The Subgraph Matching (SM) problem consists of finding all the embeddings of a given small graph, called the query, into a large graph, called the target. The SM problem has been widely studied for simple graphs, i.e. graphs where there is exactly one edge between two nodes and nodes have single labels, but few approaches have been devised for labeled multigraphs, i.e. graphs having possibly multiple labels on nodes in which pair of nodes may have multiple labeled edges between them. Here we present MultiRI, a novel algorithm for the Sub-Multigraph Matching (SMM) problem, i.e. subgraph matching in labeled multigraphs. MultiRI improves on the state-of-the-art by computing compatibility domains and symmetry breaking conditions on query nodes to filter the search space of possible solutions. Empirically, we show that MultiRI outperforms the state-of-the-art method for the SMM problem in both synthetic and real graphs, with a multiplicative speedup between five and ten for large graphs, by using a limited amount of memory.

中文翻译：

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MultiRI：标记多重图中的快速子图匹配

子图匹配 (SM) 问题包括将给定的小图（称为查询）的所有嵌入查找到称为目标的大图中。SM 问题已被广泛研究用于简单图，即两个节点之间恰好有一条边且节点具有单个标签的图，但很少有人为带标签的多重图设计了方法，即在节点上可能有多个标签的图，其中一对节点之间可能有多个标记的边。在这里，我们提出了 MultiRI，这是一种用于子多重图匹配 (SMM) 问题的新算法，即标记多重图中的子图匹配。MultiRI 通过计算查询节点上的兼容性域和对称破坏条件来过滤可能解决方案的搜索空间，从而改进了最新技术。根据经验，