Unsupervised graph alignment finds the node correspondence between a pair of attributed graphs by only exploiting graph structure and node features. One category of recent studies first computes the node representation and then matches nodes with the largest embedding-based similarity, while the other category reduces the problem to optimal transport (OT) via Gromov-Wasserstein learning. However, it remains largely unexplored in the model expressiveness, as well as how theoretical expressivity impacts prediction accuracy. We investigate the model expressiveness from two aspects. First, we characterize the model'sdiscriminative powerin distinguishing matched and unmatched node pairs across two graphs. Second, we study the model's capability of guaranteeingnode matching propertiessuch as one-to-one matching and mutual alignment. Motivated by our theoretical analysis, we put forward a hybrid approach namedCombAlignwith stronger expressive power. Specifically, we enable cross-dimensional feature interaction for OT-based learning and propose an embedding-based method inspired by the Weisfeiler-Lehman test. We also apply non-uniform marginals obtained from the embedding-based modules to OT as priors for more expressiveness. Based on that, we propose a traditional algorithm-based refinement, which combines our OT and embedding-based predictions using the ensemble learning strategy and reduces the problem to maximum weight matching. With carefully designed edge weights, we ensure these matching properties and further enhance prediction accuracy. By extensive experiments, we demonstrate a significant improvement of 14.5% in alignment accuracy compared to state-of-the-art approaches and confirm the soundness of our theoretical analysis.

Map matching of sparse vehicle trajectories is a fundamental problem in location-based services, such as traffic flow analysis and vehicle routing. Existing literature mainly relies on sequence-to-sequence (Seq2Seq) models to capture theintra-trajectory correlationof an input trajectory and to sequentially predict the matched road segments. Due to the limited expressive capability of sequential models, these methods fall short of extractinginter-trajectoryandtrajectory-road correlationsas well ascorrelation between road segments. We presentGraphMM, a graph-based approach that explicitly utilizes all aforementioned correlations. Our model exploits the graph nature of map matching and incorporates graph neural networks and conditional models to leverage both road and trajectory graph topology, while manages to align road segments and trajectories in latent space. We formally analyze the expressive power of our model in capturing various correlations and propose efficient algorithms for model training and inference. In particular, our optimization techniques dramatically reduce the computational complexity, making our model feasible on datasets with thousands of road segments. Extensive experiments show that our model significantly enhances prediction accuracy, while improving training and inference efficiency by up to an order of magnitude over both the industrial implementation of the hidden Markov model and state-of-the-art Seq2Seq-based methods.

Reachability is a fundamental graph operator. State-of-the-art index-based reachability processing frameworks can efficiently handle static graphs, but the recent advent of dynamic graph data poses new challenges. To address these challenges, we propose an index-free, community-aware (IFCA) reachability processing framework inspired by efficient Personalized PageRank approximation algorithms, which identifies community structures on-the-fly to accelerate query processing. On top of it, we devise a community contraction technique to bridge the gap between vertices in distinct communities, and a cost-based strategy selection procedure to efficiently handle the resulting reduced graph. We conduct experiments with realistic query workloads over large-scale real dynamic graphs, showing our approach’s superior efficiency compared with index-based and index-free state-of-the-art methods.

SimRank-based similarity joins, which mainly include threshold-based and top- k similarity joins, are important types of all-pair SimRank queries. Although a line of related algorithms have been proposed recently, they still fall short of providing approximation guarantee and suffer from scalability issues on medium and large graphs. Meanwhile, we also lack an extensive analysis of existing techniques in terms of accuracy and efficiency. Motivated by these challenges, we first conduct detailed analysis of state-of-the-art algorithms and provide additional theoretical results. Second, to address the limitations of existing techniques, we propose simple yet effective algorithm frameworks for both queries to theoretically guarantee the approximation bound, and present a more efficient all-pair algorithm inspired by randomized local push of Personalized PageRank. Next, we analyze the algorithmic complexity of threshold-based and top- k similarity joins by leveraging a reasonable assumption of SimRank distribution. Through extensive experiments, we find that our proposed methods far exceed existing ones with respect to query efficiency, approximation guarantee and practical accuracy, while our theoretical analysis nicely matches the empirical study.

Real-world graphs exhibit many interesting properties that differentiate them from random graphs, which have been extensively studied for the past decades. For various proposed generative models, a majority of them build the graph by sequentially adding each node and the attached edges. However, the growth of many real-world graphs, such as social networks, is naturally modeled by the sequential insertion of edges. Unfortunately, to the best of our knowledge, no generative model has been proposed to reveal this process. We propose the first sequence-of-edges model, denoted as temporal preferential attachment (TPA). It relies on preferential attachment (PA), one of the most influential mechanisms to generate scale-free graphs, and takes time-decay effect and node fitness into consideration. Empirical analysis demonstrates that our model preserves several key properties of the real-world graphs, including both the properties observed from the snapshot graphs (e.g., power-law distribution) and temporal properties observed from the graph generation process (e.g., shrinking diameter). Meanwhile, our model is sufficiently general to accommodate several forms of time decay and fitness distributions. Then, we design two efficient algorithms that generate TPA graphs with billions of edges in several minutes.

