Given a data graph G, a source vertex u and a target vertex v of a reachability query, the reachability query is used to answer whether there exists a path from u to v in G. Reachability query processing is one of the fundamental operations in graph data management, which is widely used in biological networks, communication networks, and social networks to assist data analysis. The data graphs in practical applications usually contain information such as quantization weights associated with the structural relationships, in addition to the structural relationships between vertices. Thus, in addition to the traditional reachability relationships, users may want to further understand whether such reachability relationships satisfy specific constraints. In this paper, we study the problem of efficiently processing k -step reachability queries with weighted constraints in weighted graphs. The k -step weighted reachability query questions are used to answer the question of whether there exists a path from a source vertex u to a goal vertex v in a given weighted graph. If it exists, the path needs to satisfy 1) all edges in the path satisfy the given weight constraints, and 2) the length of the path does not exceed the given distance threshold k. To address the problem, firstly, WKRI index supporting k -step weighted reachability query processing and index construction methods based on efficient pruning strategies are proposed. Secondly, the idea of constructing index based on part of the vertexs is proposed to reduce the size of the index. We design and implement two optimized indexes GWKRI and LWKRI based on the vertex coverage set. Finally, experiments are conducted on several real datasets. The experimental results verify the efficiency of the method proposed in this paper in answering k -step weighted reachability queries.

中文翻译：

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高效的k步加权可达性查询处理算法

给定数据图G、可达性查询的源顶点u和目标顶点v，可达性查询用于回答G中是否存在从u到v的路径。可达性查询处理是图的基本操作之一数据管理，广泛应用于生物网络、通信网络、社交网络等领域，辅助数据分析。实际应用中的数据图除了包含顶点之间的结构关系外，通常还包含与结构关系相关的量化权重等信息。因此，除了传统的可达性关系之外，用户可能还想进一步了解这种可达性关系是否满足特定的约束。在本文中，我们研究了在加权图中使用加权约束有效处理 k 步可达性查询的问题。 k步加权可达性查询问题用于回答给定加权图中是否存在从源顶点u到目标顶点v的路径的问题。如果存在，则路径需要满足：1）路径中的所有边满足给定的权重约束，2）路径的长度不超过给定的距离阈值k。针对该问题，首先提出了支持k步加权可达性查询处理的WKRI索引以及基于高效剪枝策略的索引构建方法。其次，提出了基于部分顶点构建索引的思想，以减小索引的大小。我们基于顶点覆盖集设计并实现了两个优化索引GWKRI和LWKRI。最后，在几个真实数据集上进行了实验。实验结果验证了本文提出的方法在回答k步加权可达性查询方面的效率。