We consider the classical single-source shortest path problem in directed weighted graphs. D. Eppstein proved recently an Ω(n³) lower bound for oblivious algorithms that use relaxation operations to update the tentative distances from the source vertex. We generalize this result by extending this Ω(n³) lower bound to adaptive algorithms that, in addition to relaxations, can perform queries involving some simple types of linear inequalities between edge weights and tentative distances. Our model captures as a special case the operations on tentative distances used by Dijkstra’s algorithm.
@InProceedings{atalig_et_al:LIPIcs.ISAAC.2024.8, author = {Atalig, Sunny and Hickerson, Alexander and Srivastav, Arrdya and Zheng, Tingting and Chrobak, Marek}, title = {{Lower Bounds for Adaptive Relaxation-Based Algorithms for Single-Source Shortest Paths}}, booktitle = {35th International Symposium on Algorithms and Computation (ISAAC 2024)}, pages = {8:1--8:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-354-6}, ISSN = {1868-8969}, year = {2024}, volume = {322}, editor = {Mestre, Juli\'{a}n and Wirth, Anthony}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.8}, URN = {urn:nbn:de:0030-drops-221356}, doi = {10.4230/LIPIcs.ISAAC.2024.8}, annote = {Keywords: single-source shortest paths, lower bounds, decision trees} }
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