A note on finding minimum cuts in directed planar networks by parallel computations

We consider the problem of finding a maximum subset of a given set of wires connecting two rows of terminals with fixed positions, such that no wires in the subset cross. We derive an algorithm that runs in O(p + (n ? p) ? g(p + 1)) time, where n is the number of wires given and p is the maximum number of noncrossing wires; in many practically relevant cases, e.g., when p is very high, it needs only linear time. We show how an extension of the algorithm solves the more general problem, where the positions of some terminals have some flexibility, within the same time bound.