  Charged particle reconstruction in the presence of many simultaneous
proton-proton ($pp$) collisions in the LHC is a challenging task for the ATLAS
experiment's reconstruction software due to the combinatorial complexity. This
paper describes the major changes made to adapt the software to reconstruct
high-activity collisions with an average of 50 or more simultaneous $pp$
interactions per bunch crossing (pile-up) promptly using the available
computing resources. The performance of the key components of the track
reconstruction chain and its dependence on pile-up are evaluated, and the
improvement achieved compared to the previous software version is quantified.
For events with an average of 60 $pp$ collisions per bunch crossing, the
updated track reconstruction is twice as fast as the previous version, without
significant reduction in reconstruction efficiency and while reducing the rate
of combinatorial fake tracks by more than a factor two.
