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In this paper, we address the problem of practical manipulation planning for rearrangement tasks of many movable objects. We study a special case of the rearrangement task, where the only allowed manipulation is pushing. While problems of this kind are known to be PSPACE-hard, we search for algorithms that can provide practical planning time for most common scenarios. We present a hierarchical classification of manipulation problems into several classes, each characterized by properties of thedoi:10.1109/70.704220 fatcat:gwugmacuijb33az723dhh5dwui