique ID (amount of bias) and is ordered separately. Samza also supports batch processing, such as processing multiple messages successively from the same stream partition. Figure3 shows the principle diagram of Samza streaming.Figure 3
Schematic diagram of Samza streaming processing.


## 2.2. Multidimensional Analysis Technology

Multidimensional data analysis refers to a data analysis process that summarizes data across multiple dimensions and displays query results to users. The definition of dimension is very important for multidimensional analysis. It is a collection of several attributes, which represents a specific angle of observation data, such as time and place. Online analysis and processing is a specific solution for realizing multidimensional data analysis. The data is combined in a multidimensional form to form a data cube structure, allowing users to access and process online data for a specific topic. OLAP technology has become the preferred solution for multidimensional data analysis. The core of OLAP technology is to build a data cube, which is composed of dimensions and measures.


### 2.2.1. ROLAP Technology

ROLAP uses relational or expanded relational DBMS to store and manage the data that needs to be analyzed and divides the multidimensional structure into a number of two-dimensional fact tables and dimensional table structures for storage. The fact table contains a large number of records, which are used to store specific business data, specifically to store the measures at the intersection of dimensions and the key values of each dimension; the dimension table is used to store the dimension information of the observation data, and it only contains the attributes recorded in the fact table details.In practical applications, in order to improve the analysis efficiency of ROLAP, a batch of physical views can be selectively defined according to specific needs, and these views can be stored in the database. For example, for queries with a high query frequency and a large amount of calculation, the query results are stored on the hard disk. When the OLAP server receives the query request, the stored and calculated query results are first used to execute the query, thereby improving the query performance. At the same time, the RDBMS can be optimized accordingly, such as parallel storage, parallel query, parallel data management, query optimization based on cost estimation, bitmap index, and SQL OLAP extension. Accessing relational databases through multidimensional logic model DMR for multidimensional analysis belongs to ROLAP.


### 2.2.2. MOLAP Technology

MOLAP physically stores the multidimensional data used in OLAP analysis in the form of a multidimensional array, forming a “cube” structure. The attribute value of the dimension is mapped to the subscript value or the range of the subscript of the multidimensional array, and the summary data is stored in the unit of the array as the value of the multidimensional array. Because MOLAP adopts a new storage structure, starting from the physical layer, it is also called physical OLAP, while ROLAP is mainly implemented through some software tools or intermediate software, and the physical layer still uses the storage structure of a relational database, so it is called virtual OLAP.


### 2.2.3. HOLAP Technology

There are advantages and disadvantages to using ROLAP and MOLAP. ROLAP’s multidimensional learning space has better scalability, can handle large-scale datasets, and has higher flexibility and higher adaptability to data changes, but the query efficiency is relatively low, and the multidimensional computing capability is weak; MOLAP has higher query efficiency and supports complex calculations between dimensions, but the dataset that can be processed is limited and requires higher computer hardware.The design principles and system architectures of ROLAP and MOLAP are obviously different, and they have their own usage scenarios. In order to support more OLAP applications, the industry has proposed a hybrid OLAP. HOLAP organically combines ROLAP and MOLAP and, at the same time, has the advantages of both, which can satisfy more complex analysis requests.


## 2.2.1. ROLAP Technology

ROLAP uses relational or expanded relational DBMS to store and manage the data that needs to be analyzed and divides the multidimensional structure into a number of two-dimensional fact tables and dimensional table structures for storage. The fact table contains a large number of records, which are used to store specific business data, specifically to store the measures at the intersection of dimensions and the key values of each dimension; the dimension table is used to store the dimension information of the observation data, and it only contains the attributes recorded in the fact table details.In practical applications, in order to improve the analysis efficiency of ROLAP, a batch of physical views can be selectively defined according to specific needs, and these views can be stored in the database. For example, for queries with a high query frequency and a large amount of calculation, the query results are stored on the hard disk. When the OLAP server receives the query request, the stored and calculated query results are first used to execute the query, thereby improving the query performance. At the same time, the RDBMS can be optimized accordingly, such as parallel storage, parallel query, parallel data management, query optimization based on cost estimation, bitmap index, and SQL OLAP extension. Accessing relational databases through multidimensional logic model DMR for multidimensional analysis belongs to ROLAP.


