Text sparsification via local maxima

Abstract

In this paper we investigate some properties and algorithms related to a text sparsification technique based on the identification of local maxima in the given string. As the number of local maxima depends on the order assigned to the alphabet symbols, we first consider the case in which the order can be chosen in an arbitrary way. We show that looking for an order that minimizes the number of local maxima in the given text string is an NP-hard problem. Then, we consider the case in which the order is fixed a priori. Even though the order is not necessarily optimal, we can exploit the property that the average number of local maxima induced by the order in an arbitrary text is approximately one third of the text length. In particular, we describe how to iterate the process of selecting the local maxima by one or more iterations, so as to obtain a sparsified text. We show how to use this technique to filter the access to unstructured texts, which appear to have no natural division in words. Finally, we experimentally show that our approach can be successfully used in order to create a space efficient index for searching sufficiently long patterns in a DNA sequence as quickly as a full index.