{"publication_identifier":{"eisbn":["978-1-61197-340-2"],"isbn":["978-1-61197-338-9"]},"language":[{"iso":"eng"}],"date_updated":"2023-02-17T11:58:42Z","type":"conference","extern":"1","publication":"25th Annual ACM-SIAM Symposium on Discrete Algorithms","publication_status":"published","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We study dynamic (1 + ∊)-approximation algorithms for the single-source shortest paths problem in an unweighted undirected n-node m-edge graph under edge deletions. The fastest algorithm for this problem is an algorithm with O(n2+o(1)) total update time and constant query time by Bernstein and Roditty (SODA 2011). In this paper, we improve the total update time to O(n1.8+o(1) + m1+o(1)) while keeping the query time constant. This running time is essentially tight when m = Ω(n1.8) since we need Ω(m) time even in the static setting. For smaller values of m, the running time of our algorithm is subquadratic, and is the first that breaks through the quadratic time barrier.\r\n\r\nIn obtaining this result, we develop a fast algorithm for what we call center cover data structure. We also make non-trivial extensions to our previous techniques called lazy-update and monotone Even-Shiloach trees (ICALP 2013 and FOCS 2013). As by-products of our new techniques, we obtain two new results for the decremental all-pairs shortest-paths problem. Our first result is the first approximation algorithm whose total update time is faster than Õ(mn) for all values of m. Our second result is a new trade-off between the total update time and the additive approximation guarantee."}],"author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H"},{"last_name":"Krinninger","first_name":"Sebastian","full_name":"Krinninger, Sebastian"},{"full_name":"Nanongkai, Danupon","first_name":"Danupon","last_name":"Nanongkai"}],"doi":"10.1137/1.9781611973402.79","conference":{"end_date":"2014-01-07","start_date":"2014-01-05","location":"Portland, OR, United States","name":"SODA: Symposium on Discrete Algorithms"},"_id":"11876","main_file_link":[{"url":"https://doi.org/10.1137/1.9781611973402.79","open_access":"1"}],"title":"A subquadratic-time algorithm for decremental single-source shortest paths","quality_controlled":"1","scopus_import":"1","citation":{"apa":"Henzinger, M. H., Krinninger, S., &#38; Nanongkai, D. (2014). A subquadratic-time algorithm for decremental single-source shortest paths. In <i>25th Annual ACM-SIAM Symposium on Discrete Algorithms</i> (pp. 1053–1072). Portland, OR, United States: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611973402.79\">https://doi.org/10.1137/1.9781611973402.79</a>","chicago":"Henzinger, Monika H, Sebastian Krinninger, and Danupon Nanongkai. “A Subquadratic-Time Algorithm for Decremental Single-Source Shortest Paths.” In <i>25th Annual ACM-SIAM Symposium on Discrete Algorithms</i>, 1053–72. Society for Industrial and Applied Mathematics, 2014. <a href=\"https://doi.org/10.1137/1.9781611973402.79\">https://doi.org/10.1137/1.9781611973402.79</a>.","ista":"Henzinger MH, Krinninger S, Nanongkai D. 2014. A subquadratic-time algorithm for decremental single-source shortest paths. 25th Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 1053–1072.","ieee":"M. H. Henzinger, S. Krinninger, and D. Nanongkai, “A subquadratic-time algorithm for decremental single-source shortest paths,” in <i>25th Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Portland, OR, United States, 2014, pp. 1053–1072.","short":"M.H. Henzinger, S. Krinninger, D. Nanongkai, in:, 25th Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2014, pp. 1053–1072.","ama":"Henzinger MH, Krinninger S, Nanongkai D. A subquadratic-time algorithm for decremental single-source shortest paths. In: <i>25th Annual ACM-SIAM Symposium on Discrete Algorithms</i>. Society for Industrial and Applied Mathematics; 2014:1053-1072. doi:<a href=\"https://doi.org/10.1137/1.9781611973402.79\">10.1137/1.9781611973402.79</a>","mla":"Henzinger, Monika H., et al. “A Subquadratic-Time Algorithm for Decremental Single-Source Shortest Paths.” <i>25th Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Society for Industrial and Applied Mathematics, 2014, pp. 1053–72, doi:<a href=\"https://doi.org/10.1137/1.9781611973402.79\">10.1137/1.9781611973402.79</a>."},"date_created":"2022-08-16T12:58:31Z","month":"01","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2014-01-01T00:00:00Z","oa":1,"page":"1053-1072","publisher":"Society for Industrial and Applied Mathematics","status":"public","year":"2014","day":"01"}