## 2.2.2. MOLAP Technology

MOLAP physically stores the multidimensional data used in OLAP analysis in the form of a multidimensional array, forming a “cube” structure. The attribute value of the dimension is mapped to the subscript value or the range of the subscript of the multidimensional array, and the summary data is stored in the unit of the array as the value of the multidimensional array. Because MOLAP adopts a new storage structure, starting from the physical layer, it is also called physical OLAP, while ROLAP is mainly implemented through some software tools or intermediate software, and the physical layer still uses the storage structure of a relational database, so it is called virtual OLAP.


## 2.2.3. HOLAP Technology

There are advantages and disadvantages to using ROLAP and MOLAP. ROLAP’s multidimensional learning space has better scalability, can handle large-scale datasets, and has higher flexibility and higher adaptability to data changes, but the query efficiency is relatively low, and the multidimensional computing capability is weak; MOLAP has higher query efficiency and supports complex calculations between dimensions, but the dataset that can be processed is limited and requires higher computer hardware.The design principles and system architectures of ROLAP and MOLAP are obviously different, and they have their own usage scenarios. In order to support more OLAP applications, the industry has proposed a hybrid OLAP. HOLAP organically combines ROLAP and MOLAP and, at the same time, has the advantages of both, which can satisfy more complex analysis requests.


## 3. Fair Distribution of Dynamic Discrete Multidimensional Learning Resources with Efficiency Perception

### 3.1. Resource Distribution of Dynamic Discrete Learning Space

After the user submits the application to YARN, the resource manager allocates the first “Container” for the application and asks his corresponding node manager to start the corresponding application management program in the “Container.” The application management program uses the polling method to apply for and receive resources from the resource manager through the RPC protocol. The calculation node manager sends information at a fixed time and reports back the current node’s resource usage and the operation of the “Container” it contains. YARN’s resource management architecture is shown in Figure4.Figure 4
YARN’s resource management architecture.Through the allocation process, we can find that the resource allocation process is not strictly continuous allocation, but the situation where existing resources are updated at intervals (typically greater than 300 milliseconds) is mainly due to the load on the resource manager and node manager functions. It is such a compromise operation that makes the cluster resources distributed on different servers with a high probability at a certain moment. Assuming thatg “containers” are distributed on n servers, the probability that x (1 ≤ x ≤ g) “Containers” are distributed on different servers is(1)px=1−n1−x.Suppose the average service time of system tasks (each task corresponds to a “Container”) is 1/t. Then, in a cluster system with g tasks, the expected number of tasks released by the system within the interval ∆t (also known as “Container”) is ∆t × g × t. Therefore, within ∆t, when the system has resources released, the probability that the resources are distributed on different servers can be defined as(2)pΔt=1−n1−gtΔt,gtΔt>0.In order to view the change of this probability more intuitively, we setg = 4n (that is, an average server is divided into 4 “Containers”). At present, the heartbeat cycle of cluster systems for big data applications is generally greater than ≥300 ms. In addition, the larger the cluster size, the greater the possibility that resources are distributed on different servers. It can be seen that, in the process of dynamic resource allocation, it is a very common scenario for resources to be distributed on different servers.


