Exploring Shortest Path-Based Queries on Massive Graphs

Qingshuai Feng

Abstract: Graph is a fundamental structure in both theoretical and applied computer science, extensively utilized for modeling relationships across various domains such as social networks, transportation systems, and communication networks. Among the myriad of problems associated with graph analysis, the study of shortest paths is crucial due to its wide-ranging applications. This thesis delves into several shortest path-based problems in graph analysis, focusing on the shortest path counting and shortest cycle counting queries on dynamic graphs, as well as top-k nearest neighbor (kNN) search in public transportation networks. The first study explores the problem of counting shortest paths on dynamic graphs, a critical component for applications such as friend recommendation and betweenness centrality analysis. While a hub labeling technique has been used to provide realtime responses to shortest path counting queries on static graphs, our work extends this to dynamic settings. To efficiently accommodate graph changes such as edge and vertex updates, we introduce novel incremental (IncSPC) and decremental (DecSPC) algorithms. These algorithms dynamically maintain the shortest path counting index by applying a partial update strategy, significantly enhancing the speed of updates without having to rebuild the entire index. The second study also addresses dynamic graphs by focusing on shortest cycle counting problem, a key pattern for detecting anomalies like fraud. We introduce a novel 2-hop labeling-based algorithm called Counting Shortest Cycle (CSC for short) for realtime shortest cycle counting. This approach utilizes an innovative bipartite conversion technique to restructure the initial graph before constructing the CSC index. To enhance the speed of index construction, we implement effective pruning strategies and an index merge mechanism that aggregates related label entries, thereby reducing the label size. Additionally, we have developed an update algorithm to maintain the index. Extensive evaluations of our methods confirm their effectiveness and efficiency. The third study investigates the problem of top-k nearest neighbor search in public transportation networks, a fundamental problem in location-based services. Traditional methods like Dijkstra’s algorithm have proven inefficient for processing queries. While other works rely on a path index also suffer from slow query processing and poor scalability for large graphs. To overcome these challenges, we developed a novel index, TNN-Index, using a simple yet effective structure that optimizes kNN queries with near-optimal time complexity and avoids reliance on resource-intensive path indexes. Extensive experiments on real-world datasets shows that our method significantly outperforms existing solutions in both query processing and index construction. Overall, this thesis explores three problems of shortest path-based queries in both dynamic and static graph settings, and provides efficient and scalable solutions which advance the field of graph analytics.