{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T07:53:16Z","timestamp":1717228396100},"reference-count":18,"publisher":"Association for Computing Machinery (ACM)","issue":"3","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2008,6]]},"abstract":"\n In the rectangle stabbing problem, we are given a set of axis parallel rectangles and a set of horizontal and vertical lines, and our goal is to find a minimum size subset of lines that intersect all the rectangles. In this article, we study the capacitated version of this problem in which the input includes an integral capacity for each line. The capacity of a line bounds the number of rectangles that the line can cover. We consider two versions of this problem. In the first, one is allowed to use only a single copy of each line (\n hard capacities<\/jats:italic>\n ), and in the second, one is allowed to use multiple copies of every line, but the multiplicities are counted in the size (or weight) of the solution (\n soft capacities<\/jats:italic>\n ).\n <\/jats:p>\n \n We present an exact polynomial-time algorithm for the weighted one dimensional case with hard capacities that can be extended to the one dimensional weighted case with soft capacities. This algorithm is also extended to solve a certain capacitated multi-item\n lot-sizing<\/jats:italic>\n inventory problem with joint set-up costs. For the case of\n d<\/jats:italic>\n -dimensional rectangle stabbing with soft capacities, we present a 3\n d<\/jats:italic>\n -approximation algorithm for the unweighted case. For\n d<\/jats:italic>\n -dimensional rectangle stabbing problem with hard capacities, we present a bi-criteria algorithm that computes 4\n d<\/jats:italic>\n -approximate solutions that use at most two copies of every line. Finally, we present hardness results for rectangle stabbing when the dimension is part of the input and for a two-dimensional weighted version with hard capacities.\n <\/jats:p>","DOI":"10.1145\/1367064.1367074","type":"journal-article","created":{"date-parts":[[2008,7,2]],"date-time":"2008-07-02T12:09:19Z","timestamp":1215000559000},"page":"1-17","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":28,"title":["Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs"],"prefix":"10.1145","volume":"4","author":[{"given":"Guy","family":"Even","sequence":"first","affiliation":[{"name":"Tel-Aviv University, Tel-Aviv, Israel"}]},{"given":"Retsef","family":"Levi","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology, MIT Cambridge, MA"}]},{"given":"Dror","family":"Rawitz","sequence":"additional","affiliation":[{"name":"University of Haifa, Haifa, Israel"}]},{"given":"Baruch","family":"Schieber","sequence":"additional","affiliation":[{"name":"IBM T.J. Watson Research Center, Yorktown Heights, NY"}]},{"given":"Shimon (Moni)","family":"Shahar","sequence":"additional","affiliation":[{"name":"Tel-Aviv University, Tel-Aviv, Israel"}]},{"given":"Maxim","family":"Sviridenko","sequence":"additional","affiliation":[{"name":"IBM T.J. Watson Research Center, Yorktown Heights, NY"}]}],"member":"320","published-online":{"date-parts":[[2008,7,4]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.1030.0080"},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","unstructured":"Anily S. Tzur M. and Wolsey L. A. 2005. Multi-item lot-sizing with joint set-up cost. Submitted for publication. Anily S. Tzur M. and Wolsey L. A. 2005. Multi-item lot-sizing with joint set-up cost. Submitted for publication.","DOI":"10.2139\/ssrn.885931"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.5555\/1109557.1109598"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(99)00130-9"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539703422479"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/11758471_5"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/285055.285059"},{"key":"e_1_2_1_8_1","first-page":"669","article-title":"Deterministic production planning: Algorithms and complexity. Manage","volume":"26","author":"Florian M.","year":"1980","unstructured":"Florian , M. , Lenstra , J. K. , and Rinooy Kan , A. H. G. 1980 . Deterministic production planning: Algorithms and complexity. Manage . Sci. 26 , 669 -- 679 . Florian, M., Lenstra, J. K., and Rinooy Kan, A. H. G. 1980. Deterministic production planning: Algorithms and complexity. Manage. Sci. 26, 669--679.","journal-title":"Sci."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2005.06.004"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.2002.1221"},{"key":"e_1_2_1_11_1","volume-title":"Algorithmic Graph Theory and Perfect Graphs","author":"Golumbic M. C.","unstructured":"Golumbic , M. C. 1980. Algorithmic Graph Theory and Perfect Graphs . Academic Press , New York . Golumbic, M. C. 1980. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0196-6774(03)00053-1"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(91)90011-K"},{"key":"e_1_2_1_14_1","volume-title":"Proceedings of the 12th European Symposium on Algorithms. Lecture Notes in Computer Science","volume":"3221","author":"Kovaleva S.","unstructured":"Kovaleva , S. , and Spieksma , F. C. R. 2004. Approximation of rectangle stabbing and interval stabbing problems . In Proceedings of the 12th European Symposium on Algorithms. Lecture Notes in Computer Science , vol. 3221 . Springer-Verlag, New York, 426--435. Kovaleva, S., and Spieksma, F. C. R. 2004. Approximation of rectangle stabbing and interval stabbing problems. In Proceedings of the 12th European Symposium on Algorithms. Lecture Notes in Computer Science, vol. 3221. Springer-Verlag, New York, 426--435."},{"key":"e_1_2_1_15_1","volume-title":"Combinatorial Optimization: Networks and matroids","author":"Lawler E.","year":"2001","unstructured":"Lawler , E. 2001 . Combinatorial Optimization: Networks and matroids . Courier Dover Publications . Lawler, E. 2001. Combinatorial Optimization: Networks and matroids. Courier Dover Publications."},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-72792-7_34"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/258533.258641"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579435"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1367064.1367074","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T08:48:22Z","timestamp":1672303702000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1367064.1367074"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,6]]}},"alternative-id":["10.1145\/1367064.1367074"],"URL":"http:\/\/dx.doi.org\/10.1145\/1367064.1367074","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"value":"1549-6325","type":"print"},{"value":"1549-6333","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,6]]},"assertion":[{"value":"2005-12-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2007-07-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2008-07-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}
