  Simultaneous localization and mapping (SLAM) is a critical capability in
autonomous navigation, but memory and computational limits make long-term
application of common SLAM techniques impractical; a robot must be able to
determine what information should be retained and what can safely be forgotten.
In graph-based SLAM, the number of edges (measurements) in a pose graph
determines both the memory requirements of storing a robot's observations and
the computational expense of algorithms deployed for performing state
estimation using those observations, both of which can grow unbounded during
long-term navigation. Motivated by these challenges, we propose a new general
purpose approach to sparsify graphs in a manner that maximizes algebraic
connectivity, a key spectral property of graphs which has been shown to control
the estimation error of pose graph SLAM solutions. Our algorithm, MAC (for
maximizing algebraic connectivity), is simple and computationally inexpensive,
and admits formal post hoc performance guarantees on the quality of the
solution that it provides. In application to the problem of pose-graph SLAM, we
show on several benchmark datasets that our approach quickly produces
high-quality sparsification results which retain the connectivity of the graph
and, in turn, the quality of corresponding SLAM solutions.
