document: Constant-factor approximation algorithms for identifying dynamic communities We propose two approximation algorithms for identifying communities in dynamic social networks . Communities are intuitively characterized as `` unusually densely knit '' subsets of a social network . This notion becomes more problematic if the social interactions change over time . Aggregating social networks over time can radically misrepresent the existing and changing community structure . Recently , we have proposed an optimization-based framework for modeling dynamic community structure . Also , we have proposed an algorithm for finding such structure based on maximum weight bipartite matching . In this paper , we analyze its performance guarantee for a special case where all actors can be observed at all times . In such instances , we show that the algorithm is a small constant factor approximation of the optimum . We use a similar idea to design an approximation algorithm for the general case where some individuals are possibly unobserved at times , and to show that the approximation factor increases twofold but remains a constant regardless of the input size . This is the first algorithm for inferring communities in dynamic networks with a provable approximation guarantee . We demonstrate the general algorithm on real data sets . The results confirm the efficiency and effectiveness of the algorithm in identifying dynamic communities .
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