Hierarchical Heavy Hitter Mining on Streams

Synonyms

HHH

Definition

Given a multiset Sof N elements from a hierarchical domain D and a count thres hold φ ∈ (0,1), Hierarchical Heavy Hitters (HHH) summarize the distribution of S projected along the hierarchy of D as a set of prefixes P ⊆ D, and are defined inductively as the nodes in the hierarchy such that their “HHH count” exceeds ϕ N, where the HHH count is the sum of all descendant nodes having no HHH ancestors. The approximate HHH problem over a data stream of elements e is defined with an additional error parameter ε ∈ (0,φ), where a set of prefixes P ⊆ D and estimates of their associated frequencies, with accuracy bounds on the frequency of each p ∈ P, f_min and f_max , is output with f_min (p) ≤ f^∗(p) ≤ f_max (p) such that f^∗(p) is the true frequency of p in S (i.e., f^∗(p) = ∑_epf(e)) and f_max (p) − f_min (p) ≤ εN. Additionally, there is a coverage guarantee that, for all prefixes q ∉ P, φ N > ∑ f(e): (e q) ∧ (e P), with denoting prefix containment and (e P) denoting (∃p ∈ P: e...