{"date_created":"2022-08-08T12:50:25Z","month":"07","citation":{"apa":"Henzinger, M. H., &#38; King, V. (1999). Randomized fully dynamic graph algorithms with polylogarithmic time per operation. <i>Journal of the ACM</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/320211.320215\">https://doi.org/10.1145/320211.320215</a>","ista":"Henzinger MH, King V. 1999. Randomized fully dynamic graph algorithms with polylogarithmic time per operation. Journal of the ACM. 46(4), 502–516.","chicago":"Henzinger, Monika H, and Valerie King. “Randomized Fully Dynamic Graph Algorithms with Polylogarithmic Time per Operation.” <i>Journal of the ACM</i>. Association for Computing Machinery, 1999. <a href=\"https://doi.org/10.1145/320211.320215\">https://doi.org/10.1145/320211.320215</a>.","ieee":"M. H. Henzinger and V. King, “Randomized fully dynamic graph algorithms with polylogarithmic time per operation,” <i>Journal of the ACM</i>, vol. 46, no. 4. Association for Computing Machinery, pp. 502–516, 1999.","short":"M.H. Henzinger, V. King, Journal of the ACM 46 (1999) 502–516.","mla":"Henzinger, Monika H., and Valerie King. “Randomized Fully Dynamic Graph Algorithms with Polylogarithmic Time per Operation.” <i>Journal of the ACM</i>, vol. 46, no. 4, Association for Computing Machinery, 1999, pp. 502–16, doi:<a href=\"https://doi.org/10.1145/320211.320215\">10.1145/320211.320215</a>.","ama":"Henzinger MH, King V. Randomized fully dynamic graph algorithms with polylogarithmic time per operation. <i>Journal of the ACM</i>. 1999;46(4):502-516. doi:<a href=\"https://doi.org/10.1145/320211.320215\">10.1145/320211.320215</a>"},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"1999-07-01T00:00:00Z","day":"01","page":"502-516","article_type":"original","publisher":"Association for Computing Machinery","status":"public","year":"1999","language":[{"iso":"eng"}],"intvolume":"        46","publication_identifier":{"issn":["0004-5411"],"eissn":["1557-735X"]},"type":"journal_article","extern":"1","volume":46,"date_updated":"2022-09-12T10:50:08Z","oa_version":"None","abstract":[{"text":"This paper solves a longstanding open problem in fully dynamic algorithms: We present the first fully dynamic algorithms that maintain connectivity, bipartiteness, and approximate minimum spanning trees in polylogarithmic time per edge insertion or deletion. The algorithms are designed using a new dynamic technique that combines a novel graph decomposition with randomization. They are Las-Vegas type randomized algorithms which use simple data structures and have a small constant factor.\r\nLet n denote the number of nodes in the graph. For a sequence of Ω(m0) operations, where m0 is the number of edges in the initial graph, the expected time for p updates is O(p log3 n) (througout the paper the logarithms are based 2) for connectivity and bipartiteness. The worst-case time for one query is O(log n/log log n). For the k-edge witness problem (“Does the removal of k given edges disconnect the graph?”) the expected time for p updates is O(p log3 n) and the expected time for q queries is O(qk log3 n). Given a graph with k different weights, the minimum spanning tree can be maintained during a sequence of p updates in expected time O(pk log3 n). This implies an algorithm to maintain a 1 + ε-approximation of the minimum spanning tree in expected time O((p log3 n logU)/ε) for p updates, where the weights of the edges are between 1 and U.","lang":"eng"}],"publication":"Journal of the ACM","issue":"4","publication_status":"published","title":"Randomized fully dynamic graph algorithms with polylogarithmic time per operation","scopus_import":"1","quality_controlled":"1","author":[{"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":"King","first_name":"Valerie","full_name":"King, Valerie"}],"doi":"10.1145/320211.320215","_id":"11769"}