### 3.2. Fairness Constraint Efficiency Optimization Multidimensional Learning Resource Allocation

In this research, we have defined the dynamic sharing of multidimensional learning resources for large-scale cluster systems for big data applications based on various practical application constraints.Supposedti is the amount of shared resource dominance of user i at time t. According to the definition of dominance resources, in the dynamic discrete learning space resource allocation scenario, dti can be defined as(3)dti=maxj=0,…,m−1∏l=0n−1At⋅∏l=0n−1Rlj,where At is the number of jth dimension resources allocated by user i on server l at time t and Rlj is the total supply of jth dimension resources of server l. This research defines the problem of efficient and fair multidimensional learning resource allocation as follows:(4)U=maxUA,j,t=∏i=0k−1∏l=0n−1At,∏l=0n−1At<Rlj,j=0,1,2,…,m−1.This ensures that the resource requests of all users on the server 1 are less than the server’s own supply capacity. The efficient and fair allocation of multidimensional learning resources is a constrained combinatorial optimization problem. The definition of this research question considers the practical application needs of dynamic discrete learning space resource allocation and the pursuit of system resource allocation efficiency.


### 3.3. Analysis of Job Resource Request Characteristics of Big Data Application Cluster System

We analyzed the situation of Google’s one-month job resource request. The focus is on the distribution of the job scale (we use the number of subtasks in the job to measure) distribution in our research.Most of the jobs in cluster applications are small jobs (jobs with small computing scales), but most of the resources in the cluster provide a small proportion of large jobs (jobs with large computing scales). In fact, it is not difficult to find the cause of this phenomenon as long as we further analyze it carefully. In hybrid big data analysis applications, most of them are query analysis tasks, and only a few are large-scale batch processing or learning tasks, and there is a huge gap in the computing scale between the two. For example, the batch processing job of a web crawler for Clueweb2012 contains 27 TB of 700 million web pages data.


### 3.4. Fair Distribution of Multidimensional Learning Resources Based on Dynamic Allocation Efficiency Perception

It can be learned from the above analysis that the fair and efficient allocation of dynamic discrete multidimensional learning resources is a very meaningful topic. In addition, an important phenomenon has been observed, that is, most of the jobs submitted by many big data application cluster systems are small jobs, and most of the system’s resources are supplied to a few large jobs. In other words, the fairness of the cluster system is mainly affected by small operations, while the efficiency of resource allocation is mainly determined by large operations. Inspired by this observation, this research proposes a dynamic multidimensional learning resource allocation method that expects the least remaining resources to be given priority to the server for resource allocation for large assignments, while only considering fairness for small assignments. This method is called an efficiency-sensing fair allocation method for dynamic discrete multidimensional resource allocation. This method can be applied to the dynamic resource supply framework of the big data application cluster system with the following characteristics: jobs are submitted in the form of bag-of-tasks, and the system uses clock heartbeats for resource allocation. In the proposed dynamic multidimensional learning resource allocation method, we suppose the job of useri at time t is a large-scale computing job (the resource requirements of this type of job are often not met by a server), and its subtasks are placed on server l; the remaining resources expected by the server 1 can be defined as(5)Et=∏j=0m−1Sljt−minStDt,l⟶Ft.Among them,(6)St=Rl−∏i=0k−1Ati,Ft=St−Dtj,j=0,1,2,…,m−1.The server with the least expected remaining resources for the job task of useri at time t is(7)y′=argminl=0,1,2,…,n−1Etl.In the DEF algorithm flow, the user (x′) who currently has the least resources at the present is selected according to the DRF’s rules of maximum and minimum user-dominated resources. Then, we classify the job according to the number of subtasks of the job. If the job is a large-scale computing job (large job for short), the job task selects a resource that is expected to have the least remaining resources and allocates it to it; if it is a small-scale computing job (small job for short), it will be satisfied. The resources on the required server are allocated to the job task. The algorithm runs cyclically until the system shuts down. Among them, the size evaluation of the operation calculation scale can be self-defined according to the average supply capacity of the cluster system and the actual optimization scenario.


