Exploiting topological structures for graph compression based on quadtrees

In the age of big data, the need for efficient data processing and computation has been in the forefront of research endeavors. The process of extracting information from huge data sets require novel storage techniques to aid the computing devices to perform necessary computation. With pervasive use of heterogeneous systems and advent of non-traditional computing units like GPUs, with limited memory, it has become relevant to underline the relevance of data storage, especially to utilize such computing devices. Graphs contain a plethora of information, and also can be used to represent data from a broad range of domains; real-world big data sets are effectively represented by graphs. Efficient graph compression is therefore essential for performing computations on large data sets. Quadtrees, generally used to represent images, can be used as an effective technique to perform compression. Using additional topological information that depict certain patterns for the data sets, further improvements can be made to the space complexity of storing graph data. In this paper we describe algorithms that take into consideration the properties of graphs, and perform compression based on quadtrees. The introduced techniques achieve up to 70% compression as compared to adjacency matrix representation; when compared to existing quadtree based compression method, the proposed algorithms achieve an additional 50% improvement. Techniques to both compress data and also perform queries on the compressed data itself are introduced and discussed in detail.