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Data structures that allow efficient distance estimation have been extensively studied both in centralized models and classical distributed models. We initiate their study in newer (and arguably more realistic) models of distributed computation: the Congested Clique model and the Massively Parallel Computation (MPC) model. In MPC we give two main results: an algorithm that constructs stretch/space optimal distance sketches but takes a (small) polynomial number of rounds, and an algorithm thatdoi:10.4230/lipics.disc.2019.42 dblp:conf/wdag/DinitzN19 fatcat:3xjwtruhrvfbllwl5lwflt4pcu