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The increasing integration of patient-specific genomic data into clinical practice and research raises serious privacy concerns. Various systems have been proposed that protect privacy by removing or encrypting explicitly identifying information, such as name or social security number, into pseudonyms. Though these systems claim to protect identity from being disclosed, they lack formal proofs. In this paper, we study the erosion of privacy when genomic data, either pseudonymous or data believed to be anonymous, are released into a distributed healthcare environment. Several algorithms are introduced, collectively called RE-Identification of Data In Trails (REIDIT), which link genomic data to named individuals in publicly available records by leveraging unique features in patient-location visit patterns. Algorithmic proofs of re-identification are developed and we demonstrate, with experiments on real-world data, that susceptibility to re-identification is neither trivial nor the result of bizarre isolated occurrences. We propose that such techniques can be applied as system tests of privacy protection capabilities.