{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:42:00Z","timestamp":1740109320243,"version":"3.37.3"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2015,3,31]],"date-time":"2015-03-31T00:00:00Z","timestamp":1427760000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2015,12]]},"DOI":"10.1007\/s10107-015-0885-2","type":"journal-article","created":{"date-parts":[[2015,3,30]],"date-time":"2015-03-30T09:58:41Z","timestamp":1427709521000},"page":"381-406","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Simple extensions of polytopes"],"prefix":"10.1007","volume":"154","author":[{"given":"Volker","family":"Kaibel","sequence":"first","affiliation":[]},{"given":"Matthias","family":"Walter","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,3,31]]},"reference":[{"key":"885_CR1","first-page":"57","volume-title":"Automata, Languages, and Programming, volume 7965 of Lecture Notes in Computer Science","author":"D Avis","year":"2013","unstructured":"Avis, D., Tiwary, H.R.: On the extension complexity of combinatorial polytopes. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M.Z., Peleg, D. (eds.) Automata, Languages, and Programming, volume 7965 of Lecture Notes in Computer Science, pp. 57\u201368. Springer, Berlin (2013)"},{"key":"885_CR2","volume-title":"Disjunctive Programming: Properties of the Convex Hull of Feasible Points","author":"E Balas","year":"1974","unstructured":"Balas, E.: Disjunctive Programming: Properties of the Convex Hull of Feasible Points. MSRR 348, Carnegie Mellon University, Pittsburg, PA (1974)"},{"key":"885_CR3","doi-asserted-by":"crossref","unstructured":"Balas, E.: Disjunctive programming. In: Johnson, E.L., Hammer, P.L., Korte, B.H. (eds.) Discrete Optimization II. Annals of Discrete Mathematics, vol. 5, pp. 3\u201351. Elsevier (1979). http:\/\/dx.doi.org\/10.1016\/S0167-5060(08)70342-X","DOI":"10.1016\/S0167-5060(08)70342-X"},{"issue":"3","key":"885_CR4","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.orl.2007.09.003","volume":"36","author":"D Bienstock","year":"2008","unstructured":"Bienstock, D.: Approximate formulations for 0\u20131 knapsack sets. Oper. Res. Lett. 36(3), 317\u2013320 (2008)","journal-title":"Oper. Res. Lett."},{"key":"885_CR5","first-page":"1","volume-title":"Tutorials on Emerging Methodologies and Applications in Operations Research volume 76 of International Series in Operations Research and Management Science, chapter 2","author":"RD Carr","year":"2005","unstructured":"Carr, R.D., Konjevod, G.: Polyhedral combinatorics. In: Greenberg, H.J. (ed.) Tutorials on Emerging Methodologies and Applications in Operations Research volume 76 of International Series in Operations Research and Management Science, chapter 2, pp. 1\u201346. Springer, Berlin (2005)"},{"issue":"2","key":"885_CR6","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/0095-8956(75)90041-6","volume":"18","author":"V Chv\u00e1tal","year":"1975","unstructured":"Chv\u00e1tal, V.: On certain polytopes associated with graphs. J. Combin. Theory Ser. B 18(2), 138\u2013154 (1975)","journal-title":"J. Combin. Theory Ser. B"},{"key":"885_CR7","doi-asserted-by":"crossref","DOI":"10.1515\/9781400884179","volume-title":"Linear Programming and Extensions. Princeton Landmarks in Mathematics and Physics","author":"GB Dantzig","year":"1963","unstructured":"Dantzig, G.B.: Linear Programming and Extensions. Princeton Landmarks in Mathematics and Physics. Princeton University Press, Princeton (1963)"},{"issue":"1","key":"885_CR8","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.disc.2012.09.015","volume":"313","author":"S Fiorini","year":"2013","unstructured":"Fiorini, S., Kaibel, V., Pashkovich, K., Theis, D.O.: Combinatorial bounds on nonnegative rank and extended formulations. Discrete Math. 313(1), 67\u201383 (2013)","journal-title":"Discrete Math."},{"key":"885_CR9","doi-asserted-by":"crossref","unstructured":"Fiorini, S., Massar, S., Pokutta, S., Tiwary, H.R., de Wolf, R.: Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds. In: Karloff, H.J., Pitassi, T. (eds.) STOC, pp. 95\u2013106. ACM, New York (2012)","DOI":"10.1145\/2213977.2213988"},{"key":"885_CR10","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/BF02575918","volume":"15","author":"G Gallo","year":"1978","unstructured":"Gallo, G., Sodini, C.: Extreme points and adjacency relationship in the flow polytope. Calcolo 15, 277\u2013288 (1978). doi: 10.1007\/BF02575918","journal-title":"Calcolo"},{"key":"885_CR11","unstructured":"Gillmann, R.: 0\/1-Polytopes typical and extremal properties. PhD thesis, Technische Universit\u00e4t, Berlin (2007)"},{"key":"885_CR12","unstructured":"Goemans, M.: Smallest compact formulation for the permutahedron. http:\/\/www-math.mit.edu\/goemans\/publ.html (2009)"},{"key":"885_CR13","first-page":"287","volume-title":"Integer Programming and Combinatorial Optimization. Proceedings of IPCO XV, New York, NY volume 6655 of Lecture Notes in Computer Science","author":"V Kaibel","year":"2011","unstructured":"Kaibel, V., Pashkovich, K.: Constructing extended formulations from reflection relations. In: G\u00fcnl\u00fck, O., Woeginger, G. (eds.) Integer Programming and Combinatorial Optimization. Proceedings of IPCO XV, New York, NY volume 6655 of Lecture Notes in Computer Science, pp. 287\u2013300. Springer, Berlin (2011)"},{"issue":"3","key":"885_CR14","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1137\/110839813","volume":"26","author":"V Kaibel","year":"2012","unstructured":"Kaibel, V., Pashkovich, K., Theis, D.O.: Symmetry matters for sizes of extended formulations. SIAM J. Discrete Math. 26(3), 1361\u20131382 (2012)","journal-title":"SIAM J. Discrete Math."