A $k-\text{Way}$ Partitioning Framework for Compression on Social Networks

Social networks have been studied in the context of matrices or graph theory for efficient representation, and manipulation. Knowledge gleaned from these graphs are useful to better coordinate events, advertise, and in recommendation of friends or games. Many social networks represented as graphs or matrices are large containing 100's of millions or even billions of entries. Hence it has become important to store them efficiently using data compression. The authors have used different kinds of compressed data structures such as quad-tree, array of binary trees (ABT), and differential, compressed binary trees (DCBT) in previous research for representing massive social networks and performing various queries [15]–[17]. In this paper, we provide a $k-\mathbf{way}$ partitioning framework that generalizes the array of binary trees structure by providing a combinatorial basis that is shown to lead to substantial improvements in compressing social network graphs.