Offline Reconstruction Algorithms for the CMS High Granularity Calorimeter for HL-LHC

The upgraded High Luminosity LHC, after the third Long Shutdown (LS3), will provide an instantaneous luminosity of $7.5 \times 10^{34}$ cm$^{-2}$ s$^{-1}$ (levelled), at the price of extreme pileup of up to 200 interactions per crossing. Such extreme pileup poses significant challenges, in particular for forward calorimetry. As part of its HL-LHC upgrade program, the CMS collaboration is designing a High Granularity Calorimeter to replace the existing endcap calorimeters. It features unprecedented transverse and longitudinal segmentation for both electromagnetic and hadronic compartments. The electromagnetic and a large fraction of the hadronic portions will be based on hexagonal silicon sensors of 0.5 - 1 cm$^2$ cell size, with the remainder of the hadronic portion based on highly-segmented scintillators with SiPM readout. Offline clustering algorithms that make use of this extreme granularity require novel approaches to preserve the fine structure of showers and to be stable against pileup, while supporting the particle flow approach by enhancing pileup rejection and particle identification. We discuss the principle and performance of a set of clustering algorithms for the HGCAL based on techniques borrowed from machine learning and computer vision. These algorithms lend themselves particularly well to be deployed on GPUs. The features of the algorithm, as well as an analysis of the CPU requirements in the presence of large pileup, are presented.