{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T15:31:16Z","timestamp":1786980676475,"version":"build-2736575974"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,3,13]],"date-time":"2020-03-13T00:00:00Z","timestamp":1584057600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,3,13]],"date-time":"2020-03-13T00:00:00Z","timestamp":1584057600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2020,12]]},"DOI":"10.1007\/s10479-020-03557-0","type":"journal-article","created":{"date-parts":[[2020,3,13]],"date-time":"2020-03-13T07:03:06Z","timestamp":1584082986000},"page":"37-73","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Robust vertex enumeration for convex hulls in high dimensions"],"prefix":"10.1007","volume":"295","author":[{"given":"Pranjal","family":"Awasthi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bahman","family":"Kalantari","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yikai","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,3,13]]},"reference":[{"key":"3557_CR1","unstructured":"Anandkumar, A., Foster, D. P., Hsu, D. J., Kakade, S. M. & Liu, Y.-K. (2012). A spectral algorithm for latent dirichlet allocation. In Advances in neural information processing systems (pp. 917\u2013925)."},{"key":"3557_CR2","unstructured":"Arora, S., Ge, R., Halpern, Y., Mimno, D., Moitra, A., Sontag, D., et al. (2013). A practical algorithm for topic modeling with provable guarantees. In International conference on machine learning (pp. 280\u2013288)."},{"key":"3557_CR3","doi-asserted-by":"crossref","unstructured":"Arora, S., Ge, R., Kannan, R., & Moitra, A. (2012a). Computing a nonnegative matrix factorization\u2014provably. In Proceedings of the forty-fourth annual ACM symposium on theory of computing (pp. 145\u2013162). ACM.","DOI":"10.1145\/2213977.2213994"},{"key":"3557_CR4","doi-asserted-by":"crossref","unstructured":"Arora, S., Ge, R., & Moitra, A. (2012b). Learning topic models\u2014going beyond SVD. In 2012 IEEE 53rd annual symposium on foundations of computer science (FOCS), (pp. 1\u201310). IEEE.","DOI":"10.1109\/FOCS.2012.49"},{"key":"3557_CR5","unstructured":"Bansal, T., Bhattacharyya, C., & Kannan, R. (2014) A provable SVD-based algorithm for learning topics in dominant admixture corpus. In Advances in neural information processing systems (pp. 1997\u20132005)."},{"issue":"4","key":"3557_CR6","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1145\/235815.235821","volume":"22","author":"CB Barber","year":"1996","unstructured":"Barber, C. B., Dobkin, D. P., & Huhdanpaa, H. (1996). The quickhull algorithm for convex hulls. ACM Transactions on Mathematical Software (TOMS), 22(4), 469\u2013483.","journal-title":"ACM Transactions on Mathematical Software (TOMS)"},{"issue":"4","key":"3557_CR7","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1145\/2133806.2133826","volume":"55","author":"DM Blei","year":"2012","unstructured":"Blei, D. M. (2012). Probabilistic topic models. Communications of the ACM, 55(4), 77\u201384.","journal-title":"Communications of the ACM"},{"issue":"Jan","key":"3557_CR8","first-page":"993","volume":"3","author":"DM Blei","year":"2003","unstructured":"Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent dirichlet allocation. Journal of Machine Learning Research, 3(Jan), 993\u20131022.","journal-title":"Journal of Machine Learning Research"},{"key":"3557_CR9","doi-asserted-by":"crossref","unstructured":"Blum, A., Har-Peled, S., & Raichel, B. (2016). Sparse approximation via generating point sets. In Proceedings of the twenty-seventh annual ACM-SIAM symposium on discrete algorithms (pp. 548\u2013557). Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9781611974331.ch40"},{"issue":"2","key":"3557_CR10","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1023\/A:1009715923555","volume":"2","author":"CJC Burges","year":"1998","unstructured":"Burges, C. J. C. (1998). A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2), 121\u2013167.","journal-title":"Data Mining and Knowledge Discovery"},{"issue":"4","key":"3557_CR11","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/BF02712873","volume":"16","author":"TM Chan","year":"1996","unstructured":"Chan, T. M. (1996a). Optimal output-sensitive convex hull algorithms in two and three dimensions. Discrete & Computational Geometry, 16(4), 361\u2013368.","journal-title":"Discrete & Computational Geometry"},{"issue":"4","key":"3557_CR12","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1007\/BF02712874","volume":"16","author":"TM Chan","year":"1996","unstructured":"Chan, T. M. (1996b). Output-sensitive results on convex hulls, extreme points, and related problems. Discrete & Computational Geometry, 16(4), 369\u2013387.","journal-title":"Discrete & Computational Geometry"},{"issue":"1","key":"3557_CR13","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1007\/BF02573985","volume":"10","author":"B Chazelle","year":"1993","unstructured":"Chazelle, B. (1993). An optimal convex hull algorithm in any fixed dimension. Discrete & Computational Geometry, 10(1), 377\u2013409.","journal-title":"Discrete & Computational Geometry"},{"key":"3557_CR14","volume-title":"Linear programming","author":"V Chvatal","year":"1983","unstructured":"Chvatal, V. (1983). Linear programming. New York: Macmillan."},{"key":"3557_CR15","doi-asserted-by":"crossref","unstructured":"Clarkson, K. L. (1994). More output-sensitive geometric algorithms. In 1994 Proceedings of the 35th annual symposium on foundations of computer science (pp. 695\u2013702). IEEE.","DOI":"10.1109\/SFCS.1994.365723"},{"issue":"4","key":"3557_CR16","first-page":"63","volume":"6","author":"KL Clarkson","year":"2010","unstructured":"Clarkson, K. L. (2010). Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm. ACM Transactions on Algorithms (TALG), 6(4), 63.","journal-title":"ACM Transactions on Algorithms (TALG)"},{"key":"3557_CR17","first-page":"1202","volume":"3","author":"W Ding","year":"2013","unstructured":"Ding, W., Rohban, M. H., Ishwar, P., & Saligrama, V. (2013). Topic discovery through data dependent and random projections. ICML, 3, 1202\u20131210.","journal-title":"ICML"},{"key":"3557_CR18","unstructured":"Donoho, D., & Stodden, V. (2003). When does non-negative matrix factorization give a correct decomposition into parts? In Advances in neural information processing systems."},{"issue":"1\u20132","key":"3557_CR19","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1002\/nav.3800030109","volume":"3","author":"M Frank","year":"1956","unstructured":"Frank, M., & Wolfe, P. (1956). An algorithm for quadratic programming. Naval Research Logistics (NRL), 3(1\u20132), 95\u2013110.","journal-title":"Naval Research Logistics (NRL)"},{"key":"3557_CR20","doi-asserted-by":"crossref","unstructured":"G\u00e4rtner, B., & Jaggi, M. (2009). Coresets for polytope distance. In Proceedings of the twenty-fifth annual symposium on computational geometry (pp. 33\u201342). ACM.","DOI":"10.1145\/1542362.1542370"},{"issue":"1","key":"3557_CR21","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1137\/0304007","volume":"4","author":"EG Gilbert","year":"1966","unstructured":"Gilbert, E. G. (1966). An iterative procedure for computing the minimum of a quadratic form on a convex set. SIAM Journal on Control, 4(1), 61\u201380.","journal-title":"SIAM Journal on Control"},{"key":"3557_CR22","unstructured":"Jaggi, M. (2013). Revisiting Frank\u2013Wolfe: projection-free sparse convex optimization."},{"issue":"2\u20133","key":"3557_CR23","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1016\/j.laa.2005.12.022","volume":"416","author":"Y Jin","year":"2006","unstructured":"Jin, Y., & Kalantari, B. (2006). A procedure of chv\u00e1tal for testing feasibility in linear programming and matrix scaling. Linear Algebra and its Applications, 416(2\u20133), 795\u2013798.","journal-title":"Linear Algebra and its Applications"},{"issue":"189\u2013206","key":"3557_CR24","first-page":"1","volume":"26","author":"WB Johnson","year":"1984","unstructured":"Johnson, W. B., & Lindenstrauss, J. (1984). Extensions of lipschitz mappings into a hilbert space. Contemporary Mathematics, 26(189\u2013206), 1.","journal-title":"Contemporary Mathematics"},{"issue":"1","key":"3557_CR25","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s10479-014-1707-2","volume":"226","author":"B Kalantari","year":"2015","unstructured":"Kalantari, B. (2015). A characterization theorem and an algorithm for a convex hull problem. Annals of Operations Research, 226(1), 301\u2013349.","journal-title":"Annals of Operations Research"},{"key":"3557_CR26","doi-asserted-by":"crossref","unstructured":"Karmarkar, N. (1984). A new polynomial-time algorithm for linear programming. In Proceedings of the sixteenth annual ACM symposium on theory of computing (pp. 302\u2013311). ACM.","DOI":"10.1145\/800057.808695"},{"issue":"1","key":"3557_CR27","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/0041-5553(80)90061-0","volume":"20","author":"LG Khachiyan","year":"1980","unstructured":"Khachiyan, L. G. (1980). Polynomial algorithms in linear programming. USSR Computational Mathematics and Mathematical Physics, 20(1), 53\u201372.","journal-title":"USSR Computational Mathematics and Mathematical Physics"},{"key":"3557_CR28","unstructured":"Lee, D. D. & Seung, H. S. (2001). Algorithms for non-negative matrix factorization. In Advances in neural information processing systems (pp. 556\u2013562)."},{"key":"3557_CR29","unstructured":"Stevens, K., Kegelmeyer, P., Andrzejewski, D., & Buttler, D. (2012). Exploring topic coherence over many models and many topics. In Proceedings of the 2012 joint conference on empirical methods in natural language processing and computational natural language learning (pp. 952\u2013961). Association for Computational Linguistics."},{"key":"3557_CR30","doi-asserted-by":"publisher","DOI":"10.1201\/9781420035315","volume-title":"Handbook of discrete and computational geometry","author":"CD Toth","year":"2004","unstructured":"Toth, C. D., O\u2019Rourke, J., & Goodman, J. E. (2004). Handbook of discrete and computational geometry. Boca Raton: CRC Press."},{"key":"3557_CR31","unstructured":"Vu, K., Poirion, P.-L., & Liberti, L. (2017). Random projections for linear programming. arXiv preprint arXiv:1706.02768."},{"key":"3557_CR32","doi-asserted-by":"crossref","unstructured":"Yao, L., Mimno, D., & McCallum, A. (2009). Efficient methods for topic model inference on streaming document collections. In Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining (pp. 937\u2013946). ACM.","DOI":"10.1145\/1557019.1557121"},{"issue":"3","key":"3557_CR33","doi-asserted-by":"publisher","first-page":"682","DOI":"10.1109\/TIT.2002.808136","volume":"49","author":"T Zhang","year":"2003","unstructured":"Zhang, T. (2003). Sequential greedy approximation for certain convex optimization problems. IEEE Transactions on Information Theory, 49(3), 682\u2013691.","journal-title":"IEEE Transactions on Information Theory"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-020-03557-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-020-03557-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-020-03557-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T19:33:15Z","timestamp":1615577595000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-020-03557-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,13]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["3557"],"URL":"https:\/\/doi.org\/10.1007\/s10479-020-03557-0","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,13]]},"assertion":[{"value":"13 March 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}