Subgraph Isomorphism Search Research Articles

Stable Subgraph Isomorphism Search in Temporal Networks

Stable Subgraph Isomorphism Search in Temporal Networks

DotMotif: an open-source tool for connectome subgraph isomorphism search and graph queries

Recent advances in neuroscience have enabled the exploration of brain structure at the level of individual synaptic connections. These connectomics datasets continue to grow in size and complexity; methods to search for and identify interesting graph patterns offer a promising approach to quickly reduce data dimensionality and enable discovery. These graphs are often too large to be analyzed manually, presenting significant barriers to searching for structure and testing hypotheses. We combine graph database and analysis libraries with an easy-to-use neuroscience grammar suitable for rapidly constructing queries and searching for subgraphs and patterns of interest. Our approach abstracts many of the computer science and graph theory challenges associated with nanoscale brain network analysis and allows scientists to quickly conduct research at scale. We demonstrate the utility of these tools by searching for motifs on simulated data and real public connectomics datasets, and we share simple and complex structures relevant to the neuroscience community. We contextualize our findings and provide case studies and software to motivate future neuroscience exploration.

Efficient streaming subgraph isomorphism with graph neural networks

Queries to detect isomorphic subgraphs are important in graph-based data management. While the problem of subgraph isomorphism search has received considerable attention for the static setting of a single query, or a batch thereof, existing approaches do not scale to a dynamic setting of a continuous stream of queries. In this paper, we address the scalability challenges induced by a stream of subgraph isomorphism queries by caching and re-use of previous results. We first present a novel subgraph index based on graph embeddings that serves as the foundation for efficient stream processing. It enables not only effective caching and re-use of results, but also speeds-up traditional algorithms for subgraph isomorphism in case of cache misses. Moreover, we propose cache management policies that incorporate notions of reusability of query results. Experiments using real-world datasets demonstrate the effectiveness of our approach in handling isomorphic subgraph search for streams of queries.

Correct filtering for subgraph isomorphism search in compressed vertex-labeled graphs

We present a revised filtering process that corrects an error in our previous work on subgraph isomorphism search over compressed graphs. We provide additional experiments to test the contribution of the compression itself and the candidate filtering to the performance of four representative backtracking-based subgraph isomorphism search algorithms.

Querying massive graph data: A compress and search approach

Querying graph data is a fundamental problem that witnesses an increasing interest especially for massive graph databases which come as a promising alternative to relational databases for big data modeling. In this paper, we study the problem of subgraph isomorphism search which consists to enumerate the embedding of a query graph in a data graph. The most known solutions of this NP-complete problem are backtracking-based and result in a high computational cost when we deal with massive graph databases. We address this problem and its challenges via graph compression with modular decomposition. In our approach, subgraph isomorphism search is performed on compressed graphs without decompressing them yielding substantial reduction of the search space and consequently a significant saving in processing time as well as in storage space for the graphs. We evaluated our algorithms on nine real-word datasets. The experimental results show that our approach is efficient and scalable.

Multi-query optimization for subgraph isomorphism search

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.

GPU acceleration of subgraph isomorphism search in large scale graph

A novel framework for parallel subgraph isomorphism on GPUs is proposed, named GPUSI, which consists of GPU region exploration and GPU subgraph matching. The GPUSI iteratively enumerates subgraph instances and solves the subgraph isomorphism in a divide-and-conquer fashion. The framework completely relies on the graph traversal, and avoids the explicit join operation. Moreover, in order to improve its performance, a task-queue based method and the virtual-CSR graph structure are used to balance the workload among warps, and warp-centric programming model is used to balance the workload among threads in a warp. The prototype of GPUSI is implemented, and comprehensive experiments of various graph isomorphism operations are carried on diverse large graphs. The experiments clearly demonstrate that GPUSI has good scalability and can achieve speed-up of 1.4–2.6 compared to the state-of-the-art solutions.

A mathematical exploitation of simulated uniform scanning botnet propagation dynamics for early stage detection and management

The contribution of this paper is two-fold. Firstly, we propose a botnet detection approach that is sufficiently timely to enable a containment of the botnet outbreak in a supervised network. Secondly, we show that mathematical models of botnet propagation dynamics are a viable means of achieving that level of defense from bot infections in a supervised network. Our approach is built on the idea of processing network traffic such as to localize a weakly connected subgraph within a graph that models network communications between hosts, and thus consider that subgraph as representative of a suspected botnet. We devise applied statistics to infer the propagation dynamics that would characterize the suspected botnet if this latter were indeed a botnet. The inferred dynamics are materialized into a model graph. A subgraph isomorphism search determines whether or not there is an approximate match between the model graph and any subgraph of the weakly connected subgraph. An approximate match between the two leads to a timely identification of infected hosts. We have implemented this research in the Matlab and Perl programming languages, and have validated it in practice in the Emulab network testbed. In the paper, we describe our approach in detail, and discuss experiments along with experimental data that are indicative of the effectiveness of our approach.

Molecular Query Language (MQL)A Context-Free Grammar for Substructure Matching

We have developed a Java library for substructure matching that features easy-to-read syntax and extensibility. This molecular query language (MQL) is grounded on a context-free grammar, which allows for straightforward modification and extension. The formal description of MQL is provided in this paper. Molecule primitives are atoms, bonds, properties, branching, and rings. User-defined features can be added via a Java interface. In MQL, molecules are represented as graphs. Substructure matching was implemented using the Ullmann algorithm because of favorable run-time performance. The Ullmann algorithm carries out a fast subgraph isomorphism search by combining backtracking with effective forward checking. MQL software design was driven by the aim to facilitate the use of various cheminformatics toolkits. Two Java interfaces provide a bridge from our MQL package to an external toolkit: the first one provides the matching rules for every feature of a particular toolkit; the second one converts the found match from the internal format of MQL to the format of the external toolkit. We already implemented these interfaces for the Chemistry Development Toolkit.

Representation and searching of carbohydrate structures using graph-theoretic techniques

This paper describes how the carbohydrate structures in the Complex Carbohydrate Structure Database (CCSD) can be represented by labelled graphs, in which the nodes and edges of a graph are used to denote the residues and the inter-residue linkages, respectively, of a carbohydrate. These graph representations are then searched with a subgraph-isomorphism algorithm. We describe the use of one such algorithm, that due to Ullmann, and demonstrate that it provides a very precise way of searching the structures in CCSD. We also describe the use of screening techniques that can eliminate many of the CCSD structures from the subgraph-isomorphism search, with a consequent increase in the speed of the search.