Heavy Hitters via Cluster-Preserving Clustering
We develop a new algorithm for the turnstile heavy hitters problem in general turnstile streams, the EXPANDERSKETCH, which finds the approximate top-k items in a universe of size n using the same asymptotic O(k log n) words of memory and O(log n) update time as the COUNTMIN and COUNTSKETCH, but requiring only O(k poly(log n)) time to answer queries instead of the O(n log n) time of the other two. The notion of "approximation" is the same l2 sense as the COUNTSKETCH, which given known lower bounds is the strongest guarantee one can achieve in sublinear memory. Our main innovation is an efficient reduction from the heavy hitters problem to a clustering problem in which each heavy hitter is encoded as some form of noisy spectral cluster in a graph, and the goal is to identify every cluster.