## 3.1. Resource Distribution of Dynamic Discrete Learning Space

After the user submits the application to YARN, the resource manager allocates the first “Container” for the application and asks his corresponding node manager to start the corresponding application management program in the “Container.” The application management program uses the polling method to apply for and receive resources from the resource manager through the RPC protocol. The calculation node manager sends information at a fixed time and reports back the current node’s resource usage and the operation of the “Container” it contains. YARN’s resource management architecture is shown in Figure4.Figure 4
YARN’s resource management architecture.Through the allocation process, we can find that the resource allocation process is not strictly continuous allocation, but the situation where existing resources are updated at intervals (typically greater than 300 milliseconds) is mainly due to the load on the resource manager and node manager functions. It is such a compromise operation that makes the cluster resources distributed on different servers with a high probability at a certain moment. Assuming thatg “containers” are distributed on n servers, the probability that x (1 ≤ x ≤ g) “Containers” are distributed on different servers is(1)px=1−n1−x.Suppose the average service time of system tasks (each task corresponds to a “Container”) is 1/t. Then, in a cluster system with g tasks, the expected number of tasks released by the system within the interval ∆t (also known as “Container”) is ∆t × g × t. Therefore, within ∆t, when the system has resources released, the probability that the resources are distributed on different servers can be defined as(2)pΔt=1−n1−gtΔt,gtΔt>0.In order to view the change of this probability more intuitively, we setg = 4n (that is, an average server is divided into 4 “Containers”). At present, the heartbeat cycle of cluster systems for big data applications is generally greater than ≥300 ms. In addition, the larger the cluster size, the greater the possibility that resources are distributed on different servers. It can be seen that, in the process of dynamic resource allocation, it is a very common scenario for resources to be distributed on different servers.


## 3.2. Fairness Constraint Efficiency Optimization Multidimensional Learning Resource Allocation

In this research, we have defined the dynamic sharing of multidimensional learning resources for large-scale cluster systems for big data applications based on various practical application constraints.Supposedti is the amount of shared resource dominance of user i at time t. According to the definition of dominance resources, in the dynamic discrete learning space resource allocation scenario, dti can be defined as(3)dti=maxj=0,…,m−1∏l=0n−1At⋅∏l=0n−1Rlj,where At is the number of jth dimension resources allocated by user i on server l at time t and Rlj is the total supply of jth dimension resources of server l. This research defines the problem of efficient and fair multidimensional learning resource allocation as follows:(4)U=maxUA,j,t=∏i=0k−1∏l=0n−1At,∏l=0n−1At<Rlj,j=0,1,2,…,m−1.This ensures that the resource requests of all users on the server 1 are less than the server’s own supply capacity. The efficient and fair allocation of multidimensional learning resources is a constrained combinatorial optimization problem. The definition of this research question considers the practical application needs of dynamic discrete learning space resource allocation and the pursuit of system resource allocation efficiency.


## 3.3. Analysis of Job Resource Request Characteristics of Big Data Application Cluster System

We analyzed the situation of Google’s one-month job resource request. The focus is on the distribution of the job scale (we use the number of subtasks in the job to measure) distribution in our research.Most of the jobs in cluster applications are small jobs (jobs with small computing scales), but most of the resources in the cluster provide a small proportion of large jobs (jobs with large computing scales). In fact, it is not difficult to find the cause of this phenomenon as long as we further analyze it carefully. In hybrid big data analysis applications, most of them are query analysis tasks, and only a few are large-scale batch processing or learning tasks, and there is a huge gap in the computing scale between the two. For example, the batch processing job of a web crawler for Clueweb2012 contains 27 TB of 700 million web pages data.


