Efficient Similarity Search on Quasi-Metric Graphs

Similarity search in metric spaces finds similar objects to a given object, which has received much attention as it is able to support various data types and flexible similarity metrics. In real-life applications, metric spaces might be combined with graphs, resulting in geo-social network, citation graph, social image graph, to name but a few. In this paper, we introduce a new notion called quasi-metric graph that connects metric data using a graph, and formulate similarity search on quasi-metric graphs based on the combined similarity metric considering both the metric data similarity and graph similarity. We propose two simple efficient approaches, the best-first method and the breadth-first method, which traverse the quasi-metric graph following the best-first and the breadth-first paradigms, respectively, and utilize the triangle inequality to prune unnecessary evaluation. Extensive experiments with three real datasets demonstrate, compared with several baseline methods, the effectiveness and efficiency of our proposed methods.