Leveraging graph dimensions in online graph search

Abstract

Graphs have been widely used due to its expressive power to model complicated relationships. However, given a graph database D g = { g 1 , g 2 , · · ·, g n }, it is challenging to process graph queries since a basic graph query usually involves costly graph operations such as maximum common subgraph and graph edit distance computation, which are NP-hard. In this paper, we study a novel DS-preserved mapping which maps graphs in a graph database D g onto a multidimensional space M g under a structural dimension M using a mapping function φ(). The DS-preserved mapping preserves two things: distance and structure. By the distance-preserving, it means that any two graphs g i and g j in D g must map to two data objects φ( g i ) and φ( g j ) in M g , such that the distance, d (φ( g i ), φ( g j )), between φ( g i ) and φ( g j ) in M g approximates the graph dissimilarity δ( g i , g j ) in D g . By the structure-preserving, it further means that for a given unseen query graph q , the distance between q and any graph g i in D g needs to be preserved such that δ( q , g i ) ≈ d (φ( q ), φ( g i )). We discuss the rationality of using graph dimension M for online graph processing, and show how to identify a small set of subgraphs to form M efficiently. We propose an iterative algorithm DSPM to compute the graph dimension, and discuss its optimization techniques. We also give an approximate algorithm DSPMap in order to handle a large graph database. We conduct extensive performance studies on both real and synthetic datasets to evaluate the top- k similarity query which is to find top- k similar graphs from D g for a query graph, and show the effectiveness and efficiency of our approaches.