{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T22:43:55Z","timestamp":1791067435389,"version":"4.1.0"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>Given a directed graph $G$, a set of $k$ terminals, and an integer $p$, the Directed Vertex Multiway Cut problem asks whether there is a set $S$ of at most $p$ (nonterminal) vertices whose removal disconnects each terminal from all other terminals. Directed Edge Multiway Cut is the analogous problem where $S$ is a set of at most $p$ edges. These two problems are indeed known to be equivalent. A natural generalization of the multiway cut is the Multicut problem, in which we want to disconnect only a set of $k$ given pairs instead of all pairs. Marx [Theoret. Comput. Sci., 351 (2006), pp. 394--406] showed that in undirected graphs Vertex\/Edge Multiway cut is fixed-parameter tractable (FPT) parameterized by $p$. Marx and Razgon [Proceedings of the 43rd ACM Symposium on Theory of Computing, 2011, pp. 469--478] showed that undirected Multicut is FPT and Directed Multicut is W[1]-hard parameterized by $p$. We complete the picture here by our main result, which is that both Directed Vertex Multiway Cut and Directed Edge Multiway Cut can be solved in time $2^{2^{O(p)}}n^{O(1)}$, i.e., FPT parameterized by size $p$ of the cutset of the solution. This answers an open question raised by the aforementioned papers. It follows from our result that Directed Edge\/Vertex Multicut is FPT for the case of $k=2$ terminal pairs, which answers another open problem raised by Marx and Razgon.<\/jats:p>","DOI":"10.1137\/12086217x","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T13:53:30Z","timestamp":1375797210000},"page":"1674-1696","source":"Crossref","is-referenced-by-count":40,"title":["Fixed-Parameter Tractability of Directed Multiway Cut Parameterized by the Size of the Cutset"],"prefix":"10.1137","volume":"42","author":[{"given":"Rajesh","family":"Chitnis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MohammadTaghi","family":"Hajiaghayi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D\u00e1niel","family":"Marx","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,8,6]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"N. 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