Linear verification for spanning trees

AbstractGiven a rooted tree with values associated with then vertices and a setA of directed paths (queries), we describe an algorithm which finds the maximum value of every one of the given paths, and which uses only $$5n + n\log \frac{{\left| A \right| + n}}{n}$$ comparisons.This leads to a spanning tree verification algorithm usingO(n+e) comparisons in a graph withn vertices ande edges.No implementation is offered.