Two-Dimensional Block Trees

TL;DR

This paper introduces a two-dimensional extension of the Block Tree data structure to efficiently compress collections of images, graphs, and maps, achieving significant space reductions while supporting direct access and navigation.

Contribution

It extends the Block Tree to two dimensions, enabling effective compression of image and graph collections, with a specialized variant for Web graph adjacency matrices.

Findings

Achieves up to 50% space reduction over the $k^2$-tree for Web graphs.

Supports efficient direct access and navigation in compressed data.

Effectively compresses repetitive image and graph collections.

Abstract

The Block Tree (BT) is a novel compact data structure designed to compress sequence collections. It obtains compression ratios close to Lempel-Ziv and supports efficient direct access to any substring. The BT divides the text recursively into fixed-size blocks and those appearing earlier are represented with pointers. On repetitive collections, a few blocks can represent all the others, and thus the BT reduces the size by orders of magnitude. In this paper we extend the BT to two dimensions, to exploit repetitiveness in collections of images, graphs, and maps. This two-dimensional Block Tree divides the image regularly into subimages and replaces some of them by pointers to other occurrences thereof. We develop a specific variant aimed at compressing the adjacency matrices of Web graphs, obtaining space reductions of up to 50\% compared with the $k^2$-tree, which is the best alternative supporting direct and reverse navigation in the graph.