Abstract
We present au intuitive and simple O( log 2 n log Φ) time, O(n2 M(n)) processor parallel algorithm for finding a perfect matching in a planar graph, where n is the order, Φ is the number of the distinct perfect matchings of the graph and M(n) is the best sequential complexity of matrix multiplication of size n. The algorithm runs on a CRCW PRAM. Clearly, our algorithm belongs to the class NC if the number of perfect matchings is polynomially bounded in the size of the input graph.
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