Building Fault-Tolerant Overlays With Low Node Degrees for Topic-Based Publish/Subscribe

Abstract

We present a new approach for designing reliable and scalable overlay networks to support topic-based pub/sub communication. We propose the <inline-formula><tex-math notation="LaTeX">${{\mathsf {MinAvg}}-{k}{\mathsf {TCO}}}$</tex-math></inline-formula> problem parameterized by <inline-formula><tex-math notation="LaTeX">${k}$</tex-math></inline-formula> : use the minimum number of edges to create a <i><inline-formula><tex-math notation="LaTeX">${k}$</tex-math><alternatives><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq3-3080281.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/></alternatives></inline-formula>-topic-connected overlay</i> ( <inline-formula><tex-math notation="LaTeX">${{k}TCO}$</tex-math></inline-formula> ) for pub/sub systems, i.e., for each topic, the sub-overlay induced by nodes interested in the topic is <inline-formula><tex-math notation="LaTeX">${k}$</tex-math></inline-formula> -connected. We prove the NP-completeness of <inline-formula><tex-math notation="LaTeX">${{\mathsf {MinAvg}}-{k}{\mathsf {TCO}}}$</tex-math></inline-formula> and show a lower-bound for the hardness of its approximation. For <inline-formula><tex-math notation="LaTeX">${{\mathsf {MinAvg}}-{2}{\mathsf {TCO}}}$</tex-math></inline-formula> , we present GM2, the first polynomial-time algorithm with an approximation ratio. For <inline-formula><tex-math notation="LaTeX">${{\mathsf {MinAvg}}-{k}{\mathsf {TCO}}}$</tex-math></inline-formula> , where <inline-formula><tex-math notation="LaTeX">${k} \geq {2}$</tex-math></inline-formula> , we propose HararyPT, a simple and efficient heuristic that aligns nodes across different sub-overlays. We experimentally demonstrate the scalability of GM2 and HararyPT with regards to overlay quality under representative pub/sub workloads. GM2 outputs <inline-formula><tex-math notation="LaTeX">${{2}TCO}$</tex-math></inline-formula> with an empirically insignificant increase in the average node degree, e.g., an increase by 4 in a 1000-node network, as compared to the baseline <inline-formula><tex-math notation="LaTeX">${{1}TCO}$</tex-math></inline-formula> produced by the best-known algorithm. Moreover, GM2 reduces the topic diameters by around 50 percent with respect to those in <inline-formula><tex-math notation="LaTeX">${{1}TCO}$</tex-math></inline-formula> .