{"year":"2019","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","day":"04","date_published":"2019-07-04T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4230/LIPIcs.ICALP.2019.13"}],"quality_controlled":"1","scopus_import":"1","title":"Algorithms and hardness for diameter in dynamic graphs","oa_version":"Published Version","intvolume":"       132","language":[{"iso":"eng"}],"status":"public","external_id":{"arxiv":["811.12527"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"article_processing_charge":"No","citation":{"apa":"Ancona, B., Henzinger, M. H., Roditty, L., Williams, V. V., &#38; Wein, N. (2019). Algorithms and hardness for diameter in dynamic graphs. In <i>46th International Colloquium on Automata, Languages, and Programming</i> (Vol. 132). Patras, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.13\">https://doi.org/10.4230/LIPICS.ICALP.2019.13</a>","chicago":"Ancona, Bertie, Monika H Henzinger, Liam Roditty, Virginia Vassilevska Williams, and Nicole Wein. “Algorithms and Hardness for Diameter in Dynamic Graphs.” In <i>46th International Colloquium on Automata, Languages, and Programming</i>, Vol. 132. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. <a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.13\">https://doi.org/10.4230/LIPICS.ICALP.2019.13</a>.","ista":"Ancona B, Henzinger MH, Roditty L, Williams VV, Wein N. 2019. Algorithms and hardness for diameter in dynamic graphs. 46th International Colloquium on Automata, Languages, and Programming. ICALP: International Colloquium on Automata, Languages, and Programming, LIPIcs, vol. 132, 13.","ieee":"B. Ancona, M. H. Henzinger, L. Roditty, V. V. Williams, and N. Wein, “Algorithms and hardness for diameter in dynamic graphs,” in <i>46th International Colloquium on Automata, Languages, and Programming</i>, Patras, Greece, 2019, vol. 132.","short":"B. Ancona, M.H. Henzinger, L. Roditty, V.V. Williams, N. Wein, in:, 46th International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019.","mla":"Ancona, Bertie, et al. “Algorithms and Hardness for Diameter in Dynamic Graphs.” <i>46th International Colloquium on Automata, Languages, and Programming</i>, vol. 132, 13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, doi:<a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.13\">10.4230/LIPICS.ICALP.2019.13</a>.","ama":"Ancona B, Henzinger MH, Roditty L, Williams VV, Wein N. Algorithms and hardness for diameter in dynamic graphs. In: <i>46th International Colloquium on Automata, Languages, and Programming</i>. Vol 132. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019. doi:<a href=\"https://doi.org/10.4230/LIPICS.ICALP.2019.13\">10.4230/LIPICS.ICALP.2019.13</a>"},"month":"07","date_created":"2022-08-12T08:14:51Z","_id":"11826","doi":"10.4230/LIPICS.ICALP.2019.13","conference":{"location":"Patras, Greece","name":"ICALP: International Colloquium on Automata, Languages, and Programming","start_date":"2019-07-09","end_date":"2019-07-12"},"author":[{"last_name":"Ancona","first_name":"Bertie","full_name":"Ancona, Bertie"},{"last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530"},{"last_name":"Roditty","full_name":"Roditty, Liam","first_name":"Liam"},{"full_name":"Williams, Virginia Vassilevska","first_name":"Virginia Vassilevska","last_name":"Williams"},{"first_name":"Nicole","full_name":"Wein, Nicole","last_name":"Wein"}],"alternative_title":["LIPIcs"],"publication":"46th International Colloquium on Automata, Languages, and Programming","publication_status":"published","abstract":[{"lang":"eng","text":"The diameter, radius and eccentricities are natural graph parameters. While these problems have been studied extensively, there are no known dynamic algorithms for them beyond the ones that follow from trivial recomputation after each update or from solving dynamic All-Pairs Shortest Paths (APSP), which is very computationally intensive. This is the situation for dynamic approximation algorithms as well, and even if only edge insertions or edge deletions need to be supported.\r\nThis paper provides a comprehensive study of the dynamic approximation of Diameter, Radius and Eccentricities, providing both conditional lower bounds, and new algorithms whose bounds are optimal under popular hypotheses in fine-grained complexity. Some of the highlights include:\r\n- Under popular hardness hypotheses, there can be no significantly better fully dynamic approximation algorithms than recomputing the answer after each update, or maintaining full APSP.\r\n- Nearly optimal partially dynamic (incremental/decremental) algorithms can be achieved via efficient reductions to (incremental/decremental) maintenance of Single-Source Shortest Paths. For instance, a nearly (3/2+epsilon)-approximation to Diameter in directed or undirected n-vertex, m-edge graphs can be maintained decrementally in total time m^{1+o(1)}sqrt{n}/epsilon^2. This nearly matches the static 3/2-approximation algorithm for the problem that is known to be conditionally optimal."}],"article_number":"13","date_updated":"2023-02-16T10:48:24Z","volume":132,"extern":"1","type":"conference","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-109-2"]}}