Linear Index for Logarithmic Search-Time for any String under any Internal Node in Suffix Trees

Suffix trees are key and efficient data structure for solving string problems. A suffix tree is a compressed trie containing all the suffixes of a given text of length $n$ with a linear construction cost. In this work, we introduce an algorithm to build a linear index that allows finding a pattern of any length under any internal node in a suffix tree in O(logn) time.