{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:48:29Z","timestamp":1787323709296,"version":"build-2736575974"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>We consider the Steiner k-cut problem which generalizes both the k-cut problem and the multiway cut problem. The Steiner k-cut problem is defined as follows. Given an edge-weighted undirected graph $G=(V, E)$, a subset of vertices $X \\subseteq V$ called {\\em terminals}, and an integer $k \\le |X|$, the objective is to find a minimum weight set of edges whose removal results in k disconnected components, each of which contains at least one terminal. We give two approximation algorithms for the problem: a greedy $(2-\\frac{2}{k})$-approximation based on Gomory--Hu trees, and a $(2 - \\frac{2}{|X|})$-approximation based on rounding a linear program. We use the insight from the rounding to develop an exact bidirected formulation for the global minimum cut problem (the k-cut problem with $k=2$).<\/jats:p>","DOI":"10.1137\/s0895480104445095","type":"journal-article","created":{"date-parts":[[2006,3,27]],"date-time":"2006-03-27T21:00:21Z","timestamp":1143493221000},"page":"261-271","source":"Crossref","is-referenced-by-count":17,"title":["The Steiner k-Cut Problem"],"prefix":"10.1137","volume":"20","author":[{"given":"Chandra","family":"Chekuri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sudipto","family":"Guha","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joseph (Seffi)","family":"Naor","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1999.1687"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539792225297"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.6028\/jres.071B.032"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793242618"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1287\/moor.19.1.24"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1145\/234533.234534"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1030.0086"},{"key":"R8","first-page":"98","author":"Maeda Naohisa","year":"1993","journal-title":"S\u016brikaisekikenky\u016bsho K\u014dky\u016broku"},{"key":"R9","unstructured":"JosephNaor, YuvalRabani, Tree packing and approximatingk\u2010cuts, SIAM, Philadelphia, PA, 2001, 26\u201327MR1958388"},{"key":"R10","unstructured":"R. Ravi and A. Sinha,\n                      Approximating k\u2010cuts via network strength\n                      , in Proceedings of the 13th Annual ACM\u2010SIAM Symposium on Discrete Algorithms, San Francisco, 2002, pp. 621\u2013622."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539792251730"},{"key":"R12","volume-title":"Approximation algorithms","author":"Vazirani Vijay","year":"2001"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011620607786"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-004-0510-2"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895480104445095","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:12:27Z","timestamp":1787321547000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895480104445095"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/S0895480104445095"],"URL":"https:\/\/doi.org\/10.1137\/s0895480104445095","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}