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Continuous processing of a streaming graph maintains an approximate result of the iterative computation on a recent version of the graph. Upon a user query, the accurate result on the current graph can be quickly computed by feeding the approximate results to the iterative computation --- a form of incremental computation that corrects the (small amount of) error in the approximate result. Despite the effectiveness of this approach in processing growing graphs, it is generally not applicable when edge deletions are present --- existing approximations can lead to either incorrect results (e.g., monotonic computations terminate at an incorrect minima/maxima) or poor performance (e.g., with approximations, convergence takes longer than performing the computation from scratch).
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Vora et al. (2017) studied this question.
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