  Flow cardinality estimation is the problem of estimating the number of
distinct elements in a data flow, often with a stringent memory constraint. It
has wide applications in network traffic measurement and in database systems.
The virtual LogLog algorithm proposed recently by Xiao, Chen, Chen and Ling
estimates the cardinalities of a large number of flows with a compact memory.
The purpose of this thesis is to explore two new perspectives on the estimation
process of this algorithm. Firstly, we propose and investigate a family of
estimators that generalizes the original vHLL estimator and evaluate the
performance of the vHLL estimator compared to other estimators in this family.
Secondly, we propose an alternative solution to the estimation problem by
deriving a maximum-likelihood estimator. Empirical evidence from both
perspectives suggests the near-optimality of the vHLL estimator for per-flow
estimation, analogous to the near-optimality of the HLL estimator for
single-flow estimation.
