Abstract

Recall from last lecture that we are looking at the document-retrieval problem. The problem can be stated as follows: Given a set of texts T1, T2,..., Tk and a pattern P, determine the distinct texts in which the patterns occurs. In particular, we are allowed to preprocess the texts in order to be able to answer the query faster. Our preprocessing choice was the use of a single suffix tree, in which all the suffixes of all the texts appear, each suffix ending with a distinct symbol that determines the text in which the suffix appears. In order to answer the query we reduced the problem to range-min queries, which in turn was reduced to the least common ancestor (LCA) problem on the cartesian tree of an array of numbers. The cartesian tree is constructed recursively by setting its root to be the minimum element of the array and recursively constructing its two subtrees using the left and right partitions of the array. The range-min query of an interval [i, j] is then equivalent to finding the LCA of the two nodes of the cartesian tree that correspond to i and j. In this lecture we continue to see how we can solve the LCA problem on any static tree. This will involve a reduction of the LCA problem back to the range-min query problem (!) and then a

Citations