Parameterized maximum and average degree approximation in topic-based publish-subscribe overlay network design

Publish/subscribe communication systems where nodes subscribe to many different topics of interest are becoming increasingly more common. Designing overlay networks that connect the nodes subscribed to each distinct topic is hence a fundamental problem in these systems. For scalability and efficiency, it is important to keep the degree of the nodes in the publish/subscribe system low. Ideally one would like to be able not only to keep the average degree of the nodes low, but also to ensure that all nodes have equally the same degree, giving rise to the following problem: Given a collection of nodes and their topic subscriptions, connect the nodes into a graph with low average and maximum degree such that for each topic t, the graph induced by the nodes interested in t is connected. We present the first polynomial time parameterized sublinear approximation algorithm for this problem.We also propose a heuristic for constructing topic-connected networks with low average degree and diameter 2 and validate our results through simulations.