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Current sketch recognition systems treat sketches as images or a collection of strokes, rather than viewing sketching as an interactive and incremental process. We show how viewing sketching as an interactive process allows us to recognize sketches using Hidden Markov Models. We report results of a user study indicating that in certain domains people draw objects using consistent stroke orderings. We show how this consistency, when present, can be used to perform sketch recognition efficiently. This novel approach enables us to have polynomial time algorithms for sketch recognition and segmentation, unlike conventional methods with exponential complexity.