{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T10:42:44Z","timestamp":1789641764340,"version":"4.0.0"},"reference-count":46,"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":[[2014,1]]},"abstract":"<jats:p>Given an undirected graph $G$, a collection $\\{(s_1,t_1), \\dots, (s_{k},t_{k})\\}$ of pairs of vertices, and an integer ${{p}}$, the Edge Multicut problem asks if there is a set $S$ of at most ${{p}}$ edges such that the removal of $S$ disconnects every $s_i$ from the corresponding $t_i$. Vertex Multicut is the analogous problem where $S$ is a set of at most ${{p}}$ vertices. Our main result is that both problems can be solved in time $2^{O({{p}}^3)}\\cdot n^{O(1)}$, i.e., fixed-parameter tractable parameterized by the size ${{p}}$ of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form $f({{p}})\\cdot n^{O(1)}$ exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset.<\/jats:p>","DOI":"10.1137\/110855247","type":"journal-article","created":{"date-parts":[[2014,3,4]],"date-time":"2014-03-04T11:59:18Z","timestamp":1393934358000},"page":"355-388","source":"Crossref","is-referenced-by-count":57,"title":["Fixed-Parameter Tractability of Multicut Parameterized by the Size of the Cutset"],"prefix":"10.1137","volume":"43","author":[{"given":"D\u00e1niel","family":"Marx","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Igor","family":"Razgon","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,3,4]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1145\/1502793.1502794"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1023\/B:MACH.0000033116.57574.95"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2009.12.016"},{"key":"atypb4","first-page":"459","author":"Bousquet N.","year":"2011","journal-title":"New York"},{"key":"atypb5","first-page":"183","author":"Bousquet N.","year":"2009","journal-title":"Germany"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/S0196-6774(03)00073-7"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s00037-006-0210-9"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-007-9130-6"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1145\/1411509.1411511"},{"key":"atypb10","first-page":"230","author":"Chitnis R.","year":"2012","journal-title":"UK"},{"key":"atypb11","first-page":"313","author":"Chitnis R.","year":"2013","journal-title":"New York"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/12086217X"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1145\/1502793.1502795"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1145\/2462896.2462899"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539792225297"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2006.05.008"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"R. 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