  At the LHC, tagging boosted heavy particle resonances which decay
hadronically, such as top quarks and Higgs bosons, can play an essential role
in new physics searches. In events with high multiplicity, however, the
standard approach to tag boosted resonances by a large-radius fat jet becomes
difficult because the resonances are not well-separated from other hard
radiation. In this paper, we propose a different approach to tag and
reconstruct boosted resonances by using the recently proposed mass-jump jet
algorithm. A key feature of the algorithm is the flexible radius of the jets,
which results from a terminating veto that prevents the recombination of two
hard prongs if their combined jet mass is substantially larger than the masses
of the separate prongs. The idea of collecting jets in "buckets" is also used.
As an example, we consider the fully hadronic final state of pair-produced
vectorlike top partners at the LHC, $pp\to T\bar{T}\to t\bar{t}HH$, and show
that the new approach works better than the corresponding generalized $k_T$ jet
clustering algorithm. We also show that tagging and kinematic reconstruction of
boosted top quarks and Higgs bosons are possible with good quality even in
these very busy final states. The vectorlike top partners are kinematically
reconstructed, which allows their direct mass measurement.
