I/O Efficient Label-Constrained Reachability Queries in Large Graphs

Computing the reachability between two vertices in a graph is a fundamental problem in graph data analysis. Most of the existing works assume that the edges in the graph have no labels, but in many real application scenarios, edges naturally come with edge-labels, and label constraints may be placed on the edges appearing on a valid path between two query vertices. Therefore, we study the label-constrained reachability (LCR) queries in this paper, where we are given a source vertex s , a target vertex t , a label set Δ, and the goal is to check whether there exists any path from s to t such that all the labels of edges on the path belong to Δ. A plethora of methods have been proposed in the literature to support the LCR queries. All these methods take the assumption that the graph is resident in the main memory of a machine. Nevertheless, the graphs in many real application scenarios are generally big and may not reside in memory. In these cases, existing methods suffer from serious scalability problem, i.e., result in huge I/O costs. Motivated by this, in this paper, we study the I/O efficient LCR query problem and aim to efficiently answer the LCR queries when the graph cannot fit in the main memory. To achieve this goal, we propose a reduction-based indexing approach. We introduce two elegant graph reduction operators which aims to reduce the size of the graph loaded in memory while preserving the LCR information among the remaining vertices. With these two operators, we devise an index named LCR-Index and propose algorithms to adaptively construct the index based on the available memory. Equipped with LCR-Index, we can answer a LCR query by only scanning the LCR-Index sequentially. Experiments demonstrate our query processing algorithm can handle graphs with billions of edges.