Linear verification for spanning trees


Given 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

$$5n + n\log \frac{{\left| A \right| + n}}{n}$$


This leads to a spanning tree verification algorithm usingO(n+e) comparisons in a graph withn vertices ande edges.

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Komlós, J. Linear verification for spanning trees. Combinatorica 5, 57–65 (1985).

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AMS subject classification (1980)

  • 68 F. 10