  As the Large Hadron Collider (LHC) continues its upward progression in energy
and luminosity towards the planned High-Luminosity LHC (HL-LHC) in 2025, the
challenges of the experiments in processing increasingly complex events will
also continue to increase. Improvements in computing technologies and
algorithms will be a key part of the advances necessary to meet this challenge.
Parallel computing techniques, especially those using massively parallel
computing (MPC), promise to be a significant part of this effort. In these
proceedings, we discuss these algorithms in the specific context of a
particularly important problem: the reconstruction of charged particle tracks
in the trigger algorithms in an experiment, in which high computing performance
is critical for executing the track reconstruction in the available time. We
discuss some areas where parallel computing has already shown benefits to the
LHC experiments, and also demonstrate how a MPC-based trigger at the CMS
experiment could not only improve performance, but also extend the reach of the
CMS trigger system to capture events which are currently not practical to
reconstruct at the trigger level.
