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Research on new queries for finding dense subgraphs and groups has been actively pursued due to their many applications, especially in social network analysis and graph mining. However, existing work faces two major weaknesses: i) incapability of supporting personalized neighborhood density, and ii) inability to find sparse groups. To tackle the above issues, we propose a new query, called Density-Customized Social Group Query (DCSGQ), that accommodates the need for personalized density by allowing individual users to flexibly configure their social tightness (and sparseness) for the target group. The proposed DCSGQ is general due to flexible in configuration of neighboring social density in queries. We prove the NP-hardness and inapproximability of DCSGQ, formulate an Integer Program (IP) as a baseline, and propose an efficient algorithm, FSGSel-RR, by relaxing the IP. We then propose a fixed-parameter tractable algorithm with a performance guarantee, named FSGSel-TD, and further combine it with FSGSel-RR into a hybrid approach, named FSGSel-Hybrid, in order to strike a good balance between solution quality and efficiency. Extensive experiments on multiple large real datasets demonstrate the superior solution quality and efficiency of our approaches over existing subgraph and group queries.

Shopping in VR malls has been regarded as a paradigm shift for E-commerce, but most of the conventional VR shopping platforms are designed for a single user. In this paper, we envisage a scenario of VR group shopping, which brings major advantages over conventional group shopping in brick-and-mortar stores and Web shopping: 1) configure flexible display of items and partitioning of subgroups to address individual interests in the group, and 2) support social interactions in the subgroups to boost sales. Accordingly, we formulate the Social-aware VR Group-Item Configuration (SVGIC) problem to configure a set of displayed items for flexibly partitioned subgroups of users in VR group shopping. We prove SVGIC is NP-hard to approximate within $\frac{32}{31} - \epsilon$. We design an approximation algorithm based on the idea of Co-display Subgroup Formation (CSF) to configure proper items for display to different subgroups of friends. Experimental results on real VR datasets and a user study with hTC VIVE manifest that our algorithms outperform baseline approaches by at least 30.1% of solution quality., Comment: 32 pages, 16 figures (41 subfigures). A shorter version of this paper has been submitted to the 46th International Conference on Very Large Databases (VLDB 2020); this is an expanded version containing supplementary details

Spatial proximity is one of the most important factors for the quick deployment of the task groups in various time-sensitive missions. This article proposes a new spatial query, Spatio-Social Team Query (SSTQ) , that forms a strong task group by considering (1) the group’s spatial distance (i.e., transportation time), (2) skills of the candidate group members, and (3) social rapport among the candidates. Efficient processing of SSTQ is very challenging, because the aforementioned spatial, skill, and social factors need to be carefully examined. In this article, therefore, we first formulate two subproblems of SSTQ, namely Hop-Constrained Team Problem (HCTP) and Connection-Oriented Team Query (COTQ) . HCTP is a decision problem that considers only social and skill dimensions. We prove that HCTP is NP-Complete. Moreover, based on the hardness of HCTP, we prove that SSTQ is NP-Hard and inapproximable within any factor . On the other hand, COTQ is a special case of SSTQ that relaxes the social constraint. We prove that COTQ is NP-Hard and propose an approximation algorithm for COTQ, namely COTprox . Furthermore, based on the observations on COTprox, we devise an approximation algorithm, SSTprox , with a guaranteed error bound for SSTQ. Finally, to efficiently obtain the optimal solution to SSTQ for small instances, we design two efficient algorithms, SpatialFirst and SkillFirst , with different scenarios in mind. These two algorithms incorporate various effective ordering and pruning techniques to reduce the search space for answering SSTQ. Experimental results on real datasets indicate that the proposed algorithms can efficiently answer SSTQ under various parameter settings.

Three essential criteria are important for activity planning, including: (1) finding a group of attendees familiar with the initiator, (2) ensuring each attendee in the group to have tight social relations with most of the members in the group, and (3) selecting an activity period available for all attendees. Therefore, this paper proposes Social-Temporal Group Query to find the activity time and attendees with the minimum total social distance to the initiator. Moreover, this query incorporates an acquaintance constraint to avoid finding a group with mutually unfamiliar attendees. Efficient processing of the social-temporal group query is very challenging. We show that the problem is NP-hard via a proof and formulate the problem with Integer Programming. We then propose two efficient algorithms, SGSelect and STGSelect, which include effective pruning techniques and employ the idea of pivot time slots to substantially reduce the running time, for finding the optimal solutions. Experimental results indicate that the proposed algorithms are much more efficient and scalable. In the comparison of solution quality, we show that STGSelect outperforms the algorithm that represents manual coordination by the initiator., VLDB2011