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How to find local minimum of t using only o(log n) to node t

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Consider an n-node complete binary tree T, where n=2^d - 1 for some d. Each node v of T is labeled with a real number x_v. You may assume that the real numbers labeling the nodes are all distinct. A node v of T is a local minimum if the label x_v is less than the label x_w for all nodes w that are joined to v by an edge.

You are given such a complete binary tree T, but the labeling is only specified in the following implicit way: for each node v, you can determine the value x_v by probing the node v. Show how to find a local minimum of T using only O(log n) probes to the nodes of T.

Reference no: EM13948700

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