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This paper describes a new solution of the simultaneous localization and mapping (SLAM) problem. Instead of building one global consistent map, aimed by the most common SLAM techniques, we compute a set of local metrical maps and fuse them to a graph-like structure resulting in a topological map. Thus, our approach does not require a global metrical map consistency. The main contribution of this paper is an algorithm for closing spatial loops. Loop closing means, that a subset of the edges of the graph representing the topological map forms a cycle. To this end we describe a very efficient enhancement of the well-known RANSAC technique for actively recognizing regions explored by the robot previously. This improvement exploits the theory of the birthday attack whose mathematical background is known from cryptography. A fast sample-based scan matcher is employed to compute the local maps. We derive the covariance of the current robot pose from the sample distribution in order to perform a recognition only when loop closing is very likely. Our approach has been implemented and experimental results show its excellent performance.