Dynamic Data Structures for Document Collections and Graphs

TL;DR

This paper introduces a novel framework that overcomes previous limitations in dynamic compressed data structures, enabling efficient updates and queries for document collections, graphs, and relations, thus nearly closing the gap with static solutions.

Contribution

The authors present a new framework that allows dynamizing static compressed data structures, improving dynamic document indexing and graph representations.

Findings

Circumvents the rank query lower bound in dynamic indexing

Nearly closes the gap between static and dynamic data structures

Applies to dynamic graphs and binary relations

Abstract

In the dynamic indexing problem, we must maintain a changing collection of text documents so that we can efficiently support insertions, deletions, and pattern matching queries. We are especially interested in developing efficient data structures that store and query the documents in compressed form. All previous compressed solutions to this problem rely on answering rank and select queries on a dynamic sequence of symbols. Because of the lower bound in [Fredman and Saks, 1989], answering rank queries presents a bottleneck in compressed dynamic indexing. In this paper we show how this lower bound can be circumvented using our new framework. We demonstrate that the gap between static and dynamic variants of the indexing problem can be almost closed. Our method is based on a novel framework for adding dynamism to static compressed data structures. Our framework also applies more generally to dynamizing other problems. We show, for example, how our framework can be applied to develop compressed representations of dynamic graphs and binary relations.