  We propose an algorithm, deployable on a highly-parallelized graph computing
architecture, to perform rapid reconstruction of charged-particle trajectories
in the high energy collisions at the Large Hadron Collider and future
colliders. We use software emulation to show that the algorithm can achieve an
efficiency in excess of 99.95% for reconstruction with good accuracy. The
algorithm can be implemented on silicon-based integrated circuits using
field-programmable gate array technology. Our approach can enable a fast
trigger for massive charged particles that decay invisibly in the tracking
volume, as in some new-physics scenarios related to particulate dark matter. If
production of dark matter or other new neutral particles is mediated by
metastable charged particles and is not associated with other triggerable
energy deposition in the detectors, our method would be useful for triggering
on the charged mediators using the small-radius silicon detectors.
