DescriptionRepresentative paths analysis generalizes and improves MPI critical path analysis. To improve diagnostic insight, we sample the distribution of program path costs and retain k representative paths. We describe scalable algorithms to collect representative paths and path profiles. To collect full paths efficiently, we introduce path pruning that reduces permanent space requirements from a trace (proportional to ranks) to path length (the minimum). To make space requirements independent of ranks and execution time --- a small constant in practice --- we profile program paths. Avoiding the limitations of prior path profiling approaches, we dynamically discover tasks and attribute costs in high resolution. We evaluate our algorithms on seven applications scaled up to 7000 MPI ranks. Full program paths use as little as 0.01% the permanent space of current methods; profiles require a nearly constant 100--1000 KB. Execution overhead is under 5% when synchronization intervals are sufficiently large (a few milliseconds).