  We present \textsc{P2PTFHH} (Peer--to--Peer Time--Faded Heavy Hitters) which,
to the best of our knowledge, is the first distributed algorithm for mining
time--faded heavy hitters on unstructured P2P networks. \textsc{P2PTFHH} is
based on the \textsc{FDCMSS} (Forward Decay Count--Min Space-Saving) sequential
algorithm, and efficiently exploits an averaging gossip protocol, by merging in
each interaction the involved peers' underlying data structures. We formally
prove the convergence and correctness properties of our distributed algorithm
and show that it is fast and simple to implement. Extensive experimental
results confirm that \textsc{P2PTFHH} retains the extreme accuracy and error
bound provided by \textsc{FDCMSS} whilst showing excellent scalability. Our
contributions are three-fold: (i) we prove that the averaging gossip protocol
can be used jointly with our augmented sketch data structure for mining
time--faded heavy hitters; (ii) we prove the error bounds on frequency
estimation; (iii) we experimentally prove that \textsc{P2PTFHH} is extremely
accurate and fast, allowing near real time processing of large datasets.
