{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:31:08Z","timestamp":1787340668681,"version":"build-2736575974"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1991,4]]},"abstract":"<jats:p>An efficient parallel algorithm for testing whether a graph G is k-vertex connected is presented. The algorithm runs in $O(k^2 \\log n)$ time and uses $(n + k^2 )kC(n,m)$ processors on a CROW PRAM, where n and m are the number of vertices and edges of G, and $C(n,m)$ is the number of processors required to compute the connected components of G in logarithmic time. For fixed k, the algorithm runs in logarithmic time and uses $nC(n,m)$ processors. To develop our algorithm, an efficient parallel algorithm is designed for the following disjoint s-t paths problem. Given a graph G, and two specified vertices s and t, find k vertex disjoint paths between s and t, if they exist. If no such paths exist, find a set of at most $k-1$ vertices whose removal disconnects s and t. The parallel algorithm for this problem runs in $O(k^2 \\log n)$ time and uses $kC(n,m)$ processors. The way to modify the algorithm to find k-edge disjoint paths, if they exist, is shown. This yields an efficient parallel algorithm for testing whether a graph G is k-edge connected. The algorithm runs in $O(k^2 \\log n)$ time and uses $nkC(n,kn)$ processors on a CROW PRAM. Finally, more applications of the disjoint s-t paths algorithm are described.<\/jats:p>","DOI":"10.1137\/0220022","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T06:34:57Z","timestamp":1109226897000},"page":"352-375","source":"Crossref","is-referenced-by-count":25,"title":["Efficient Parallel Algorithms for Testing\n                    <i>k<\/i>\n                    and Finding Disjoint\n                    <i>s<\/i>\n                    -\n                    <i>t<\/i>\n                    Paths in Graphs"],"prefix":"10.1137","volume":"20","author":[{"given":"Samir","family":"Khuller","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Baruch","family":"Schieber","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0040376"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(85)90222-1"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(82)90046-1"},{"key":"R4","volume-title":"Graphs and hypergraphs","author":"Berge Claude","year":"1976"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"R. 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