There are many different algorithms that have been shown to solve the simultaneous localization and mapping (SLAM) problem depending on the type of input data. Many of these algorithms use some form of cumulative current position as a state variable and only store landmarks in their globally mapped form, discarding past data. This thesis takes a different approach in not using current position as a cumulative state variable and storing and using past data. Landmarks are mapped relative to each other in their untransformed states and use either three points or one plane to maintain translation and rotation invariance. The Relative algorithms can use both current and past data for accuracy purposes. Using this approach, the SLAM problem is solved by data structures and algorithms rather than probabilistic modeling. The Relative algorithms are shown to be good solutions to the simulated SLAM problems tested in this thesis. In particular the Relative Point algorithm is shown to have a worst case computation complexity of O(nslogns). ns is the average quantity of points observed in a given observation and is not related to the total quantity of points on the map. The Relative Point algorithm is able to identify points with movement that is not correlated to the viewpoint at a low cost, and has comparable accuracy to a 6D no odometry Extended Kalman Filter.