Primary vertex reconstruction on heterogeneous architectures.

The future development projects for the Large Hadron Collider will constantly bring nominal luminosity increase, with the ultimate goal of reaching a peak luminosity of $5 \times$ 10^$34 {cm^{-2}\,s^{-1}}$. This would result in up to 200 simultaneous proton collisions (pileup), posing significant challenges for the CMS detector reconstruction. The CMS primary vertex (PV) reconstruction is a two-step procedure consisting of vertex finding and fitting. First, the Deterministic Annealing algorithm clusters tracks coming from the same interaction vertex. Secondly, an Adaptive Vertex Fit computes the best estimate of the vertex position in three or four dimensions. For High-Luminosity LHC (HL-LHC) conditions the reconstruction of PVs is expected to be extremely time expensive (up to $6%$ of reconstruction time). In this contribution we present our studies on the rethinking and porting of PV reconstruction algorithms in order to be run on heterogeneous architectures that allows us to exploit parallelization techniques to significantly reduce the processing time. We will show the results obtained focussing on computing and physics performance for both Run3 and HL-LHC conditions.