A learned data structure maintains (1+epsilon)-approximate single-source shortest paths under edge insertions in O~(m min_tau {tau+|HIGH(tau)|} log W/epsilon) total time, with an offline building block running in near-linear time.
Fully dynamic (2+ ε) approximate all-pairs shortest paths with fast query and close to linear update time
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Incremental Approximate Single-Source Shortest Paths with Predictions
A learned data structure maintains (1+epsilon)-approximate single-source shortest paths under edge insertions in O~(m min_tau {tau+|HIGH(tau)|} log W/epsilon) total time, with an offline building block running in near-linear time.