Efficient Sampling Algorithms for Approximate Motif Counting in Temporal Graph Streams

A great variety of complex systems, from user interactions in communication networks to transactions in financial markets, can be modeled as temporal graphs consisting of a set of vertices and a series of timestamped and directed edges. Temporal motifs are generalized from subgraph patterns in static graphs which consider edge orderings and durations in addition to topologies. Counting the number of occurrences of temporal motifs is a fundamental problem for temporal network analysis. However, existing methods either cannot support temporal motifs or suffer from performance issues. Moreover, they cannot work in the streaming model where edges are observed incrementally over time. In this paper, we focus on approximate temporal motif counting via random sampling. We first propose two sampling algorithms for temporal motif counting in the offline setting. The first is an edge sampling (ES) algorithm for estimating the number of instances of any temporal motif. The second is an improved edge-wedge sampling (EWS) algorithm that hybridizes edge sampling with wedge sampling for counting temporal motifs with $3$ vertices and $3$ edges. Furthermore, we propose two algorithms to count temporal motifs incrementally in temporal graph streams by extending the ES and EWS algorithms referred to as SES and SEWS. We provide comprehensive analyses of the theoretical bounds and complexities of our proposed algorithms. Finally, we perform extensive experimental evaluations of our proposed algorithms on several real-world temporal graphs. The results show that ES and EWS have higher efficiency, better accuracy, and greater scalability than state-of-the-art sampling methods for temporal motif counting in the offline setting. Moreover, SES and SEWS achieve up to three orders of magnitude speedups over ES and EWS while having comparable estimation errors for temporal motif counting in the streaming setting.Comment: 27 pages, 11 figures; overlapped with arXiv:2007.1402

Detecting Small Query Graphs in A Large Graph via Neural Subgraph Search

Recent advances have shown the success of using reinforcement learning and search to solve NP-hard graph-related tasks, such as Traveling Salesman Optimization, Graph Edit Distance computation, etc. However, it remains unclear how one can efficiently and accurately detect the occurrences of a small query graph in a large target graph, which is a core operation in graph database search, biomedical analysis, social group finding, etc. This task is called Subgraph Matching which essentially performs subgraph isomorphism check between a query graph and a large target graph. One promising approach to this classical problem is the "learning-to-search" paradigm, where a reinforcement learning (RL) agent is designed with a learned policy to guide a search algorithm to quickly find the solution without any solved instances for supervision. However, for the specific task of Subgraph Matching, though the query graph is usually small given by the user as input, the target graph is often orders-of-magnitude larger. It poses challenges to the neural network design and can lead to solution and reward sparsity. In this paper, we propose NSUBS with two innovations to tackle the challenges: (1) A novel encoder-decoder neural network architecture to dynamically compute the matching information between the query and the target graphs at each search state; (2) A novel look-ahead loss function for training the policy network. Experiments on six large real-world target graphs show that NSUBS can significantly improve the subgraph matching performance

Efficient Algorithms for Node Disjoint Subgraph Homeomorphism Determination

Recently, great efforts have been dedicated to researches on the management of large scale graph based data such as WWW, social networks, biological networks. In the study of graph based data management, node disjoint subgraph homeomorphism relation between graphs is more suitable than (sub)graph isomorphism in many cases, especially in those cases that node skipping and node mismatching are allowed. However, no efficient node disjoint subgraph homeomorphism determination (ndSHD) algorithms have been available. In this paper, we propose two computationally efficient ndSHD algorithms based on state spaces searching with backtracking, which employ many heuristics to prune the search spaces. Experimental results on synthetic data sets show that the proposed algorithms are efficient, require relative little time in most of the testing cases, can scale to large or dense graphs, and can accommodate to more complex fuzzy matching cases.Comment: 15 pages, 11 figures, submitted to DASFAA 200

GraphMineSuite: Enabling High-Performance and Programmable Graph Mining Algorithms with Set Algebra

We propose GraphMineSuite (GMS): the first benchmarking suite for graph mining that facilitates evaluating and constructing high-performance graph mining algorithms. First, GMS comes with a benchmark specification based on extensive literature review, prescribing representative problems, algorithms, and datasets. Second, GMS offers a carefully designed software platform for seamless testing of different fine-grained elements of graph mining algorithms, such as graph representations or algorithm subroutines. The platform includes parallel implementations of more than 40 considered baselines, and it facilitates developing complex and fast mining algorithms. High modularity is possible by harnessing set algebra operations such as set intersection and difference, which enables breaking complex graph mining algorithms into simple building blocks that can be separately experimented with. GMS is supported with a broad concurrency analysis for portability in performance insights, and a novel performance metric to assess the throughput of graph mining algorithms, enabling more insightful evaluation. As use cases, we harness GMS to rapidly redesign and accelerate state-of-the-art baselines of core graph mining problems: degeneracy reordering (by up to >2x), maximal clique listing (by up to >9x), k-clique listing (by 1.1x), and subgraph isomorphism (by up to 2.5x), also obtaining better theoretical performance bounds

Parallelizing Maximal Clique Enumeration on GPUs

We present a GPU solution for exact maximal clique enumeration (MCE) that performs a search tree traversal following the Bron-Kerbosch algorithm. Prior works on parallelizing MCE on GPUs perform a breadth-first traversal of the tree, which has limited scalability because of the explosion in the number of tree nodes at deep levels. We propose to parallelize MCE on GPUs by performing depth-first traversal of independent subtrees in parallel. Since MCE suffers from high load imbalance and memory capacity requirements, we propose a worker list for dynamic load balancing, as well as partial induced subgraphs and a compact representation of excluded vertex sets to regulate memory consumption. Our evaluation shows that our GPU implementation on a single GPU outperforms the state-of-the-art parallel CPU implementation by a geometric mean of 4.9x (up to 16.7x), and scales efficiently to multiple GPUs. Our code has been open-sourced to enable further research on accelerating MCE