Graph data are pervasive worldwide, e.g., social networks, citation networks, and web graphs. A real-world graph can be huge and requires heavy computational and storage resources for processing. Various graph compression techniques have been presented to accelerate the processing time and utilize memory efficiently. SOTA approaches decompose a graph into fixed-size submatrices and compress it by applying the existing graph compression algorithm. This approach is promising if the input graph is dense. Otherwise, an optimal graph compression ratio cannot be achieved. Graphs such as those used by social networks exhibit a power-law distribution. Thus, applying compression to the fixed-size block of a matrix could lead to the empty cell processing of that matrix. In this paper, we solve the problem of ordered matrix compression on a deep level, dividing the block into sub-blocks to achieve the best compression ratio. We observe that the ordered matrix compression ratio could be improved by adopting variable-shape regions, considering both horizontal- and vertical-shaped regions. In our empirical evaluation, the proposed approach achieved a 93.8% compression ratio on average, compared with existing SOTA graph compression techniques.
Keywords: adjacency matrix regions; graph compression; graph computation algorithms; graph mining.