Activity Organization for Friend-Making Optimization in Online Social Networks

Abstract

The social presence theory in social psychology suggests that computer-mediated online interactions are inferior to face-to-face, in-person interactions. Thus, it's important to organize social activities for online social network users to meet in person. In this paper, we consider the scenarios of organizing in person friend-making social activities via online social networks (OSNs) and formulate a new research problem, namely, <i>Hop-bounded Maximum Group Friending (HMGF)</i> , that takes into consideration both existing friendships and the likelihood of new friend making in organization of the targeted in person friend-making social activities. To find a set of attendees for such social activities, HMGF is unique and challenging due to the interplay of the group size, the constraint on existing friendships, and the objective of maximizing the likelihood of friend making. We prove that HMGF is NP-Hard, and there exists no approximation algorithm for it unless <inline-formula><tex-math notation="LaTeX">$P=NP$</tex-math></inline-formula> . We also provide an Integer Linear Programming (ILP) formulation for the HMGF problem. The ILP formulation, which can be solved efficiently by a commercial solver to obtain the optimal solution for small HMGF instances, acts as a baseline approach for comparison in the evaluation of the proposed algorithm. We further propose an error-bounded approximation algorithm, <i>MaxGF</i> , to efficiently obtain the solutions very close to the optimal solutions. To boost the performance, we devise two graph-theoretical pruning strategies, namely <i>Neighbor Pruning</i> and <i>Core Pruning</i> , which can effectively avoid redundant graph explorations to improve the performance of HMGF. We also study HMGF on a class of special graphs, <i>threshold graphs</i> , which have properties very similar to many online social networks. We prove that MaxGF can obtain the optimal solution to HMGF on threshold graphs in polynomial time. We conduct a user study to validate our problem formulation and perform extensive experiments on real datasets to demonstrate the efficiency and effectiveness of our proposed algorithm. The experimental results manifest that our proposed algorithms outperform the baselines, including the ILP formulation.