An Information-theoretic Framework for the Lossy Compression of Link Streams

Abstract: Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the study of real, large-scale, and complex graphs which cannot be grasped at first glance. This article proposes a framework for the compression of temporal graphs, that is for the compression of graphs that evolve with time. This framework first builds on a simple and limited scheme, exploiting structural equivalence for the lossless compression of static graphs, then generalises it to the lossy compression of link streams, a recent formalism for the study of temporal graphs. Such generalisation relies on the natural extension of (bidimensional) relational data by the addition of a third temporal dimension. Moreover, we introduce an information-theoretic measure to quantify and to control the information that is lost during compression, as well as an algebraic characterisation of the space of possible compression patterns to enhance the expressiveness of the initial compression scheme. These contributions lead to the definition of a combinatorial optimisation problem, that is the Lossy Multistream Compression Problem, for which we provide an exact algorithm.