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• W3208513294 abstract "Previous chapter Next chapter Full AccessProceedings Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Incremental SSSP for Sparse Digraphs Beyond the Hopset BarrierRasmus Kyng, Simon Meierhans, and Maximilian Probst GutenbergRasmus Kyng, Simon Meierhans, and Maximilian Probst Gutenbergpp.3452 - 3481Chapter DOI:https://doi.org/10.1137/1.9781611977073.137PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Given a directed, weighted graph G = (V, E) undergoing edge insertions, the incremental single-source shortest paths (SSSP) problem asks for the maintenance of approximate distances from a dedicated source s while optimizing the total time required to process the insertion sequence of m edges. Recently, Gutenberg, Williams and Wein [STOC'20] introduced a deterministic Õ(n2) algorithm for this problem, achieving near linear time for very dense graphs. For sparse graphs, Chechik and Zhang [SODA'21] recently presented a deterministic Õ(m5/3) algorithm, and an adaptive randomized algorithm with run-time . This algorithm is remarkable for two reasons: 1) in very spare graphs it reaches the directed hopset barrier of Ω(n3/2) that applied to all previous approaches for partially-dynamic SSSP [STOC'14, SODA'20, FOCS'20] and 2) it does not resort to a directed hopset technique itself. In this article we introduce propagation synchronization, a new technique for controlling the error build-up on paths throughout batches of insertions. This leads us to a significant improvement of the approach in [SODA'21] yielding a deterministic O(m3/2) algorithm for the problem. By a very careful combination of our new technique with the sampling approach from [SODA'21], we further obtain an adaptive randomized algorithm with total update time Õ(m4/3). This is the first partially-dynamic SSSP algorithm in sparse graphs to bypass the notorious directed hopset barrier which is often seen as the fundamental challenge towards achieving truly near-linear time algorithms. Previous chapter Next chapter RelatedDetails Published:2022eISBN:978-1-61197-707-3 https://doi.org/10.1137/1.9781611977073Book Series Name:ProceedingsBook Code:PRDA22Book Pages:xvii + 3771" @default.
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• W3208513294 title "Incremental SSSP for Sparse Digraphs Beyond the Hopset Barrier" @default.
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