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- W3033174434 abstract "Abstract Given a constant number d of n × n matrices with total m non-infinity entries, we show how to construct in (essentially optimal) O ˜ ( m n + n 2 ) time a data structure that can compute in (essentially optimal) O ˜ ( n 2 ) time the distance product of these matrices after incrementing the value (possibly to infinity) of a constant number k of entries. Our result is obtained by designing an oracle for single source replacement paths that is suited for short distances: Given a graph G = ( V , E ) , a source vertex s, and a shortest paths tree T of depth d rooted at s, the oracle can be constructed in O ˜ ( m d k ) time for any constant k. Then, given an arbitrary set S of at most k = O ( 1 ) edges and an arbitrary vertex t, the oracle in O ˜ ( 1 ) time either reports the length of the shortest s-to-t path in ( V , E ∖ S ) or otherwise reports that any such shortest path must use more than d edges." @default.
- W3033174434 created "2020-06-12" @default.
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- W3033174434 date "2020-09-01" @default.
- W3033174434 modified "2023-10-17" @default.
- W3033174434 title "Incremental distance products via faulty shortest paths" @default.
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- W3033174434 doi "https://doi.org/10.1016/j.ipl.2020.105977" @default.
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