## 5 Conclusions  
In the research and application of urban residential vacancy rate observation, algorithms, as a powerful tool, have gradually shown their unique value and potential. Faced with the challenges of complex environment, diverse data sources and urban development needs, the application of algorithms not only improves the accuracy of observation, but also enhances the understanding of urban residential use conditions. By combining and analyzing current research results, it can be seen that algorithms play a vital role in addressing these challenges. First, in view of the complexity of the urban environment, algorithms can effectively process and analyze a large amount of complex spatial data, such as geographic information system (GIS) data and remote sensing images, thereby revealing the distribution characteristics and laws of residential vacancy at the macro and micro levels. In addition, by introducing a spatiotemporal analysis model, the algorithm can take into account the dynamic changes in urban development and provide more comprehensive and dynamic decision-making support for policy makers and urban planners. From the perspective of the complexity of urban environment, the algorithm can efficiently process and analyze massive complex spatial data, such as geographic information system (GIS) data and remote sensing images, and then reveal the distribution characteristics and laws of residential vacancy at the macro and micro levels. For example, the analysis of high-resolution remote sensing images with the help of deep learning algorithms can accurately identify the residential vacancy situation in different areas and provide a detailed basis for urban planning. In addition, by introducing a spatiotemporal analysis model, the algorithm can fully consider the dynamic changes in urban development, and provide more comprehensive and dynamic decision support for policy makers and urban planners. Taking the construction of a new urban area as an example, the algorithm can predict the change of residential vacancy rate in different stages according to the regional development planning, the trend of population flow and other factors, and assist in the formulation of reasonable housing policies. In terms of the diversity of data sources, the use of algorithms has achieved the integration and fusion of data from different sources and types, making the observation results more accurate and comprehensive. For example, by combining multiple data sources such as government statistical data, social media data and mobile communication data, machine learning algorithms can be used to mine potential vacant residential information, making up for the limitations of a single data source. At the same time, with the development of big data technology, the scale of data that algorithms can process is getting larger and larger, and the data types are becoming more and more abundant, which provides a broader perspective for the observation of urban residential vacancy rates. Through the integration of multi-source data, the vacancy rate can be analyzed from multiple dimensions, such as combining traffic flow data and commercial activity data, to deeply explore the association with the residential vacancy rate. The challenge of urban development needs lies in how to combine vacancy rate observation with urban sustainable development strategies. In this process, the application of algorithms not only stops at the quantitative analysis of vacancy rates, but also includes in-depth exploration of the socioeconomic factors behind vacancy. Through algorithms such as cluster analysis and association rule mining, researchers can find the key factors affecting residential vacancy rates, thereby providing a scientific basis for the formulation of urban housing policies.