Abstract
This paper presents an algorithm for recognizing two dimensional partial orders. The algorithm accepts as input an arbitrary partial order G and responds “yes” if the dimension of G is less than or equal to two and responds “no” otherwise. As part of the recognition process, the algorithm decomposes the partial order in a canonical way which can be used to determine whether two partial orders of dimension two are isomorphic. Both the recognition and the isomorphism algorithms can be implemented to run in time O(n2) when the input is a partial order on n elements. The best previously known algorithms for these two tasks had a worst case behavior of O(n3).
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