## 1 Introduction
The primary motivation behind our focus on algorithms for urban residential vacancy rate observation is deeply rooted in the current urban development landscape. The rapid urbanization in China has led to an unprecedented expansion of cities. This growth has outpaced the capabilities of traditional vacancy rate observation methods. For instance, traditional field surveys can no longer cover large-scale newly developed areas effectively. In a certain large-scale city, as mentioned earlier, the traditional field survey method can only cover less than 30% of the newly developed areas in a year. Moreover, the data obtained from such surveys is often marred by inaccuracies due to subjective factors. Questionnaire surveys, on the other hand, face a low response rate, sometimes less than 50% in some communities, and it is difficult to ensure data integrity and accuracy. On the contrary, algorithms offer a promising solution. Their powerful data mining capabilities enable them to sift through massive amounts of complex data. For example, in the era of big data, algorithms can analyze large datasets from various sources, such as real estate transaction records, census data and remote sensing images, to extract valuable information related to residential vacancy rates. However, despite the potential of algorithms, there is currently a lack of a comprehensive understanding of how different types of algorithms, including traditional statistical learning, machine learning, deep learning and ensemble learning, perform in the context of urban residential vacancy rate observation. Each algorithm has its own strengths and limitations, and their effectiveness can vary depending on factors like data characteristics and the specific urban environment. This knowledge gap is precisely what our review aims to fill. By comprehensively evaluating these algorithms, we can provide a more solid foundation for urban planners, policy makers and real estate developers to make informed decisions. This paper will first systematically sort out the existing research results and carefully analyze the actual application effects of different algorithms in urban residential vacancy rate observation; secondly, from the three dimensions of complex environment, diverse data sources and urban development needs, it will deeply explore the difficulties faced by the current research; finally, it will propose practical solutions to these challenges and make reasonable prospects for future research directions. Our research has important purposes and significance. In terms of research purpose, our study aims to comprehensively explore the application status, technical development level and challenges of algorithms in urban residential vacancy rate observation. By comprehensively combining and comparing various algorithms, we can clarify their advantages and disadvantages in dealing with complex environments, diverse data sources and meeting the needs of urban development. At the same time, with the help of empirical research and rich case analysis, we explore feasible solutions to improve the accuracy and efficiency of residential vacancy rate observation using algorithms, so as to provide scientific and efficient decision-making support tools for urban managers, real estate developers and relevant policy makers, and ultimately achieve the optimal allocation of urban resources and promote sustainable urban development. In terms of research significance, the value of this study is reflected in several key areas. On the one hand, by in-depth research on the application of algorithms in urban residential vacancy rate observation, it provides new technical means and methodology for solving the problem of urban residential vacancy, thereby improving the level of urban management and governance capabilities. On the other hand, this study helps to integrate and utilize multi-source data, enhance data-driven decision-making capabilities, and effectively promote the construction of smart cities.