Graph compression based on transitivity for neighborhood query

In recent years, many graph compression methods have been introduced. One successful category of them is based on local decompression designed to answer neighborhood queries. These techniques mainly rely on local similarities of vertices. Besides, their performance is usually a function of graph sparsity. The proposed approach, in this paper, is a lossy compression technique used to answer neighborhood queries with a more general precondition, called transitivity. The output of this method is a sparse graph optimized to keep original adjacent vertices, in at most 2-distance from each other and vice versa. In other words, by traversing a compressed graph by depth of 2, from any desired vertex, its original adjacency list is reconstructed, with an acceptable error. This paper models an optimization problem to solve the inverse problem of finding the best compressed graph in order to minimize the reconstruction error. Then, this NP problem is approximated by a heuristic with a low degree polynomial time-complexity near to the complexity of the forward problem. The results of applying the proposed method on toy and real datasets are compared with the state of the art that improves compression ratio and performance with an acceptable query response time.