The Phase-II upgrades to the Large Hadron Collider will introduce a variety of new measurement devices to the CMS, including the High-Granularity Calorimeter (HGCAL). The increase in luminosity from these upgrades will also have the undesired side effect of vastly increasing pileup to a level at which the current machine learning vertex reconstruction (vertexing) algorithms cease to be effective. This will necessitate the development of further vertexing algorithms. Using high precision timing measurements from simulated events in the HGCAL, we design a vertex reconstruction algorithm that requires only the spatiotemporal arrival coordinates to reconstruct the interaction vertex of a collision with sub-millimeter resolution. We also analyse how particle energy and simulated time smearing affect this resolution and we apply this algorithm to more realistic H->γγ sets. To do this, we implement a set of filters to remove poorly-reconstructed events and introduce a new algorithm capable of reconstructing interaction vertices given the pointing data and arrival data of a single cluster. Progress on this work was ultimately hindered by extensive errors in the clustering algorithms used the generation of the datasets; should these errors be resolved, further work would include integration with tracker information and the application of these algorithms to high-pileup scenarios and QCD jets
