Subgraph matching (or subgraph isomorphism) is one of the fundamental problems in graph analysis. Extensive research has been done to develop practical solutions for subgraph matching. The state-of-the-art algorithms such as \textsfCFL-Match and \textsfTurbo\textsubscriptiso convert a query graph into a spanning tree for obtaining candidates for each query vertex and obtaining a good matching order with the spanning tree. However, by using the spanning tree instead of the original query graph, it could lead to lower pruning power and a sub-optimal matching order. Another limitation is that they perform redundant computation in search without utilizing the knowledge learned from past computation. In this paper, we introduce three novel concepts to address these inherent limitations: 1) dynamic programming between a directed acyclic graph (DAG) and a graph, 2) adaptive matching order with DAG ordering, and 3) pruning by failing sets, which together lead to a much faster algorithm \textsfDAF for subgraph matching. Extensive experiments with real datasets show that \textsfDAF outperforms the fastest existing solution by up to orders of magnitude in terms of recursive calls as well as in terms of the elapsed time.

Efficient Subgraph Matching: Harmonizing Dynamic Programming, Adaptive Matching Order, and Failing Set Together

We study the performance of eight representative in-memory subgraph matching algorithms. Specifically, we put QuickSI, GraphQL, CFL, CECI, DP-iso, RI and VF2++ in a common framework to compare them on the following four aspects: (1) method of filtering candidate vertices in the data graph; (2) method of ordering query vertices; (3) method of enumerating partial results; and (4) other optimization techniques. Then, we compare the overall performance of these algorithms with Glasgow, an algorithm based on the constraint programming. Through experiments, we find that (1) the filtering method of GraphQL is competitive to that of the latest algorithms CFL, CECI and DP-iso in terms of pruning power; (2) the ordering methods in GraphQL and RI are usually the most effective; (3) the set intersection based local candidate computation in CECI and DP-iso performs the best in the enumeration; and (4) the failing sets pruning in DP-iso can significantly improve the performance when queries become large. Our source code is publicly available at https://github.com/RapidsAtHKUST/SubgraphMatching.

In-Memory Subgraph Matching: An In-depth Study

We study the problem of optimizing subgraph queries using the new worst-case optimal join plans. Worst-case optimal plans evaluate queries by matching one query vertex at a time using multiway intersections. The core problem in optimizing worst-case optimal plans is to pick an ordering of the query vertices to match. We design a cost-based optimizer that (i) picks efficient query vertex orderings for worst-case optimal plans; and (ii) generates hybrid plans that mix traditional binary joins with worst-case optimal style multiway intersections. Our cost metric combines the cost of binary joins with a new cost metric called intersection-cost. The plan space of our optimizer contains plans that are not in the plan spaces based on tree decompositions from prior work. In addition to our optimizer, we describe an adaptive technique that changes the orderings of the worst-case optimal sub-plans during query execution. We demonstrate the effectiveness of the plans our optimizer picks and adaptive technique through extensive experiments. Our optimizer is integrated into the Graphflow DBMS.

pdf/optimizing-subgraph-queries-by-combining-binary-and-worst-3z5nsz8086.pdf

Optimizing Subgraph Queries by Combining Binary and Worst-Case Optimal Joins.

We study the problem of finding and monitoring fixed-size subgraphs in a continually changing large-scale graph. We present the first approach that (i) performs worst-case optimal computation and c...

Distributed evaluation of subgraph queries using worst-case optimal low-memory dataflows

Recently there emerge many distributed algorithms that aim at solving subgraph matching at scale. Existing algorithm-level comparisons failed to provide a systematic view of distributed subgraph matching mainly due to the intertwining of strategy and optimization. In this paper, we identify four strategies and three general-purpose optimizations from representative state-of-the-art algorithms. We implement the four strategies with the optimizations based on the common Timely dataflow system for systematic strategy-level comparison. Our implementation covers all representative algorithms. We conduct extensive experiments for both unlabelled matching and labelled matching to analyze the performance of distributed subgraph matching under various settings, which is finally summarized as a practical guide.

/pdf/distributed-subgraph-matching-on-timely-dataflow-178b7s87ob.pdf

Distributed subgraph matching on timely dataflow

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Distributed evaluation of subgraph queries using worst-case optimal low-memory dataflows