  Modern data management systems often need to deal with massive, dynamic and
inherently distributed data sources. We collect the data using a distributed
network, and at the same time try to maintain a global view of the data at a
central coordinator using a minimal amount of communication. Such applications
have been captured by the distributed monitoring model which has attracted a
lot of attention in recent years. In this paper we investigate the monitoring
of the entropy functions, which are very useful in network monitoring
applications such as detecting distributed denial-of-service attacks. Our
results improve the previous best results by Arackaparambil et al. [2]. Our
technical contribution also includes implementing the celebrated AMS sampling
method (by Alon et al. [1]) in the distributed monitoring model, which could be
of independent interest.
