Streaming Min-max Hypergraph Partitioning

In many applications, the data is of rich structure that can be represented by a hypergraph, where the data items are represented by vertices and the associations among items are represented by hyperedges. Equivalently, we are given an input bipartite graph with two types of vertices: items, and associations (which we refer to as topics). We consider the problem of partitioning the set of items into a given number of components such that the maximum number of topics covered by a component is minimized. This is a clustering problem with various applications, e.g. partitioning of a set of information objects such as documents, images, and videos, and load balancing in the context of modern computation platforms. In this paper, we focus on the streaming computation model for this problem, in which items arrive online one at a time and each item must be assigned irrevocably to a component at its arrival time. Motivated by scalability requirements, we focus on the class of streaming computation algorithms with memory limited to be at most linear in the number of components. We show that a greedy assignment strategy is able to recover a hidden co-clustering of items under a natural set of recovery conditions. We also report results of an extensive empirical evaluation, which demonstrate that this greedy strategy yields superior performance when compared with alternative approaches.