Analysis of Count-Min sketch under conservative update

Abstract

Count-Min sketch is a hash-based data structure to represent a dynamically changing associative array of counters. Here we analyse the counting version of Count-Min under a stronger update rule known as conservative update, assuming the uniform distribution of input keys. We show that the accuracy of conservative update strategy undergoes a phase transition, depending on the number of distinct keys in the input as a fraction of the size of the Count-Min array. We prove that below the threshold, the relative error is asymptotically o(1) (as opposed to the regular Count-Min strategy), whereas above the threshold, the relative error is Θ(1). The threshold corresponds to the peelability threshold of random k-uniform hypergraphs. We demonstrate that even for small number of keys, peelability of the underlying hypergraph is a crucial property to ensure the o(1) error.