A parallel algorithm for path-min queries in trees
Given a rooted tree T on n vertices with each vertex v having a label cost(v), preprocess T so that, given a pair of vertices v, w, the minimum-cost vertex on the path between v and w (the path-min of v and w) can be found efficiently. We give a preprocessing algorithm running in O(log n) time using O(n) processors in the CREW PRAM. After preprocessing, a path-min query can be answered in O(log n) time using a single processor.
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