{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T08:31:55Z","timestamp":1775809915206,"version":"3.50.1"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1986,3,1]],"date-time":"1986-03-01T00:00:00Z","timestamp":510019200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[1986,3]]},"DOI":"10.1007\/bf02579403","type":"journal-article","created":{"date-parts":[[2007,3,22]],"date-time":"2007-03-22T18:19:26Z","timestamp":1174587566000},"page":"1-13","source":"Crossref","is-referenced-by-count":651,"title":["On Lov\u00e1sz\u2019 lattice reduction and the nearest lattice point problem"],"prefix":"10.1007","volume":"6","author":[{"given":"L.","family":"Babai","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"BF02579403_CR1","doi-asserted-by":"crossref","unstructured":"L. Adleman, On breaking the iterated Merkle\u2014Hellman public key cryptosystem,Proc. 15th ACM Symp. on Theory of Computing, Boston (1983), 402\u2013412.","DOI":"10.1007\/978-1-4757-0602-4_29"},{"key":"BF02579403_CR2","volume-title":"An introduction to the geometry of numbers","author":"J. W. S. Cassels","year":"1971","unstructured":"J. W. S. Cassels,An introduction to the geometry of numbers, Springer, New York, (1971)."},{"key":"BF02579403_CR3","unstructured":"P. van Emde Boas, Another NP-complete partition problem and the complexity of computing short vectors in a lattice,Rep. MI\/UVA 81-04, Amsterdam (1981)."},{"key":"BF02579403_CR4","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1007\/BF02579273","volume":"1","author":"M. Gr\u00f6tschel","year":"1981","unstructured":"M. Gr\u00f6tschel, L. Lov\u00e1sz andA. Schrijver, The ellipsoid method and its consequences in combinatorial optimization,Combinatorica 1 (1981), 186\u2013197.","journal-title":"Combinatorica"},{"key":"BF02579403_CR5","series-title":"Proc. Silver Jubilee Conf. on Comb., Univ. Waterloo","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/B978-0-12-566780-7.50016-7","volume-title":"Progress in Combinatorial Optimization","author":"M. Gr\u00f6tschel","year":"1984","unstructured":"M. Gr\u00f6tschel, L. Lov\u00e1sz andA. Schrijver, Geometric methods in combinatorial optimization, in: Progress in Combinatorial Optimization (W. R. Pulleyblank, ed.),Proc. Silver Jubilee Conf. on Comb., Univ. Waterloo, Vol. 1, 1982, Acad. Press, N. Y. (1984), 167\u2013183."},{"key":"BF02579403_CR6","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/BFb0024006","volume":"182","author":"B. Helfrich","year":"1985","unstructured":"B. Helfrich, An algorithm to construct Minkowski-reduced lattice-bases, in:Proc. 2nd Ann. Symp. on Theoretical Aspects of Comp. Sci. (STACS 85),Springer Lect. Notes. in Comp. Sci. 182 (1985), 173\u2013179.","journal-title":"Springer Lect. Notes. in Comp. Sci."},{"key":"BF02579403_CR7","doi-asserted-by":"crossref","unstructured":"R. Kannan, Improved algorithms for integer programming and related lattice problems,in: Proc. 15th ACM Symp. on Theory of Comp., (1983), 193\u2013206.","DOI":"10.1145\/800061.808749"},{"key":"BF02579403_CR8","doi-asserted-by":"crossref","unstructured":"R. Kannan, A. K. Lenstra andL. Lov\u00e1sz, Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers,in: Proc. 16th Ann. ACM Symp. on Theory of Computing, Washington, D. C. (1984), 191\u2013200.","DOI":"10.1145\/800057.808681"},{"key":"BF02579403_CR9","doi-asserted-by":"crossref","unstructured":"J. Lagarias andA. M. Odlyzko, Solving low density subset sum problems,in: Proc. 24th IEEE Symp. on Foundations of Comp. Sci., (1983), 1\u201310.","DOI":"10.1109\/SFCS.1983.70"},{"key":"BF02579403_CR10","unstructured":"A. K. Lenstra, Lattices and factorization of polynomials,Report IW 190\/81, Mathematisch Centrum, Amsterdam (1981)."},{"key":"BF02579403_CR11","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/BF01457454","volume":"261","author":"A. K. Lenstra","year":"1982","unstructured":"A. K. Lenstra, H. W. Lenstra, Jr. andL. Lov\u00e1sz, Factoring polynomials with rational coefficients,Math. Ann. 261 (1982), 515\u2013534.","journal-title":"Math. Ann."},{"key":"BF02579403_CR12","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1287\/moor.8.4.538","volume":"8","author":"H. W. Lenstra Jr.","year":"1983","unstructured":"H. W. Lenstra, Jr., Integer programming with a fixed number of variables.Math. Oper. Res. 8 (1983), 538\u2013548.","journal-title":"Math. Oper. Res."},{"key":"BF02579403_CR13","unstructured":"L. Lov\u00e1sz,private communications, 1981\u20131982."},{"key":"BF02579403_CR14","first-page":"138","volume":"357","author":"A. M. Odlyzko","year":"1985","unstructured":"A. M. Odlyzko andH. te Riele, Disproof of the Mertens conjecture,J. reine angew. Math. 357 (1985), 138\u2013160.","journal-title":"J. reine angew. Math."},{"key":"BF02579403_CR15","doi-asserted-by":"crossref","unstructured":"A. Shamir, A polynomial time algorithm for breaking the Merkle\u2014Hellman cryptosystem,Proc. 23rd IEEE Symp. on Foundations of Comp. Sci., Chicago, Illinois (1982), 145\u2013152.","DOI":"10.1109\/SFCS.1982.5"},{"key":"BF02579403_CR16","unstructured":"C. P. Schnorr, A hierarchy of polynomial time basis reduction algorithms,in: Theory of Algorithms, Proc. Conf. P\u00e9cs (Hungary) 1984,Coll. Soc. J. Bolyai, to appear."},{"key":"BF02579403_CR17","unstructured":"Vera T. S\u00f3s, On the theory of diophantine approximation II,Acta Math. Acad. Sci. Hung. (1958), 229\u2013241."},{"key":"BF02579403_CR18","unstructured":"Vera T. S\u00f3s, Irregularities of partitions: Ramsey theory, uniform distribution,in: Surveys in Combinatorics, Proc. 9th British Combinatorial Conference, 1983 (E. Keith Lloyd, ed.) London Math. Soc. Lect. Notes 82, Cambridge Univ. Press 1983."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02579403.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02579403\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02579403","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T12:45:03Z","timestamp":1558183503000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02579403"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,3]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1986,3]]}},"alternative-id":["BF02579403"],"URL":"https:\/\/doi.org\/10.1007\/bf02579403","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[1986,3]]}}}