## 1 Introduction  
As China's urbanization process accelerates, the issue of urban residential vacancy rate has gradually surfaced and become a hot topic of widespread concern in all sectors of society [1; 2; 3; 4]. With the continuous development of the real estate market and the in-depth advancement of urban planning, accurately grasping the urban residential vacancy rate is of great significance for government scientific decision making, rational allocation of resources and sustainable urban development [5; 6]. However, traditional vacancy rate observation methods, such as the field survey method and questionnaire survey method, are insufficient in the face of complex and changing urban environments, a wide range of data sources and the ever-changing needs of urban development, and are unable to meet the current actual needs [7]. Regarding the papers on traditional methods, [PERSON] et al. employed field surveys in Guiyang to estimate block-level vacancy rates, highlighting the limitations of manual data collection in rapidly expanding urban areas [8]. Additionally, [PERSON] et al. compared traditional field surveys with machine learning models in Beijing, finding that algorithms significantly improved accuracy in dense urban environments [9]. Although both aimed to measure the vacancy rate, the former relied more on field surveys while the latter emphasized data-driven modeling techniques. For example, in a certain large-scale city, due to the rapid expansion of the urban area, the traditional field survey method can only cover less than 30% of the newly developed areas in a year, and the data obtained is often inaccurate due to subjective factors. The questionnaire survey method has a response rate of less than 50% in some communities, and the data integrity and accuracy are difficult to guarantee. Although the field survey method can directly obtain the use of houses, it has problems of low efficiency, limited scope and being susceptible to subjective factors; the questionnaire survey method depends on the cooperation of residents, which is difficult to guarantee the accuracy and integrity of data, and high cost for large-scale urban scope survey. Fortunately, the rapid development of cutting-edge technologies such as big data and artificial intelligence in recent years has brought new ideas and methods to the observation of urban residential vacancy rates [10; 11; 12]. With its powerful data mining capabilities, the algorithm can accurately extract valuable information from massive data, greatly improving the accuracy and efficiency of observation. However, it must be recognized that the complexity of the urban environment, the richness and diversity of data sources and the ever-changing needs of urban development have brought more stringent challengesto the application of algorithms in this field [13; 14]. How to fully integrate various data sources in complex urban scenes and adapt them to the needs of urban development has become a key problem that needs to be solved urgently in the current research [15]. In addition, urban residential vacancy rates are affected by a variety of factors, including economic development, population migration, and urban planning. These factors interact and intertwine with each other, further increasing the difficulty of vacancy rate observation [16; 17; 18; 19]. To meet these challenges, many researchers have explored the application of algorithms in urban residential vacancy rate observation from different dimensions [20; 21; 22]. However, there is still a lack of comprehensive review and in-depth analysis of existing research results, making it difficult to form a systematic reference for subsequent research. Based on this, we are committed to conducting a comprehensive review of the application of algorithms in urban residential vacancy rate observation, and to deeply explore how to deal with the challenges brought by complex environments, diverse data sources and urban development needs.