A Universal Low Complexity Compression Algorithm for Sparse Marked Graphs

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 graphs. Moreover, we investigate the performance of our algorithm through some experimental results on both synthetic and real-world data.