## 3.4. Fair Distribution of Multidimensional Learning Resources Based on Dynamic Allocation Efficiency Perception

It can be learned from the above analysis that the fair and efficient allocation of dynamic discrete multidimensional learning resources is a very meaningful topic. In addition, an important phenomenon has been observed, that is, most of the jobs submitted by many big data application cluster systems are small jobs, and most of the system’s resources are supplied to a few large jobs. In other words, the fairness of the cluster system is mainly affected by small operations, while the efficiency of resource allocation is mainly determined by large operations. Inspired by this observation, this research proposes a dynamic multidimensional learning resource allocation method that expects the least remaining resources to be given priority to the server for resource allocation for large assignments, while only considering fairness for small assignments. This method is called an efficiency-sensing fair allocation method for dynamic discrete multidimensional resource allocation. This method can be applied to the dynamic resource supply framework of the big data application cluster system with the following characteristics: jobs are submitted in the form of bag-of-tasks, and the system uses clock heartbeats for resource allocation. In the proposed dynamic multidimensional learning resource allocation method, we suppose the job of useri at time t is a large-scale computing job (the resource requirements of this type of job are often not met by a server), and its subtasks are placed on server l; the remaining resources expected by the server 1 can be defined as(5)Et=∏j=0m−1Sljt−minStDt,l⟶Ft.Among them,(6)St=Rl−∏i=0k−1Ati,Ft=St−Dtj,j=0,1,2,…,m−1.The server with the least expected remaining resources for the job task of useri at time t is(7)y′=argminl=0,1,2,…,n−1Etl.In the DEF algorithm flow, the user (x′) who currently has the least resources at the present is selected according to the DRF’s rules of maximum and minimum user-dominated resources. Then, we classify the job according to the number of subtasks of the job. If the job is a large-scale computing job (large job for short), the job task selects a resource that is expected to have the least remaining resources and allocates it to it; if it is a small-scale computing job (small job for short), it will be satisfied. The resources on the required server are allocated to the job task. The algorithm runs cyclically until the system shuts down. Among them, the size evaluation of the operation calculation scale can be self-defined according to the average supply capacity of the cluster system and the actual optimization scenario.


## 4. Experimental Analysis

### 4.1. Effectiveness of Multidimensional Learning Space Index

This experiment measures the average cost time of each learning content index establishment by changing the number of learning content input per second, so as to measure the effectiveness of the multidimensional learning spatial index. Figure5 shows the effectiveness of the multidimensional learning space index at different times, and Figure 6 shows the effectiveness of the multidimensional learning space index under different capacities. An increase in the number of learning content per second will increase the load of the system, and the indexing process will take up more resources; an increase in the number of learning content will cause more merge and copy operations, and these operating costs are also indexing costs. Capacity can also change the capacity threshold of the index level, so its average cost time will be similar to that of time. RDIBT can create an index for tens of thousands of learning content per second. Therefore, it can be inferred that the RDIBT index mode is effective, which can quickly make newly input learning content searchable.Figure 5
The effectiveness of the multidimensional learning space index at different times.Figure 6
Effectiveness of the multidimensional learning space index under different capacities.


### 4.2. Effectiveness of Multidimensional Learning Space Search

The effectiveness of multidimensional learning space search will be measured by the average operation time of the test and the completeness of the results. It is mainly to verify the effectiveness of multidimensional learning space search by changing the input volume of learning content and search input per second and compare the efficiency of RDIBT and LSII. In the experiment, a simple version of LSII will be implemented based on the LSII design concept, and it will be deployed in the same environment as RDIBT. The reason for choosing LSII is that LSII is also a hierarchical structure, and some parameter environments of LSII are similar to RDIBT.Figure7 is a comparison of the average operating time of LSII and RDIBT when changing the number of input learning content per second. From the experimental results, we can know that the average operation time of RDIBT and LSII does not show a clear trend when the number of input learning content per second is changed. This reflects on the other side that RDIBT and LSII can perform well in index update and search processing. When the system updates the index of new learning content, it will not have a great impact on search performance. However, the average operation time of RDIBT is lower than that of LSII, that is, RDIBT has better search efficiency. This is mainly because RDIBT can greatly reduce the amount of search index required during the search process, and the search can be processed in parallel.Figure 7
The average operation time for changing the input volume of learning content.Figure8 is a comparison of the average operating time of RDIBT and LSII when the input search volume per second is changed. From the experimental results, it can be known that, as the search volume increases, the average operation time of RDIBT and LSII also increases. This is mainly because the increase in the search volume will increase the system load, and the processing nodes will use more resources for the search, which will increase the search time. At the same time, it can be known that RDIBT has higher query processing performance than LSII.Figure 8
The average operation time to change the search input volume.From the above analysis, we can know that RDIBT has higher search performance than LSII, which also proves that RDIBT can improve search performance.


