  Tree path minimum query problem is a fundamental problem while processing
trees, and is used widely in minimum spanning tree verification and randomized
minimum spanning tree algorithms. In this paper, we study the possibility of
building an oracle in advance, which is able to answer the queries efficiently.
We present an algorithm based on Boruvka trees. Our algorithm is the first to
achieve a near-optimal bound on query time, while matching the currently
optimal trade-off between construction time and the number of comparisons
required at query. Particularly, in order to answer each query within $2k$
comparisons, our algorithm requires $O(n \log \lambda_k(n))$ time and space to
construct the oracle, and the oracle can answer queries in $O(k + \log
\lambda_k(n))$ time. Here $\lambda_k(n)$ is the inverse of the Ackermann
function along the $k$-th column. This algorithm not only is simpler than the
previous ones, but also gives a completely different method of solving this
problem.
