A Hierarchical Contraction Scheme for Querying Big Graphs

This paper proposes a scheme for querying big graphs with a single machine. The scheme iteratively contracts regular structures into supernodes and builds a hierarchy of contracted graphs, until the one at the top fits into the memory. For each query class Q in use, supernodes carry synopses So such that queries of Q are answered by using SO if possible, and otherwise by drilling down to the next level with decontraction of a bounded size. Moreover, we show how to adapt a variety of existing sequential (single-machine) algorithms to the hierarchy by reusing their logic and data structures. We also provide a bounded incremental algorithm to maintain the contracted graphs in response to updates, such that its cost is determined by the sizes of changes to the input and output only. Using real-life and synthetic graphs, we experimentally verify that with a single machine, the hierarchy is able to compute exact query answers when memory is as small as 7.6% of graphs, speeds up various applications by 9.8 times on average, and is even 120.1 times faster than some parallel graph systems that use 6 machines.