### 4.3. Search Completion Rate of Multidimensional Learning Space

RDIBT is a topic-based indexing mode, so related topic indexes need to be scanned in the search. Whether a search based on this index can return a complete search is a question that users are more concerned about, and this section will test the completeness rate of multidimensional learning space search under the RDIBT index.Figure9 is a test for the completeness of search results under the condition of changing the input search volume. Changes in input search volume will not have much impact on the completeness of the results. The completeness rate of the search structure under the RDIBT index is very high, and the completeness rate is above 93%. Therefore, it can be said that the search results under RDIBT are approximately complete.Figure 9
The completeness rate of RDIBT and LSII search results.


### 4.4. Scalability of Multidimensional Learning Space

RDIBT is a distributed mode, so the scalability of the multidimensional learning space is also an important factor in evaluating the performance of the index. In the experiment, the system is initialized with 10 nodes, and then, the number of nodes is gradually increased until the system has 50 nodes. Let us measure the changes in the average cost time and average operating time of the system under each node size. The experimental results are shown in Figure10.Figure 10
The average cost time of the index under the change of node size.Figure10 shows the average cost time of indexing when the number of processing nodes is changed. The more the processing nodes, the more the average cost time will dynamically change, mainly because the new node can share the work of other nodes. Therefore, the newly added learning content can be processed on the new node. The RDIBT index structure is subject-based, so the node on which the indexing work is completed is determined by the subject of the new learning content. Therefore, the processing speedup is not linear, but it can be said to be approximately linear.


## 4.1. Effectiveness of Multidimensional Learning Space Index

This experiment measures the average cost time of each learning content index establishment by changing the number of learning content input per second, so as to measure the effectiveness of the multidimensional learning spatial index. Figure5 shows the effectiveness of the multidimensional learning space index at different times, and Figure 6 shows the effectiveness of the multidimensional learning space index under different capacities. An increase in the number of learning content per second will increase the load of the system, and the indexing process will take up more resources; an increase in the number of learning content will cause more merge and copy operations, and these operating costs are also indexing costs. Capacity can also change the capacity threshold of the index level, so its average cost time will be similar to that of time. RDIBT can create an index for tens of thousands of learning content per second. Therefore, it can be inferred that the RDIBT index mode is effective, which can quickly make newly input learning content searchable.Figure 5
The effectiveness of the multidimensional learning space index at different times.Figure 6
Effectiveness of the multidimensional learning space index under different capacities.


## 4.2. Effectiveness of Multidimensional Learning Space Search

The effectiveness of multidimensional learning space search will be measured by the average operation time of the test and the completeness of the results. It is mainly to verify the effectiveness of multidimensional learning space search by changing the input volume of learning content and search input per second and compare the efficiency of RDIBT and LSII. In the experiment, a simple version of LSII will be implemented based on the LSII design concept, and it will be deployed in the same environment as RDIBT. The reason for choosing LSII is that LSII is also a hierarchical structure, and some parameter environments of LSII are similar to RDIBT.Figure7 is a comparison of the average operating time of LSII and RDIBT when changing the number of input learning content per second. From the experimental results, we can know that the average operation time of RDIBT and LSII does not show a clear trend when the number of input learning content per second is changed. This reflects on the other side that RDIBT and LSII can perform well in index update and search processing. When the system updates the index of new learning content, it will not have a great impact on search performance. However, the average operation time of RDIBT is lower than that of LSII, that is, RDIBT has better search efficiency. This is mainly because RDIBT can greatly reduce the amount of search index required during the search process, and the search can be processed in parallel.Figure 7
The average operation time for changing the input volume of learning content.Figure8 is a comparison of the average operating time of RDIBT and LSII when the input search volume per second is changed. From the experimental results, it can be known that, as the search volume increases, the average operation time of RDIBT and LSII also increases. This is mainly because the increase in the search volume will increase the system load, and the processing nodes will use more resources for the search, which will increase the search time. At the same time, it can be known that RDIBT has higher query processing performance than LSII.Figure 8
The average operation time to change the search input volume.From the above analysis, we can know that RDIBT has higher search performance than LSII, which also proves that RDIBT can improve search performance.


