Abstract
The maximal path problem is the following: Given a graph G = (V, E) and a vertex r, find a path starting at r that cannot be extended without encountering a node that is already on the path. We shall show that if all nodes have degree at most D(n), the problem can be solved in O(D(n) log 3 n) time using O(n 2) processors. We also obtain an NC algorithm for the maximal path problem in planar graphs. Finally, we show that the problem of computing the lexicographically minimal maximal path is P-complete, even when restricted to planar graphs.
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