{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:13:17Z","timestamp":1763467997375},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642141645"},{"type":"electronic","value":"9783642141652"}],"license":[{"start":{"date-parts":[[2010,1,1]],"date-time":"2010-01-01T00:00:00Z","timestamp":1262304000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-14165-2_4","type":"book-chapter","created":{"date-parts":[[2010,7,5]],"date-time":"2010-07-05T09:26:02Z","timestamp":1278321962000},"page":"31-42","source":"Crossref","is-referenced-by-count":7,"title":["The Positive Semidefinite Grothendieck Problem with Rank Constraint"],"prefix":"10.1007","author":[{"given":"Jop","family":"Bri\u00ebt","sequence":"first","affiliation":[]},{"given":"Fernando M\u00e1rio","family":"de Oliveira Filho","sequence":"additional","affiliation":[]},{"given":"Frank","family":"Vallentin","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"4_CR1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107325937","volume-title":"Special functions","author":"G.E. Andrews","year":"1999","unstructured":"Andrews, G.E., Askey, R., Roy, R.: Special functions. Cambridge University Press, Cambridge (1999)"},{"key":"4_CR2","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/s00222-005-0465-9","volume":"163","author":"N. Alon","year":"2006","unstructured":"Alon, N., Makarychev, K., Makarychev, Y., Naor, A.: Quadratic forms on graphs. Invent. Math.\u00a0163, 499\u2013522 (2006)","journal-title":"Invent. Math."},{"key":"4_CR3","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1137\/S0097539704441629","volume":"35","author":"N. Alon","year":"2006","unstructured":"Alon, N., Naor, A.: Approximating the cut-norm via Grothendieck\u2019s inequality. SIAM J. Comp.\u00a035, 787\u2013803 (2006)","journal-title":"SIAM J. Comp."},{"key":"4_CR4","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1137\/S1052623400374756","volume":"12","author":"A. Ben-Tal","year":"2002","unstructured":"Ben-Tal, A., Nemirovski, A.: On tractable approximations of uncertain linear matrix inequalities affected by interval uncertainty. SIAM J. Optim.\u00a012, 811\u2013833 (2002)","journal-title":"SIAM J. Optim."},{"key":"4_CR5","unstructured":"Bri\u00ebt, J., Buhrman, H., Toner, B.: A generalized Grothendieck inequality and entanglement in XOR games (January 2009) (preprint)"},{"key":"4_CR6","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1145\/227683.227684","volume":"42","author":"M.X. Goemans","year":"1995","unstructured":"Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM\u00a042, 1115\u20131145 (1995)","journal-title":"J. ACM"},{"key":"4_CR7","first-page":"1","volume":"8","author":"A. Grothendieck","year":"1953","unstructured":"Grothendieck, A.: R\u00e9sum\u00e9 de la th\u00e9orie m\u00e9trique des produits tensoriels topologiques. Bol. Soc. Mat. S\u00e3o Paulo\u00a08, 1\u201379 (1953)","journal-title":"Bol. Soc. Mat. S\u00e3o Paulo"},{"key":"4_CR8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511569166","volume-title":"Summing and nuclear norms in Banach space theory","author":"G.J.O. Jameson","year":"1987","unstructured":"Jameson, G.J.O.: Summing and nuclear norms in Banach space theory. Cambridge University Press, Cambridge (1987)"},{"key":"4_CR9","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1007\/11523468_84","volume-title":"Proceedings of the 32nd International Colloquium on Automata, Languages and Programming","author":"G. Karakostas","year":"2005","unstructured":"Karakostas, G.: A better approximation ratio for the vertex cover problem. In: Proceedings of the 32nd International Colloquium on Automata, Languages and Programming, pp. 1043\u20131050. Springer, Heidelberg (2005)"},{"key":"4_CR10","doi-asserted-by":"crossref","unstructured":"Khot, S.: On the power of unique 2-prover 1-round games. