Nowadays many cities and countries are creating their 3D building models for a better daily management and smarter decision making. The newly created 3D models are required to be consistent with existing 2D footprint maps. Thereby the 2D maps are usually combined with height data for the task of 3D reconstruction. Many buildings are often composed by parts that are discontinuous over height. Building parts can be reconstructed independently and combined into a complete building. Therefore, most of the state-of-the-art work on 3D building reconstruction first decomposes a footprint map into parts. However, those works usually change the footprint maps for easier partitioning and cannot detect building parts that are fully inside the footprint polygon. In order to solve those problems, we introduce two methodologies, one more dependent on height data, and the other one more dependent on footprints. We also experimentally evaluate the two methodologies and compare their advantages and disadvantages. The experiments use Airborne Laser Scanning (ALS) data and two vector maps, one with 1:10,000 scale and another one with 1:500 scale.