Fast tracking in hadron collider experiments

We present two algorithms that, when used sequentially, can reduce the combinatorics before any track reconstruction in the high occupancy tracking environments of future hadron collider experiments. The first algorithm finds the z-position of the primary physics interaction; the second selects groups of hits consistent with tracks coming from this z-position, rejecting most pile-up/noise/ghost hits. We demonstrate with examples of simulated events from ATLAS at the LHC that the algorithms are flexible, robust and efficient and at the same time fast enough to be used at the second level trigger for filtering the data before applying any tracking algorithms.