A knowledge graph (KG) represents a set of entities and their relations. To explore the content of a large and complex KG, a convenient way is keyword-based querying. Traditional methods assign small weights to salient entities or relations, and answer an exploratory keyword query by computing a group Steiner tree (GST), which is a minimum-weight subgraph that connects all the keywords in the query. Recent studies have suggested improving the semantic cohesiveness of a query answer by minimizing the pairwise semantic distances between the entities in a subgraph, but it remains unclear how to efficiently compute such a semantically cohesive subgraph. In this paper, we formulate it as a quadratic group Steiner tree problem (QGSTP) by extending the classical minimum-weight GST problem which is NP-hard. We design two approximation algorithms for QGSTP and prove their approximation ratios. Furthermore, to improve their practical performance, we present various heuristics, e.g., pruning and ranking strategies.

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