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A* graph search effectively computes the optimal solution path from start nodes to goal nodes in a graph, using a heuristic function. In some applications, the graph may change slightly in the course of its use and the solution path then needs to be updated. Very often, the new solution will differ only slightly from the old. Rather than perform the full A* on the new graph, we compute the necessary OPEN nodes from which the revised solution can be obtained by A*. In this "Differential A*" algorithm, the graph topology, transition costs, or start/goals may change simultaneously. We develop the algorithm and discuss when it gives an improvement over simply reapplying A*. We briefly discuss an application to robot path planning in configuration space, where such graph changes naturally arise.