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The solution to the simultaneous localization and map building (SLAM) problem where an autonomous vehicle starts in an unknown location in an unknown environment and then incrementally build a map of landmarks present in this environment while simultaneously using this map to compute absolute vehicle location is now well understood. Although a number of SLAM implementations have appeared in the recent literature, the need to maintain the knowledge of the relative relationships between all the landmark location estimates contained in the map makes SLAM computationally intractable in implementations containing more than a few tens of landmarks. This paper presents the theoretical basis and a practical implementation of a feature selection strategy that significantly reduces the computation requirements for SLAM. The paper shows that it is indeed possible to remove a large percentage of the landmarks from the map without making the map building process statistically inconsistent. Furthermore, it is shown that the computational cost of the SLAM algorithm can be reduced by judicious selection of landmarks to be preserved in the map.