  With increasing instantaneous luminosity at the LHC come additional
reconstruction challenges. At high luminosity, many collisions occur
simultaneously within one proton-proton bunch crossing. The isolation of an
interesting collision from the additional "pileup" collisions is needed for
effective physics performance. In the CMS Collaboration, several techniques
capable of mitigating the impact of these pileup collisions have been
developed. Such methods include charged-hadron subtraction, pileup jet
identification, isospin-based neutral particle "$\delta\beta$" correction, and,
most recently, pileup per particle identification. This paper surveys the
performance of these techniques for jet and missing transverse momentum
reconstruction, as well as muon isolation. The analysis makes use of data
corresponding to 35.9 fb$^{-1}$ collected with the CMS experiment in 2016 at a
center-of-mass energy of 13 TeV. The performance of each algorithm is discussed
for up to 70 simultaneous collisions per bunch crossing. Significant
improvements are found in the identification of pileup jets, the jet energy,
mass, and angular resolution, missing transverse momentum resolution, and muon
isolation when using pileup per particle identification.
