A novel complete area coverage algorithm is presented for autonomous vacuuming robots working in completely unknown indoor environments. The algorithm works by segments the environment into smaller regions. Each smaller region is covered in zigzag pattern. A topological world map based on natural landmarks, such as wall corners and edges, is built incrementally while the robot systematically cleans the environments. The natural landmarks are added as nodes in a partial map as they are discovered. A three-layer BP network classification is designed to identify the natural landmarks. A novel feature of the map is the use of topology to store coverage information. An environment is completely covered only when the world map is fully defined, that is, fully connected. The simulation and real robot experiments prove that the proposed algorithm is valid.