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We study the exact fully dynamic shortest paths problem. For real-weighted directed graphs, we show a deterministic fully dynamic data structure with O (mn^4/5) worst-case update time processing arbitrary s, t-distance queries in O (n^4/5) time. This constitutes the first non-trivial update/query tradeoff for this problem in the regime of sparse weighted directed graphs.
Karczmarz et al. (Mon,) studied this question.
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