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In the context of designing a scalable overlay network to supportdecentralized topic-based pub/sub communication, the Minimum Topic-ConnectedOverlay problem (Min-TCO in short) has been investigated: Given a set of ttopics and a collection of n users together with the lists of topics they areinterested in, the aim is to connect these users to a network by a minimumnumber of edges such that every graph induced by users interested in a commontopic is connected. It is known that Min-TCO is NP-hard and approximable withinO(log t) in polynomial time. In this paper, we further investigate the problemand some of its special instances. We give various hardness results forinstances where the number of topics in which an user is interested in isbounded by a constant, and also for the instances where the number of usersinterested in a common topic is constant. For the latter case, we present afirst constant approximation algorithm. We also present some polynomial-timealgorithms for very restricted instances of Min-TCO.

On the Approximability and Hardness of Minimum Topic Connected Overlay and Its Special Instances