[{"language":[{"iso":"eng"}],"keyword":["Computational Theory and Mathematics","Computational Mathematics","Control and Optimization"],"oa_version":"None","month":"02","publication":"Journal of Algorithms","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0196-6774"]},"date_published":"2000-02-01T00:00:00Z","type":"journal_article","publisher":"Elsevier","article_type":"original","page":"222-250","quality_controlled":"1","publication_status":"published","article_processing_charge":"No","date_created":"2022-07-28T08:56:10Z","title":"Computing vertex connectivity: New bounds from old techniques","intvolume":"        34","_id":"11683","scopus_import":"1","author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","first_name":"Monika H","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530"},{"full_name":"Rao, Satish","first_name":"Satish","last_name":"Rao"},{"last_name":"Gabow","first_name":"Harold N.","full_name":"Gabow, Harold N."}],"issue":"2","volume":34,"extern":"1","doi":"10.1006/jagm.1999.1055","day":"01","abstract":[{"text":"The vertex connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known deterministic algorithm for finding the vertex connectivity and a corresponding separator. The time for a digraph having n vertices and m edges is O(min{κ3 + n, κn}m); for an undirected graph the term m can be replaced by κn. A randomized algorithm finds κ with error probability 1/2 in time O(nm). If the vertices have nonnegative weights the weighted vertex connectivity is found in time O(κ1nmlog(n2/m)) where κ1 ≤ m/n is the unweighted vertex connectivity or in expected time O(nmlog(n2/m)) with error probability 1/2. The main algorithm combines two previous vertex connectivity algorithms and a generalization of the preflow-push algorithm of Hao and Orlin (1994, J. Algorithms17, 424–446) that computes edge connectivity.","lang":"eng"}],"date_updated":"2022-09-12T09:06:48Z","citation":{"apa":"Henzinger, M. H., Rao, S., &#38; Gabow, H. N. (2000). Computing vertex connectivity: New bounds from old techniques. <i>Journal of Algorithms</i>. Elsevier. <a href=\"https://doi.org/10.1006/jagm.1999.1055\">https://doi.org/10.1006/jagm.1999.1055</a>","ama":"Henzinger MH, Rao S, Gabow HN. Computing vertex connectivity: New bounds from old techniques. <i>Journal of Algorithms</i>. 2000;34(2):222-250. doi:<a href=\"https://doi.org/10.1006/jagm.1999.1055\">10.1006/jagm.1999.1055</a>","chicago":"Henzinger, Monika H, Satish Rao, and Harold N. Gabow. “Computing Vertex Connectivity: New Bounds from Old Techniques.” <i>Journal of Algorithms</i>. Elsevier, 2000. <a href=\"https://doi.org/10.1006/jagm.1999.1055\">https://doi.org/10.1006/jagm.1999.1055</a>.","ieee":"M. H. Henzinger, S. Rao, and H. N. Gabow, “Computing vertex connectivity: New bounds from old techniques,” <i>Journal of Algorithms</i>, vol. 34, no. 2. Elsevier, pp. 222–250, 2000.","mla":"Henzinger, Monika H., et al. “Computing Vertex Connectivity: New Bounds from Old Techniques.” <i>Journal of Algorithms</i>, vol. 34, no. 2, Elsevier, 2000, pp. 222–50, doi:<a href=\"https://doi.org/10.1006/jagm.1999.1055\">10.1006/jagm.1999.1055</a>.","short":"M.H. Henzinger, S. Rao, H.N. Gabow, Journal of Algorithms 34 (2000) 222–250.","ista":"Henzinger MH, Rao S, Gabow HN. 2000. Computing vertex connectivity: New bounds from old techniques. Journal of Algorithms. 34(2), 222–250."},"year":"2000"}]