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Achieving the next three orders of magnitude performance increase to move from petascale to exascale computing will require a significant advancements in several fundamental areas. Recent studies have outlined many of the challenges in hardware and software that will be needed. In this paper, we examine these challenges with respect to high-performance networking. We describe the repercussions of anticipated changes to computing and networking hardware and discuss the impact that alternative parallel programming models will have on the network software stack. We also present some ideas on possible approaches that address some of these challenges.