# A Generalized Algorithm for Publish/Subscribe Overlay Design and Its Fast Implementation

Chen Chen, Roman Vitenberg, and Hans-Arno Jacobsen.

University of Toronto, University of Oslo, 2012.

## Abstract

It is a challenging and fundamental problem to construct the underlying overlay network to support efficient and scalable information distribution in topic-based publish/subscribe systems. Existing overlay design algorithms aim to minimize the node fan-out while building topic-connected overlays, in which all nodes interested in the same topic are organized in a directly connected dissemination sub-overlay. However, most state-of-the-art algorithms suffer from high computational complexity, such as $O(|V|^4|T|)$, where $V$ is the node set and $T$ is the topic set.

We devise a general indexing data structure that %allows us to provides a significantly faster implementation, with $O(|V|^2|T|)$ running time, for different state-of-the-art algorithms. The generality of the indexing data structure is due to the fact that it enables edge lookup by both node degree and \emph{edge contribution}, a central metric in all existing algorithms. When tested on typical pub/sub workloads, the speedup observed was by a factor of over $1\,000$, thereby rendering the algorithms more suitable for practical use. For example, under a typically Zipf distributed pub/sub workload, with $1\,000$ nodes and $100$ topics, our new implementation completes in $3.823$ seconds, while the previous alternative takes over $555$ minutes.

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