## 4.3. Search Completion Rate of Multidimensional Learning Space

RDIBT is a topic-based indexing mode, so related topic indexes need to be scanned in the search. Whether a search based on this index can return a complete search is a question that users are more concerned about, and this section will test the completeness rate of multidimensional learning space search under the RDIBT index.Figure9 is a test for the completeness of search results under the condition of changing the input search volume. Changes in input search volume will not have much impact on the completeness of the results. The completeness rate of the search structure under the RDIBT index is very high, and the completeness rate is above 93%. Therefore, it can be said that the search results under RDIBT are approximately complete.Figure 9
The completeness rate of RDIBT and LSII search results.


## 4.4. Scalability of Multidimensional Learning Space

RDIBT is a distributed mode, so the scalability of the multidimensional learning space is also an important factor in evaluating the performance of the index. In the experiment, the system is initialized with 10 nodes, and then, the number of nodes is gradually increased until the system has 50 nodes. Let us measure the changes in the average cost time and average operating time of the system under each node size. The experimental results are shown in Figure10.Figure 10
The average cost time of the index under the change of node size.Figure10 shows the average cost time of indexing when the number of processing nodes is changed. The more the processing nodes, the more the average cost time will dynamically change, mainly because the new node can share the work of other nodes. Therefore, the newly added learning content can be processed on the new node. The RDIBT index structure is subject-based, so the node on which the indexing work is completed is determined by the subject of the new learning content. Therefore, the processing speedup is not linear, but it can be said to be approximately linear.


## 5. Conclusion

Multidimensional analysis technology can analyze massive data from multiple dimensions and levels and can provide powerful decision support services. At present, many big data application cluster systems have supported the supply of multidimensional learning resources. Compared with the traditional single-dimensional resource management model, this resource management model shows better resource allocation efficiency. The efficient sharing of multidimensional learning resources in cluster systems is currently attracting attention. In this part of the work, the impact of practical application constraints such as user fair sharing, discrete resource distribution, dynamic, and heterogeneous jobs on the efficient sharing of multidimensional learning resources in the cluster system is considered. The relationship between fairness and efficiency in the distribution of multidimensional learning resources is discussed, and the problem is defined as a fairness constraint efficiency optimization problem. Based on the analysis and observation of real case (Google cluster) trajectory data, the composition characteristics of the submitted job are integrated into the multidimensional learning resource allocation method. Under the premise of fairness constraints, a server with the least remaining resources is proposed to give priority to this big work. Small-scale operations only consider fair resource sharing and distribution methods. In addition, this part of the research also discusses the importance of considering resource dispersion in dynamic scenarios, which is often ignored or downplayed in traditional research. Through experiments, it can be concluded that RDIBT can quickly index the newly added learning content, so as to achieve the goal of real-time indexing. RDIBT will be able to perform operations on the index in parallel during the search process, reducing the amount of data that needs to be accessed during the search process, thereby greatly improving the search efficiency. The RDIBT index has strong scalability. When the node is expanded, the index can be expanded correspondingly so that the operating capability maintains an approximate linear acceleration ratio.



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*Source: 6583491-2021-05-19.xml*