},{"key":"885_CR15","volume-title":"Integer Programming and Combinatorial Optimization. Proceedings of IPCO XVII, Bonn, volume 8494 of Lecture Notes in Computer Science","author":"V Kaibel","year":"2014","unstructured":"Kaibel, V., Walter, M.: Simple extensions of polytopes. In: Lee, J., Vygen, J. (eds.) Integer Programming and Combinatorial Optimization. Proceedings of IPCO XVII, Bonn, volume 8494 of Lecture Notes in Computer Science. Springer, Berlin (2014)"},{"issue":"3","key":"885_CR16","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0167-6377(91)90028-N","volume":"10","author":"R Kipp Martin","year":"1991","unstructured":"Kipp Martin, R.: Using separation algorithms to generate mixed integer model reformulations. Oper. Res. Lett. 10(3), 119\u2013128 (1991)","journal-title":"Oper. Res. Lett."},{"key":"885_CR17","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/BF01585502","volume":"7","author":"MW Padberg","year":"1974","unstructured":"Padberg, M.W., Rao, M.R.: The travelling salesman problem and a class of polyhedra of diameter two. Math. Program. 7, 32\u201345 (1974). doi: 10.1007\/BF01585502","journal-title":"Math. Program."},{"issue":"4","key":"885_CR18","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1287\/moor.2014.0659","volume":"39","author":"K Pashkovich","year":"2014","unstructured":"Pashkovich, K.: Tight lower bounds on the sizes of symmetric extensions of permutahedra and similar results. Math. Oper. Res. 39(4), 1330\u20131339 (2014)","journal-title":"Math. Oper. Res."},{"issue":"4","key":"885_CR19","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.orl.2013.03.010","volume":"41","author":"S Pokutta","year":"2013","unstructured":"Pokutta, S., Van Vyve, M.: A note on the extension complexity of the knapsack polytope. Oper. Res. Lett. 41(4), 347\u2013350 (2013)","journal-title":"Oper. Res. Lett."},{"key":"885_CR20","unstructured":"Rothvoss, T.: Some 0\/1 polytopes need exponential size extended formulations. Math. Program., Ser. A 142, 255\u2013268 (2013)"},{"key":"885_CR21","doi-asserted-by":"crossref","unstructured":"Rothvoss, T.: The matching polytope has exponential extension complexity. In: Proceedings of the 46th Annual ACM Symposium on Theory of Computing, STOC\u201914, New York, NY, USA, pp. 263\u2013272. ACM, New York (2014)","DOI":"10.1145\/2591796.2591834"},{"issue":"1","key":"885_CR22","doi-asserted-by":"crossref","first-page":"383","DOI":"10.4007\/annals.2012.176.1.7","volume":"176","author":"F Santos","year":"2012","unstructured":"Santos, F.: A counterexample to the hirsch conjecture. Ann. Math. 176(1), 383\u2013412 (2012)","journal-title":"Ann. Math."},{"key":"885_CR23","volume-title":"Combinatorial Optimization\u2014Polyhedra and Efficiency","author":"A Schrijver","year":"2003","unstructured":"Schrijver, A.: Combinatorial Optimization\u2014Polyhedra and Efficiency. Springer, Berlin (2003)"},{"issue":"3","key":"885_CR24","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/0022-0000(91)90024-Y","volume":"43","author":"M Yannakakis","year":"1991","unstructured":"Yannakakis, M.: Expressing combinatorial optimization problems by linear programs. J. Comput. Syst. Sci. 43(3), 441\u2013466 (1991)","journal-title":"J. Comput. Syst. Sci."},{"key":"885_CR25","volume-title":"Lectures on Polytopes (Graduate Texts in Mathematics)","author":"GM Ziegler","year":"2001","unstructured":"Ziegler, G.M.: Lectures on Polytopes (Graduate Texts in Mathematics). Springer, Berlin (2001)"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-015-0885-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-015-0885-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-015-0885-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T06:00:07Z","timestamp":1559109607000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-015-0885-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,31]]},"references-count":25,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2015,12]]}},"alternative-id":["885"],"URL":"https:\/\/doi.org\/10.1007\/s10107-015-0885-2","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"type":"print","value":"0025-5610"},{"type":"electronic","value":"1436-4646"}],"subject":[],"published":{"date-parts":[[2015,3,31]]}}}