Brief Announcement: Streaming Balanced Clustering

Clustering of data points in metric space is among the most fundamental problems in computer science with plenty of applications in data mining, information retrieval and machine learning. Many of these applications deal with large datasets, and hence researchers focused on designing algorithms for these problems in large scale settings such as the streaming setting. One of the sweet versions of clustering problems is balanced clustering (or more generally capacitated clustering), where we do not desire to have some giant and several small clusters. Despite the importance of the context, the best known streaming algorithm for capacitated clustering is far from optimal. The state-of-the-art streaming algorithm for capacitated clustering gives an O(1)-approximate solution, requires three passes and only handles insertions (Bateni et al. NeurIPS'14). We develop the first single pass streaming algorithm for the capacitated clustering problems that includes capacitated k-median and capacitated k-means in Euclidean space, using only poly(kd epsilon(-1) log Delta) space, where k is the number of clusters, d is the dimension and. is the maximum relative range of a coordinate(1). Our algorithm gives (1 + epsilon)-approximation and only violates the capacity constraint by a (1 + epsilon) factor. Interestingly, unlike the previous algorithm, our algorithm handles both insertions and deletions of points. To provide this result we introduce a decomposition of the space via some curved half-spaces which might be of independent interest.