This paper presents a new approach to the multi-robot map-alignment problem that enables teams of robots to build joint maps without initial knowledge of their relative poses. The key contribution of this work is an optimal algorithm for merging (not necessarily overlapping) maps that are created by different robots independently. Relative pose measurements between pairs of robots are processed to compute the coordinate transformation between any two maps. Noise in the robot-to-robot observations, propagated through the map-alignment process, increases the error in the position estimates of the transformed landmarks, and reduces the overall accuracy of the merged map. When there is overlap between the two maps, landmarks that appear twice provide additional information, in the form of constraints, which increases the alignment accuracy. Landmark duplicates are identified through a fast nearest-neighbor matching algorithm. In order to reduce the computational complexity of this search process, a kd-tree is used to represent the landmarks in the original map. The criterion employed for matching any two landmarks is the Mahalanobis distance. As a means of validation, we present experimental results obtained from two robots mapping an area of 4,800 m2.