New Algorithms on Wavelet Trees and Applications to Information Retrieval

TL;DR

This paper introduces new algorithms based on wavelet trees that enhance their application in solving fundamental range queries and improve information retrieval tasks like document retrieval and inverted list representation.

Contribution

The paper presents novel algorithms for wavelet trees to efficiently perform range queries and demonstrates their applications in information retrieval systems.

Findings

Efficient algorithms for range quantile, next value, and intersection queries.

Improved document retrieval in hierarchical and temporal documents.

Enhanced representation of inverted lists using wavelet trees.

Abstract

Wavelet trees are widely used in the representation of sequences, permutations, text collections, binary relations, discrete points, and other succinct data structures. We show, however, that this still falls short of exploiting all of the virtues of this versatile data structure. In particular we show how to use wavelet trees to solve fundamental algorithmic problems such as {\em range quantile} queries, {\em range next value} queries, and {\em range intersection} queries. We explore several applications of these queries in Information Retrieval, in particular {\em document retrieval} in hierarchical and temporal documents, and in the representation of {\em inverted lists}.