{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T21:54:46Z","timestamp":1791150886057,"version":"4.1.0"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>Damaschke, M\u00fcller, and Kratsch [Inform. Process. Lett., 36 (1990), pp. 231-236] gave a polynomial-time algorithm to solve the minimum dominating set problem in convex bipartite graphs $B=(X \\cup Y,E)$, that is, where the nodes in Y can be ordered so that each node of X is adjacent to a contiguous sequence of nodes. Gamble et al. [Graphs Combin., 11 (1995), pp. 121-129] gave an extension of their algorithm to weighted dominating sets. We formulate the dominating set problem as that of finding a minimum weight subset of elements of a graphic matroid, which covers each fundamental circuit and fundamental cut with respect to some spanning tree T. When T is a directed path, this simultaneous covering problem coincides with the dominating set problem for the previously studied class of convex bipartite graphs. We describe a polynomial-time algorithm for the more general problem of simultaneous covering in the case when T is an arborescence. We also give NP-completeness results for fairly specialized classes of the simultaneous cover problem. These are based on connections between the domination and induced matching problems.<\/jats:p>","DOI":"10.1137\/s089548019828371x","type":"journal-article","created":{"date-parts":[[2003,11,7]],"date-time":"2003-11-07T11:19:22Z","timestamp":1068203962000},"page":"517-523","source":"Crossref","is-referenced-by-count":46,"title":["Bipartite Domination and Simultaneous Matroid Covers"],"prefix":"10.1137","volume":"16","author":[{"given":"C. W.","family":"Ko","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"F. B.","family":"Shepherd","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":"10.1016\/0166-218X(92)90275-F"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(90)90147-P"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(84)90088-X"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0121010"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01929481"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"RanRaz, ShmuelSafra, A sub\u2010constant error\u2010probability low\u2010degree test, and a sub\u2010constant error\u2010probability PCP characterization of NP, ACM, New York, 1999, 475\u20134841715654","DOI":"10.1145\/258533.258641"},{"key":"R7","volume-title":"Theory of linear and integer programming","author":"Schrijver Alexander","year":"1986"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.6028\/jres.069B.001"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S089548019828371X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:03:30Z","timestamp":1787321010000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S089548019828371X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S089548019828371X"],"URL":"https:\/\/doi.org\/10.1137\/s089548019828371x","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}