Abstract. Location-Based Services (LBSs) are becoming more social and Social Networks (SNs) are increasingly including location components. Geo-Social Networks are bridging the gap between virtual and physical social networks. In this paper, we propose a new type of query called Circle of Friend Query (CoFQ) to allow finding a group of friends in a Geo-Social network whose members are close to each other both socially and geographically. More specifically, the members in the group have tight social relationships with each other and they are constrained in a small region in the geospatial space as measured by a "diameter" that integrates the two aspects. We prove that algorithms for finding the Circle of Friends (CoF ) of size k is NP-hard and then propose an ε-approximate solution. The proposed ε-approximate algorithm is guaranteed to produce a group of friends with diameter within ε of the optimal solution. The performance of our algorithm is tested on the real dataset from Foursquare. The experimental results show that our algorithm is efficient and scalable: the ε-approximate algorithm runs in polynomial time and retrieves around 95% of the optimal answers for small ε.

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