{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T10:36:32Z","timestamp":1756463792253},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,5,11]],"date-time":"2012-05-11T00:00:00Z","timestamp":1336694400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2012,7]]},"DOI":"10.1007\/s10479-012-1143-0","type":"journal-article","created":{"date-parts":[[2012,5,10]],"date-time":"2012-05-10T10:20:21Z","timestamp":1336645221000},"page":"581-590","source":"Crossref","is-referenced-by-count":3,"title":["Solving market split problems with heuristical lattice reduction"],"prefix":"10.1007","volume":"196","author":[{"given":"Heiko","family":"Vogel","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,5,11]]},"reference":[{"key":"1143_CR1","series-title":"Springer lecture notes in computer science","volume-title":"Integer programming and combinatorial optimization 6","author":"K. Aardal","year":"1998","unstructured":"Aardal, K., Hurkens, C., & Lenstra, A. K. (1998). Solving a system of diophantine equations with lower and upper bounds on the variables. In Springer lecture notes in computer science: Vol.\u00a01412. Integer programming and combinatorial optimization 6."},{"key":"1143_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02579403","volume":"6","author":"L. Babai","year":"1986","unstructured":"Babai, L. (1986). On Lov\u00e0sz lattice reduction and the nearest lattice point problem. Combinatorica, 6, 1\u201313.","journal-title":"Combinatorica"},{"key":"1143_CR3","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1287\/ijoc.11.2.205","volume":"11","author":"G. Cornu\u00e9jols","year":"1999","unstructured":"Cornu\u00e9jols, G., & Dawande, M. (1999). A class of hard small 0\u20131 programs. INFORMS Journal on Computing, 11, 205\u2013210","journal-title":"INFORMS Journal on Computing"},{"key":"1143_CR4","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/BF01201999","volume":"2","author":"M. J. Coster","year":"1992","unstructured":"Coster, M. J., Joux, A., LaMacchia, B. A., Odlyzko, A. M., & Schnorr, C. P. (1992). Improved low-density subset sum algorithms. Computational Complexity, 2, 111\u2013128.","journal-title":"Computational Complexity"},{"key":"1143_CR5","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/BF01581144","volume":"66","author":"M. Euchner","year":"1994","unstructured":"Euchner, M., & Schnorr, C. P. (1994). Lattice basis reduction: improved algorithms and solving subset sum problems. Mathematical Programming, 66, 181\u2013199.","journal-title":"Mathematical Programming"},{"key":"1143_CR6","series-title":"Mathematische annalen","volume-title":"Factoring polynomials with rational coefficients","author":"A. Lenstra","year":"1982","unstructured":"Lenstra, A., Lenstra, H. W., & Lov\u00e1sz, L. (1982). Mathematische annalen: Vol. 261. Factoring polynomials with rational coefficients. Berlin: Springer."},{"key":"1143_CR7","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1515\/JMC.2008.009","volume":"1","author":"P. Q. Nguyen","year":"2008","unstructured":"Nguyen, P. Q., & Vidick, T. (2008). Sieve algorithms for the shortest vector problem are practical. Journal of Mathematical Cryptology, 1, 181\u2013207.","journal-title":"Journal of Mathematical Cryptology"},{"key":"1143_CR8","first-page":"108","volume-title":"Knapsack problems: algorithms and computer implementations","author":"S. Martello","year":"1990","unstructured":"Martello, S., & Toth, P. (1990). Knapsack problems: algorithms and computer implementations (pp. 108\u2013109). Chichester: Wiley."},{"key":"1143_CR9","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0304-3975(87)90064-8","volume":"53","author":"C. P. Schnorr","year":"1987","unstructured":"Schnorr, C. P. (1987). A hierarchy of polynomial time lattice basis reduction algorithms. Theoretical Computer Science, 53, 201\u2013224.","journal-title":"Theoretical Computer Science"},{"key":"1143_CR10","series-title":"Pure and applied mathematics","first-page":"254","volume-title":"Linear and integer programming: theory and practice","author":"G. Sierksma","year":"1996","unstructured":"Sierksma, G. (1996). Pure and applied mathematics. Linear and integer programming: theory and practice (pp. 254\u2013263). New York: Dekker."},{"key":"1143_CR11","unstructured":"Vogel, H. (2011). Gitterbasenreduktion mit Random Sampling und heuristischen Erweiterungen. Ph.D. thesis, submitted at the University of Bayreuth."},{"key":"1143_CR12","unstructured":"Wang, H. (2008). A note on solving the market split problem via branch-and-cut (Manuscript No. 251). Annuals of Operations Research."},{"key":"1143_CR13","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1013355015853","volume":"6","author":"A. Wassermann","year":"2002","unstructured":"Wassermann, A. (2002). Attacking the market split problem with lattice point enumeration. Journal of Combinatorial Optimization, 6, 5\u201316.","journal-title":"Journal of Combinatorial Optimization"},{"key":"1143_CR14","volume-title":"Model building in mathematical programming","author":"H. P. Williams","year":"1978","unstructured":"Williams, H. P. (1978). Model building in mathematical programming. New York: Wiley."}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-012-1143-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-012-1143-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-012-1143-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T14:09:35Z","timestamp":1559138975000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-012-1143-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5,11]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["1143"],"URL":"https:\/\/doi.org\/10.1007\/s10479-012-1143-0","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,5,11]]}}}