2021
DOI: 10.48550/arxiv.2107.13309
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$(1+ε)$-Approximate Shortest Paths in Dynamic Streams

Abstract: Computing approximate shortest paths in the dynamic streaming setting is a fundamental challenge that has been intensively studied during the last decade. Currently existing solutions for this problem either build a sparse multiplicative spanner of the input graph and compute shortest paths in the spanner offline, or compute an exact single source BFS tree.Solutions of the first type are doomed to incur a stretch-space tradeoff of 2κ − 1 versus n 1+1/κ , for an integer parameter κ. (In fact, existing solutions… Show more

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Cited by 1 publication
(3 citation statements)
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“…We then use the spanner thus constructed to compute (1 + ϵ )approximate S × V shortest paths from up to n 1/κ designated sources. (See Section 6 of [15] for more details.) Theorem 2.2.…”
Section: Technical Overviewmentioning
confidence: 99%
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“…We then use the spanner thus constructed to compute (1 + ϵ )approximate S × V shortest paths from up to n 1/κ designated sources. (See Section 6 of [15] for more details.) Theorem 2.2.…”
Section: Technical Overviewmentioning
confidence: 99%
“…We then use the hopset thus constructed to compute (1 + ϵ )approximate S × V shortest paths from up to n 1/κ designated sources. (See Section 8 of [15] for more details.) These algorithms extend the results of [10,11] from the static streaming setting to dynamic streaming one.…”
Section: Technical Overviewmentioning
confidence: 99%
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