Entropy Coding of Unordered Data Structures

We present shuffle coding, a general method for optimal compression of sequences of unordered objects using bits-back coding. Data structures that can be compressed using shuffle coding include multisets, graphs, hypergraphs, and others. We release an implementation that can easily be adapted to different data types and statistical models, and demonstrate that our implementation achieves state-of-the-art compression rates on a range of graph datasets including molecular data.