Give Me Some Slack: Efficient Network Measurements

Many networking applications require timely access to recent network measurements, which can be captured using a sliding window model. Maintaining such measurements is a challenging task due to the fast line speed and scarcity of fast memory in routers. In this work, we study the impact of allowing \emph{slack} in the window size on the asymptotic requirements of sliding window problems. That is, the algorithm can dynamically adjust the window size between $W$ and $W(1+\tau)$ where $\tau$ is a small positive parameter. We demonstrate this model's attractiveness by showing that it enables efficient algorithms to problems such as MAX and GENERAL-SUM that require $\Omega(W)$ bits even for constant factor approximations in the exact sliding window model. Additionally, for problems that admit sub-linear approximation algorithms such as BASIC-SUMMING and COUNT-DISTINCT, the slack model enables a further asymptotic improvement.