A Universal Low Complexity Compression Algorithm for Sparse Marked Graphs

TL;DR

This paper presents a universal, low-complexity lossless compression algorithm for sparse marked graphs, capable of achieving optimal compression rates across various graph models, supported by theoretical guarantees and experimental validation.

Contribution

It introduces a novel universal compression algorithm for sparse graphs with theoretical guarantees based on local weak convergence, and demonstrates its effectiveness on synthetic and real data.

Findings

Achieves optimal compression rates universally for sparse graphs.

Provides theoretical guarantees using local weak convergence framework.

Shows promising experimental results on diverse datasets.

Abstract

Many modern applications involve accessing and processing graphical data, i.e. data that is naturally indexed by graphs. Examples come from internet graphs, social networks, genomics and proteomics, and other sources. The typically large size of such data motivates seeking efficient ways for its compression and decompression. The current compression methods are usually tailored to specific models, or do not provide theoretical guarantees. In this paper, we introduce a low-complexity lossless compression algorithm for sparse marked graphs, i.e. graphical data indexed by sparse graphs, which is capable of universally achieving the optimal compression rate in a precisely defined sense. In order to define universality, we employ the framework of local weak convergence, which allows one to make sense of a notion of stochastic processes for sparse graphs. Moreover, we investigate the performance of our algorithm through some experimental results on both synthetic and real-world data.