An Efficient Alternative to Subgraph Isomorphism and Its Advantages

W. Zhang, George P. Chan, Wai Kin Victor Chan
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Abstract

Subgraph Isomorphism is a fundamental problem in graph theory. It has many applications in social network analysis, molecular investigations, knowledge graphs, etc. Given a Query Graph and a Data Graph, the target of Subgraph Isomorphism, i.e., Subgraph Matching, is to determine if this Query Graph is isomorphic to any subgraph of the Data Graph. This work proposes a new type of Query Graph, combined with multiple general Query Graphs. We call it Compulsory-Optional Query Graph (CO Query Graph). This new type of Query Graph contains all the vertices in the combined general Query Graph, and each vertex corresponds to a search priority. Based on CO Query Graph, the previous multiple match processes can be reduced to one. It tremendously improves search efficiency. The Subgraph Isomorphism based on this new kind of Query Graph is an extension and improvement of the previous Subgraph Isomorphism studies. We propose a backtracking-pruning-based CO solver (BPC). This algorithm builds on the backtracking-pruning framework. BPC modifies the output criterion and matching conditions to satisfy the CO query context. A case study of real-world graph data illustrates that BPC built on CO Query Graph is more efficient than conventional Query Graphs. To verify the effectiveness of our method, we conducted experiments on the synthetic graph and real-world data. The results show that the BPC can significantly reduce the search space and improve the search efficiency in the recursive calls and the response time. Experiments resulting from synthetic graph data analysis allow us to primarily identify the critical factor that affects the efficiency of the BPC primarily.
子图同构的一种有效替代方法及其优点
子图同构是图论中的一个基本问题。它在社会网络分析、分子调查、知识图谱等方面有着广泛的应用。给定一个查询图和一个数据图,子图同构即子图匹配的目标是确定该查询图是否与数据图的任何子图同构。本文提出了一种结合多种通用查询图的新型查询图。我们称之为强制-可选查询图(CO Query Graph)。这种新型查询图包含了合并后的通用查询图中的所有顶点,每个顶点对应一个搜索优先级。基于CO查询图,可以将之前的多个匹配过程简化为一个。它极大地提高了搜索效率。基于这种新型查询图的子图同构是对以往子图同构研究的扩展和改进。我们提出了一种基于回溯修剪的CO求解器(BPC)。该算法建立在回溯-剪枝框架之上。BPC修改输出标准和匹配条件以满足CO查询上下文。一个实际图形数据的案例研究表明,构建在CO查询图上的BPC比传统的查询图更有效。为了验证我们方法的有效性,我们在合成图和实际数据上进行了实验。结果表明,该算法能显著减少递归调用的搜索空间,提高递归调用的搜索效率和响应时间。合成图数据分析的实验结果使我们能够主要确定影响BPC效率的关键因素。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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