  In LHC Run 3, ALICE will increase the data taking rate significantly to
continuous readout of 50 kHz minimum bias Pb-Pb collisions. The reconstruction
strategy of the online offline computing upgrade foresees a first synchronous
online reconstruction stage during data taking enabling detector calibration,
and a posterior calibrated asynchronous reconstruction stage. We present a
tracking algorithm for the Time Projection Chamber (TPC), the main tracking
detector of ALICE. The reconstruction must yield results comparable to current
offline reconstruction and meet the time constraints like in the current High
Level Trigger (HLT), processing 50 times as many collisions per second as
today. It is derived from the current online tracking in the HLT, which is
based on a Cellular automaton and the Kalman filter, and we integrate missing
features from offline tracking for improved resolution. The continuous TPC
readout and overlapping collisions pose new challenges: conversion to spatial
coordinates and the application of time- and location dependent calibration
must happen in between of track seeding and track fitting while the TPC
occupancy increases five-fold. The huge data volume requires a data reduction
factor of 20, which imposes additional requirements: the momentum range must be
extended to identify low-pt looping tracks and a special refit in uncalibrated
coordinates improves the track model entropy encoding. Our TPC track finding
leverages the potential of hardware accelerators via the OpenCL and CUDA APIs
in a shared source code for CPUs, GPUs, and both reconstruction stages. Porting
more reconstruction steps like the remainder of the TPC reconstruction and
tracking for other detectors will shift the computing balance from traditional
processors to GPUs.
