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This paper demonstrates how the data-association technique known as the probabilistic multi-hypothesis tracker (PMHT) can be applied to the feature-based simultaneous localization and map building (SLAM) problem. The main advantage of PMHT over other conventional data-association techniques is that it has low computational complexity, while still providing good performance. Low complexity is a particularly desirable feature for the SLAM problem where the estimators used may already be costly to implement. The paper also proposes an estimation approach based on generalized expectation-maximization iterations of the PMHT SLAM problem, which is able to achieve low computation complexity at the expense of local convergence. The performance of the PMHT SLAM algorithm is compared with other approaches, and its output is demonstrated on a benchmark data set recorded in Victoria Park, Sydney, Australia. Index Terms--Data association, map building, navigation, probabilistic multi-hypothesis tracker (PMHT), simultaneous localization and map building (SLAM).