http://worldcat.org/entity/work/id/24031742

The two-processor scheduling problem is in random NC

Abstract: "An efficient parallel algorithm (RNC[superscript 2]) for the two-processor scheduling problem is presented. An interesting feature of this algorithm is that it finds a highest level first schedule: such a schedule defines a lexicographically first solution to this problem in a natural way. A key ingredient of the algorithm is a generalization of a theorem of Tutte which establishes a one-to-one correspondence between the bases of the Tutte matrix of a graph and the sets of matched nodes in maximum matchings in the graph."

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