Vertexing Algorithms with the ATLAS Detector for the HL-LHC Upgrade*

We evaluate and report on the performance of the standard vertexing algorithms used in the LHC Run 1 analyses for the ATLAS Experiment. In particular, we study the suitability of the Run 1 event categories in the high pile-up regime ($\langle\mu\rangle\sim 200$) and compare the current algorithms in terms of key metrics such as position resolution and track-vertex association. In this talk, we will discuss major features of the approaches to vertex reconstruction and their implications for vertexing in the HL-LHC upgrade, which will begin operation in mid-2026.