{"page":"194-220","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","article_type":"original","status":"public","intvolume":"        24","publisher":"Elsevier","quality_controlled":"1","issue":"1","language":[{"iso":"eng"}],"year":"1997","abstract":[{"text":"This paper presents insertions-only algorithms for maintaining the exact and/or approximate size of the minimum edge cut and the minimum vertex cut of a graph. The algorithms output the approximate or exact sizekin timeO(1) and a cut of sizekin time linear in its size. For the minimum edge cut problem and for any 0 < ε ≤ 1, the amortized time per insertion isO(1/ε2) for a (2 + ε)-approximation,O((log λ)((log n)/ε)2) for a (1 + ε)-approximation, andO(λ log n) for the exact size, wherenis the number of nodes in the graph and λ is the size of the minimum cut. The (2 + ε)-approximation algorithm and the exact algorithm are deterministic; the (1 + ε)-approximation algorithm is randomized. We also present a static 2-approximation algorithm for the size κ of the minimum vertex cut in a graph, which takes time. This is a factor of κ faster than the best algorithm for computing the exact size, which takes time. We give an insertions-only algorithm for maintaining a (2 + ε)-approximation of the minimum vertex cut with amortized insertion timeO(n/ε).","lang":"eng"}],"publication_identifier":{"issn":["0196-6774"]},"doi":"10.1006/jagm.1997.0855","title":"A static 2-approximation algorithm for vertex connectivity and incremental approximation algorithms for edge and vertex connectivity","date_updated":"2022-09-12T09:15:38Z","month":"07","author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","last_name":"Henzinger","full_name":"Henzinger, Monika H","first_name":"Monika H"}],"volume":24,"_id":"11765","article_processing_charge":"No","scopus_import":"1","date_published":"1997-07-01T00:00:00Z","publication":"Journal of Algorithms","publication_status":"published","day":"01","date_created":"2022-08-08T12:18:38Z","citation":{"chicago":"Henzinger, Monika H. “A Static 2-Approximation Algorithm for Vertex Connectivity and Incremental Approximation Algorithms for Edge and Vertex Connectivity.” <i>Journal of Algorithms</i>. Elsevier, 1997. <a href=\"https://doi.org/10.1006/jagm.1997.0855\">https://doi.org/10.1006/jagm.1997.0855</a>.","apa":"Henzinger, M. H. (1997). A static 2-approximation algorithm for vertex connectivity and incremental approximation algorithms for edge and vertex connectivity. <i>Journal of Algorithms</i>. Elsevier. <a href=\"https://doi.org/10.1006/jagm.1997.0855\">https://doi.org/10.1006/jagm.1997.0855</a>","ista":"Henzinger MH. 1997. A static 2-approximation algorithm for vertex connectivity and incremental approximation algorithms for edge and vertex connectivity. Journal of Algorithms. 24(1), 194–220.","short":"M.H. Henzinger, Journal of Algorithms 24 (1997) 194–220.","ama":"Henzinger MH. A static 2-approximation algorithm for vertex connectivity and incremental approximation algorithms for edge and vertex connectivity. <i>Journal of Algorithms</i>. 1997;24(1):194-220. doi:<a href=\"https://doi.org/10.1006/jagm.1997.0855\">10.1006/jagm.1997.0855</a>","ieee":"M. H. Henzinger, “A static 2-approximation algorithm for vertex connectivity and incremental approximation algorithms for edge and vertex connectivity,” <i>Journal of Algorithms</i>, vol. 24, no. 1. Elsevier, pp. 194–220, 1997.","mla":"Henzinger, Monika H. “A Static 2-Approximation Algorithm for Vertex Connectivity and Incremental Approximation Algorithms for Edge and Vertex Connectivity.” <i>Journal of Algorithms</i>, vol. 24, no. 1, Elsevier, 1997, pp. 194–220, doi:<a href=\"https://doi.org/10.1006/jagm.1997.0855\">10.1006/jagm.1997.0855</a>."},"type":"journal_article"}