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing, pp. 767\u2013775 (2002)","DOI":"10.1145\/509907.510017"},{"key":"4_CR11","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1137\/S0097539705447372","volume":"37","author":"S. Khot","year":"2007","unstructured":"Khot, S., Kindler, G., Mossel, E., O\u2019Donnell, R.: Optimal inapproximability results for MAX-CUT and other 2-variable CSPs? SIAM J. Comput.\u00a037, 319\u2013357 (2007)","journal-title":"SIAM J. Comput."},{"key":"4_CR12","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1109\/FOCS.2008.33","volume-title":"Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science","author":"S. Khot","year":"2008","unstructured":"Khot, S., Naor, A.: Approximate kernel clustering. In: Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science, pp. 561\u2013570. IEEE Computer Society, Los Alamitos (2008)"},{"key":"4_CR13","doi-asserted-by":"crossref","unstructured":"Khot, S., Naor, A.: Sharp kernel clustering algorithms and their associated Grothendieck inequalities, preprint (June 2009)","DOI":"10.1137\/1.9781611973075.55"},{"key":"4_CR14","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1109\/CCC.2003.1214437","volume-title":"Proceedings of the 18th Annual IEEE Conference on Computational Complexity","author":"S. Khot","year":"2003","unstructured":"Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2\u2009\u2212\u2009\u03b5. In: Proceedings of the 18th Annual IEEE Conference on Computational Complexity, pp. 379\u2013386. IEEE Computer Society, Los Alamitos (2003)"},{"key":"4_CR15","doi-asserted-by":"crossref","unstructured":"Linial, N., Shraibman, A.: Lower bounds in communication complexity based on factorization norms. In: Proceedings of the 39th Annual ACM Symposium on Theory of Computing, pp. 699\u2013708 (2007)","DOI":"10.1145\/1250790.1250892"},{"key":"4_CR16","unstructured":"Mahajan, S., Ramesh, H.: Derandomizing approximation algorithms based on semidefinite programming"},{"key":"4_CR17","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316559","volume-title":"Aspects of multivariate statistical theory","author":"R.J. Muirhead","year":"1982","unstructured":"Muirhead, R.J.: Aspects of multivariate statistical theory. John Wiley & Sons, Chichester (1982)"},{"key":"4_CR18","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1080\/10556789808805690","volume":"9","author":"Y.E. Nesterov","year":"1998","unstructured":"Nesterov, Y.E.: Semidefinite relaxation and nonconvex quadratic optimization. Optimization Methods and Software\u00a09, 141\u2013160 (1998)","journal-title":"Optimization Methods and Software"},{"key":"4_CR19","doi-asserted-by":"crossref","unstructured":"Raghavendra, P.: Optimal algorithms and inapproximability results for every csp? In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 245\u2013254 (2008)","DOI":"10.1145\/1374376.1374414"},{"key":"4_CR20","doi-asserted-by":"crossref","unstructured":"Raghavendra, P., Steurer, D.: Towards computing the Grothendieck constant. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 525\u2013534 (2009)","DOI":"10.1137\/1.9781611973068.58"},{"key":"4_CR21","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/BF02757725","volume":"19","author":"R.E. Rietz","year":"1974","unstructured":"Rietz, R.E.: A proof of the Grothendieck inequality. Israel J. Math.\u00a019, 271\u2013276 (1974)","journal-title":"Israel J. Math."},{"key":"4_CR22","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1215\/S0012-7094-42-00908-6","volume":"9","author":"I.J. Schoenberg","year":"1942","unstructured":"Schoenberg, I.J.: Positive definite functions on spheres. Duke Math. J.\u00a09, 96\u2013108 (1942)","journal-title":"Duke Math. J."}],"container-title":["Lecture Notes in Computer Science","Automata, Languages and Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-14165-2_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T15:39:36Z","timestamp":1558280376000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-14165-2_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642141645","9783642141652"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-14165-2_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2010]]}}}