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Efficiently solving large-scale sparse linear systems is important for robot mapping and navigation. Recently, the subgraph-preconditioned conjugate gradient method has been proposed to combine the advantages of two reigning paradigms, direct and iterative methods, to improve the efficiency of the solver. Yet the question of how to pick a good subgraph is still an open problem. In this paper, we propose a new metric to measure the quality of a spanning tree preconditioner based on support theory. We use this metric to develop an algorithm to find good subgraph preconditioners and apply them to solve the SLAM problem. The results show that although the proposed algorithm is not fast enough, the new metric is effective and resulting subgraph preconditioners significantly improve the efficiency of the state-of-the-art solver.