—Overlay design for topic-based publish/subscribe (pub/sub) systems is of primary importance because the overlay forms the basis for the system and directly impacts its performance. This paper focuses on the - problem: Use the minimum number of edges to construct a topic-connected overlay (TCO) such that all nodes that are interested in the same topic are organized in a directly connected dissemination suboverlay. Existing algorithms for - suffer from three key drawbacks: 1) prohibitively high runtime cost; 2) reliance on global knowledge and centralized operation; and 3) nonincremental operation by reconstructing the TCO from scratch. From a practical point of view, these are all severe limitations. To address these concerns, we develop algorithms that dynamically join multiple TCOs. Inspired by the divide-and-conquer character of this idea, we derive a number of algorithms for the original - problem that accommodate a variety of practical pub/sub workloads. Both theoretical analysi...