•Local track reconstruction algorithms can be efficiently designed for parallel architectures.•Search by triplet is an efficient local track reconstruction algorithm optimized for CPU and GPU parallel architectures.•Search by triplet performs track reconstruction of the LHCb VELO detector at a rate of up to 592 kHz in a single GPU.•Search by triplet achieves an average physics reconstruction efficiency of 98.52% for the LHCb VELO detector.•Search by triplet is one of the main track reconstruction algorithms of the first software trigger stage of LHCb. Millions of particles are collided every second at the LHCb detector placed inside the Large Hadron Collider at CERN. The particles produced as a result of these collisions pass through various detecting devices which will produce a combined raw data rate of up to 40 Tbps by 2021. These data will be fed through a data acquisition system which reconstructs individual particles and filters the collision events in real time. This process will occur in a heterogeneous farm employing exclusively off-the-shelf CPU and GPU hardware, in a two stage process known as High Level Trigger. The reconstruction of charged particle trajectories in physics detectors, also referred to as track reconstruction or tracking, determines the position, charge and momentum of particles as they pass through detectors. The Vertex Locator subdetector (VELO) is the closest such detector to the beamline, placed outside of the region where the LHCb magnet produces a sizable magnetic field. It is used to reconstruct straight particle trajectories which serve as seeds for reconstruction of other subdetectors and to locate collision vertices. The VELO subdetector will detect up to 109 particles every second, which need to be reconstructed in real time in the High Level Trigger. We present Search by triplet, an efficient track reconstruction algorithm. Our algorithm is designed to run efficiently across parallel architectures. We extend on previous work and explain the algorithm evolution since its inception. We show the scaling of our algorithm under various situations, and analyse its amortized time in terms of complexity for each of its constituent parts and profile its performance. Our algorithm is the current state-of-the-art in VELO track reconstruction on SIMT architectures, and we qualify its improvements over previous results.