  Top-$k$ frequent items detection is a fundamental task in data stream mining.
Many promising solutions are proposed to improve memory efficiency while still
maintaining high accuracy for detecting the Top-$k$ items. Despite the memory
efficiency concern, the users could suffer from privacy loss if participating
in the task without proper protection, since their contributed local data
streams may continually leak sensitive individual information. However, most
existing works solely focus on addressing either the memory-efficiency problem
or the privacy concerns but seldom jointly, which cannot achieve a satisfactory
tradeoff between memory efficiency, privacy protection, and detection accuracy.
  In this paper, we present a novel framework HG-LDP to achieve accurate
Top-$k$ item detection at bounded memory expense, while providing rigorous
local differential privacy (LDP) protection. Specifically, we identify two key
challenges naturally arising in the task, which reveal that directly applying
existing LDP techniques will lead to an inferior ``accuracy-privacy-memory
efficiency'' tradeoff. Therefore, we instantiate three advanced schemes under
the framework by designing novel LDP randomization methods, which address the
hurdles caused by the large size of the item domain and by the limited space of
the memory. We conduct comprehensive experiments on both synthetic and
real-world datasets to show that the proposed advanced schemes achieve a
superior ``accuracy-privacy-memory efficiency'' tradeoff, saving $2300\times$
memory over baseline methods when the item domain size is $41,270$. Our code is
open-sourced via the link.
