BIM models can be quite large, containing detailed information about every aspect of a building. Algorithms need to be highly optimized to handle these large data sets without sacrificing performance.
In addition to this, developing algorithms that can handle updates to the model, and keep track of different versions of the model, can be complex.
BIM models contain not just geometric data, but also non-geometric data such as material properties, cost estimates, and schedules. Algorithms need to be able to integrate this non-geometric data with the geometric data in a meaningful way.

The most challenging problem in developing geometric algorithms for Building Information Modeling (BIM) is likely the complexity of architectural models, which requires the development of sophisticated algorithms that can handle intricate geometries and interconnections. Additionally, ensuring interoperability across different software platforms and file formats is a significant hurdle, given the collaborative nature of BIM and the variety of tools used in the industry.