In this paper, we study the following problem: given a knowledge graph (KG) and a set of input vertices (representing concepts or entities) and edge labels, we aim to find the smallest connected subgraphs containing all of the inputs. This problem plays a key role in KG-based search engines and natural language question answering systems, and it is a natural extension of the Steiner tree problem, which is known to be NP-hard. We present RECON, a system for finding approximate answers. RECON aims at achieving high accuracy with instantaneous response (i.e., sub-second/millisecond delay) over KGs with hundreds of millions edges without resorting to expensive computational resources. Furthermore, when no answer exists due to disconnection between concepts and entities, RECON refines the input to a semantically similar one based on the ontology, and attempts to find answers with respect to the refined input. We conduct a comprehensive experimental evaluation of RECON. In particular we compare it with five existing approaches for finding approximate Steiner trees. Our experiments on four large real and synthetic KGs show that RECON significantly outperforms its competitors and incurs a much smaller memory footprint.

We study the subgraph enumeration problem under distributed settings. Existing solutions either suffer from severe memory crisis or rely on large indexes, which makes them impractical for very large graphs. Most of them follow a synchronous model where the performance is often bottlenecked by the machine with the worst performance. Motivated by this, in this paper, we propose RADS, a Robust Asynchronous Distributed Subgraph enumeration system. RADS first identifies results that can be found using single-machine algorithms. This strategy not only improves the overall performance but also reduces network communication and memory cost. Moreover, RADS employs a novel region-grouped multi-round expand verify & filter framework which does not need to shuffle and exchange the intermediate results, nor does it need to replicate a large part of the data graph in each machine. This feature not only reduces network communication cost and memory usage, but also allows us to adopt simple strategies for memory control and load balancing, making it more robust. Several optimization strategies are also used in RADS to further improve the performance. Our experiments verified the superiority of RADS to state-of-the-art subgraph enumeration approaches.

Existing work on subgraph isomorphism search mainly focuses on a-query-at-a-time approaches: optimizing and answering each query separately. When multiple queries arrive at the same time, sequential processing is not always the most efficient. In this paper, we study multi-query optimization for subgraph isomorphism search. We first propose a novel method for efficiently detecting useful common sub-graphs and a data structure to organize them. Then we propose a heuristic algorithm based on the data structure to compute a query execution order so that cached intermediate results can be effectively utilized. To balance memory usage and the time for cached results retrieval, we present a novel structure for caching the intermediate results. We provide strategies to revise existing single-query subgraph isomorphism algorithms to seamlessly utilize the cached results, which leads to significant performance improvement. Extensive experiments verified the effectiveness of our solution.

Subgraph Isomorphism is a fundamental problem in graph data processing. Most existing subgraph isomorphism algorithms are based on a backtracking framework which computes the solutions by incrementally matching all query vertices to candidate data vertices. However, we observe that extensive duplicate computation exists in these algorithms, and such duplicate computation can be avoided by exploiting relationships between data vertices. Motivated by this, we propose a novel approach, BoostIso , to reduce duplicate computation. Our extensive experiments with real datasets show that, after integrating our approach, most existing subgraph isomorphism algorithms can be speeded up significantly, especially for some graphs with intensive vertex relationships, where the improvement can be up to several orders of magnitude.