Real-world graphs exhibit many interesting properties that differentiate them from random graphs, which have been extensively studied for the past decades. For various proposed generative models, a majority of them build the graph by sequentially adding each node and the attached edges. However, the growth of many real-world graphs, such as social networks, is naturally modeled by the sequential insertion of edges. Unfortunately, to the best of our knowledge, no generative model has been proposed to reveal this process. We propose the first sequence-of-edges model, denoted astemporal preferential attachment (TPA). It relies onpreferential attachment (PA), one of the most influential mechanisms to generate scale-free graphs, and takes time-decay effect and node fitness into consideration. Empirical analysis demonstrates that our model preserves several key properties of the real-world graphs, including both the properties observed from the snapshot graphs (e.g., power-law distribution) and temporal properties observed from the graph generation process (e.g., shrinking diameter). Meanwhile, our model is sufficiently general to accommodate several forms of time decay and fitness distributions. Then, we design two efficient algorithms that generate TPA graphs with billions of edges in several minutes.

Triangle counting is an important problem in graph mining, which has achieved great performance improvement on GPU in recent years. Instead of proposing a new GPU triangle counting algorithm, in this paper, we propose a novel lightweight graph preprocessing method to boost many state-of-the-art GPU triangle counting algorithms without changing their implementations and data structures. Specifically, we find common computing patterns in existing algorithms, and abstract two analytic models to measure how workload imbalance and diversity in these computing patterns affect performance exactly. Then, due to the NP-hardness of the model optimization, we propose approximate solutions by determining edge directions to balance workloads and reordering vertices to maximize the degree of parallelism within GPU blocks. Finally, extensive experiments confirm the significant performance improvement and high usability of our approach.

SimRank is a classic measure of the similarities of nodes in a graph. Given a node u in graph $G =(V, E)$, a \em single-source SimRank query returns the SimRank similarities $s(u, v)$ between node u and each node $v \in V$. This type of queries has numerous applications in web search and social networks analysis, such as link prediction, web mining, and spam detection. Existing methods for single-source SimRank queries, however, incur query cost at least linear to the number of nodes n, which renders them inapplicable for real-time and interactive analysis. This paper proposes \prsim, an algorithm that exploits the structure of graphs to efficiently answer single-source SimRank queries. \prsim uses an index of size $O(m)$, where m is the number of edges in the graph, and guarantees a query time that depends on the \em reverse PageRank distribution of the input graph. In particular, we prove that \prsim runs in sub-linear time if the degree distribution of the input graph follows the power-law distribution, a property possessed by many real-world graphs. Based on the theoretical analysis, we show that the empirical query time of all existing SimRank algorithms also depends on the reverse PageRank distribution of the graph. Finally, we present the first experimental study that evaluates the absolute errors of various SimRank algorithms on large graphs, and we show that \prsim outperforms the state of the art in terms of query time, accuracy, index size, and scalability.

Single-source and top- k SimRank queries are two important types of similarity search in graphs with numerous applications in web mining, social network analysis, spam detection, etc. A plethora of techniques have been proposed for these two types of queries, but very few can efficiently support similarity search over large dynamic graphs, due to either significant preprocessing time or large space overheads. This paper presents ProbeSim , an index-free algorithm for single-source and top- k SimRank queries that provides a non-trivial theoretical guarantee in the absolute error of query results. ProbeSim estimates SimRank similarities without precomputing any indexing structures, and thus can naturally support real-time SimRank queries on dynamic graphs. Besides the theoretical guarantee, ProbeSim also offers satisfying practical efficiency and effectiveness due to non-trivial optimizations. We conduct extensive experiments on a number of benchmark datasets, which demonstrate that our solutions outperform the existing methods in terms of efficiency and effectiveness. Notably, our experiments include the first empirical study that evaluates the effectiveness of SimRank algorithms on graphs with billion edges, using the idea of pooling.

Maximum independent set (MIS) is a fundamental problem in graph theory and it has important applications in many areas such as social network analysis, graphical information systems and coding theory. The problem is NP-hard, and there has been numerous studies on its approximate solutions. While successful to a certain degree, the existing methods require memory space at least linear in the size of the input graph. This has become a serious concern in view of the massive volume of today's fast-growing graphs. In this paper, we study the MIS problem under the semi-external setting, which assumes that the main memory can accommodate all vertices of the graph but not all edges. We present a greedy algorithm and a general vertex-swap framework, which swaps vertices to incrementally increase the size of independent sets. Our solutions require only few sequential scans of graphs on the disk file, thus enabling in-memory computation without costly random disk accesses. Experiments on large-scale datasets show that our solutions are able to compute a large independent set for a massive graph with 59 million vertices and 151 million edges using a commodity machine, with a memory cost of 469MB and a time cost of three minutes, while yielding an approximation ratio that is around 99% of the theoretical optimum.