{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:32:32Z","timestamp":1787322752585,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>The problem of determining the cutwidth of a graph is a notoriously hard problem which remains NP-complete under severe restrictions on input graphs. Until recently, nontrivial polynomial-time cutwidth algorithms were known only for subclasses of graphs of bounded treewidth. Very recently, Heggernes et al. (SIAM J. Discrete Math., 25 (2011), pp. 1418--1437) initiated the study of cutwidth on graph classes containing graphs of unbounded treewidth and showed that a greedy algorithm computes the cutwidth of threshold graphs. We continue this line of research and present the first polynomial-time algorithm for computing the cutwidth of bipartite permutation graphs. Our algorithm runs in linear time. We stress that the cutwidth problem is NP-complete on bipartite graphs and its computational complexity is open even on small subclasses of permutation graphs, such as trivially perfect graphs.<\/jats:p>","DOI":"10.1137\/110830514","type":"journal-article","created":{"date-parts":[[2012,7,19]],"date-time":"2012-07-19T12:15:10Z","timestamp":1342700110000},"page":"1008-1021","source":"Crossref","is-referenced-by-count":7,"title":["Computing the Cutwidth of Bipartite Permutation Graphs in Linear Time"],"prefix":"10.1137","volume":"26","author":[{"given":"Pinar","family":"Heggernes","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pim","family":"van 't Hof","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Lokshtanov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jesper","family":"Nederlof","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,7,19]]},"reference":[{"key":"atyp_ref1","doi-asserted-by":"publisher","DOI":"10.1137\/0125042"},{"key":"atyp_ref2","first-page":"21","author":"Arora S.","year":"1996","journal-title":"IEEE"},{"key":"atyp_ref3","first-page":"271","author":"Blin G.","year":"2005","journal-title":"Berlin"},{"key":"atyp_ref4","first-page":"116","author":"R.","year":"1993","journal-title":"Information Retrieval"},{"key":"atyp_ref5","doi-asserted-by":"crossref","unstructured":"5.\u2002A. 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