Optimized Methods to Estimate Lower and Upper Bounds for Approximate Cycle Matching in Homogeneous Symmetric Pub/Sub System

In this paper we consider the problem of estimating lower and upper bounds for approximate cycle matching in homogeneous symmetric publish/subscribe system. The approximate cycle matching aims to find cycle matchings as many as possible with limited space, where a probability threshold is used to prune the space used to store the intermediate results of the approximate cycle matching. It is necessary to estimate the lower and upper bounds of the space to be saved according to the probability threshold. The existing method partitions a 2d space of possible subscriptions into rectangle zones by the probability threshold. The possible subscriptions in different zones are counted to estimate the lower and upper bounds. In order to get tighter bounds, we propose an estimation method based on the space partition with curves and prove that there exist such kind of curves, and then propose an estimation method based on dimension reduction in the case that the data distribution is previously known. The proposed methods are evaluated in a simulated environment. The results show that the proposed methods estimate the bounds tighter than the existing method, and the estimation is improved by nearly 20\% in the best case.