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In a complementary approach, we design a near-optimal two step algorithm that is simple and easy to implement. This algorithm identifies critical points of the input function in the first step, and connects the critical points in the second step to obtain the Reeb graph. Experimental results show that our two-step algorithm is an order of magnitude faster than existing methods. We also develop methods to simplify the Reeb graph, which aids in removing noise and unimportant features from the input, and produce a feature-directed layout of the Reeb graph, which helps users explore their data effectively.

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