{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T14:05:33Z","timestamp":1775484333534,"version":"3.50.1"},"publisher-location":"Cham","reference-count":32,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319328584","type":"print"},{"value":"9783319328591","type":"electronic"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-32859-1_37","type":"book-chapter","created":{"date-parts":[[2016,4,15]],"date-time":"2016-04-15T15:12:06Z","timestamp":1460733126000},"page":"429-445","source":"Crossref","is-referenced-by-count":6,"title":["Linear Programs and Convex Hulls Over Fields of Puiseux Fractions"],"prefix":"10.1007","author":[{"given":"Michael","family":"Joswig","sequence":"first","affiliation":[]},{"given":"Georg","family":"Loho","sequence":"additional","affiliation":[]},{"given":"Benjamin","family":"Lorenz","sequence":"additional","affiliation":[]},{"given":"Benjamin","family":"Schr\u00f6ter","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,4,16]]},"reference":[{"key":"37_CR1","unstructured":"Allamigeon, X., Benchimol, P., Gaubert, S., Joswig, M.: Long and winding central paths, preprint (2014). arXiv:1405.4161"},{"issue":"2","key":"37_CR2","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1137\/130936464","volume":"29","author":"X Allamigeon","year":"2015","unstructured":"Allamigeon, X., Benchimol, P., Gaubert, S., Joswig, M.: Tropicalizing the simplex algorithm. SIAM J. Discrete Math. 29(2), 751\u2013795 (2015). http:\/\/dx.doi.org\/10.1137\/130936464","journal-title":"SIAM J. Discrete Math."},{"key":"37_CR3","unstructured":"Allamigeon, X., Gaubert, S., Goubault, \u00c9.: The tropical double description method. In: STACS 2010: 27th International Symposium on Theoretical Aspects of Computer Science, LIPIcs. Leibniz International Proceedings in Informatics, vol. 5, pp. 47\u201358. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern (2010)"},{"issue":"2","key":"37_CR4","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/s00454-012-9469-6","volume":"49","author":"X Allamigeon","year":"2013","unstructured":"Allamigeon, X., Gaubert, S., Goubault, \u00c9.: Computing the vertices of tropical polyhedra using directed hypergraphs. Discrete Comput. Geom. 49(2), 247\u2013279 (2013). http:\/\/dx.doi.org\/10.1007\/s00454-012-9469-6","journal-title":"Discrete Comput. Geom."},{"key":"37_CR5","unstructured":"Benchimol, P.: Tropical aspects of linear programming. Theses, \u00c9cole Polytechnique, December 2014. https:\/\/hal-polytechnique.archives-ouvertes.fr\/tel-01198482"},{"issue":"3\u20134","key":"37_CR6","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","volume":"24","author":"W Bosma","year":"1997","unstructured":"Bosma, W., Cannon, J., Playoust, C.: The MAGMA algebra system I. The user language. J. Symbolic Comput. 24(3\u20134), 235\u2013265 (1997). http:\/\/dx.doi.org\/10.1006\/jsco.1996.0125","journal-title":"J. Symbolic Comput."},{"key":"37_CR7","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1515\/9781400869930-022","volume-title":"Proceedings of the Princeton Symposium on Mathematical Programming","author":"A. Charnes","year":"2015","unstructured":"Charnes, A., Kortanek, K.O.: On classes of convex and preemptive nuclei for $$n$$ -person games. In: Proceedings of the Princeton Symposium on Mathematical Programming (Princeton University, 1967). pp. 377\u2013390. Princeton University Press, Princeton (1970)"},{"key":"37_CR8","volume-title":"Linear Programming and Extensions","author":"GB Dantzig","year":"1963","unstructured":"Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton, N.J. (1963)"},{"issue":"3","key":"37_CR9","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1080\/10586458.2007.10129009","volume":"16","author":"M Develin","year":"2007","unstructured":"Develin, M., Yu, J.: Tropical polytopes and cellular resolutions. Experiment. Math. 16(3), 277\u2013291 (2007). http:\/\/projecteuclid.org\/euclid.em\/1204928529","journal-title":"Experiment. Math."},{"key":"37_CR10","series-title":"Adv. Mech. Math.","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/978-0-387-75714-8_7","volume-title":"Advances in Applied Mathematics and Global Optimization","author":"A Deza","year":"2009","unstructured":"Deza, A., Terlaky, T., Zinchenko, Y.: Central path curvature and iteration-complexity for redundant Klee-Minty cubes. In: Gao, D.Y., Sherali, H.D. (eds.) Advances in Applied Mathematics and Global Optimization. Adv. Mech. Math., vol. 17, pp. 223\u2013256. Springer, New York (2009). http:\/\/dx.doi.org\/10.1007\/978-0-387-75714-8_7"},{"key":"37_CR11","series-title":"EATCS Monographs on Theoretical Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61568-9","volume-title":"Algorithms in Combinatorial Geometry","author":"H Edelsbrunner","year":"1987","unstructured":"Edelsbrunner, H.: Algorithms in Combinatorial Geometry. EATCS Monographs on Theoretical Computer Science, vol. 10. Springer-Verlag, Berlin (1987). http:\/\/dx.doi.org\/10.1007\/978-3-642-61568-9"},{"key":"37_CR12","volume-title":"Modern Computer Algebra","author":"J von zur Gathen","year":"2003","unstructured":"von zur Gathen, J., Gerhard, J.: Modern Computer Algebra, 2nd edn. Cambridge University Press, Cambridge (2003)","edition":"2"},{"issue":"3","key":"37_CR13","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s10801-010-0246-4","volume":"33","author":"S Gaubert","year":"2011","unstructured":"Gaubert, S., Katz, R.D.: Minimal half-spaces and external representation of tropical polyhedra. J. Algebraic Combin. 33(3), 325\u2013348 (2011). http:\/\/dx.doi.org\/10.1007\/s10801-010-0246-4","journal-title":"J. Algebraic Combin."},{"key":"37_CR14","series-title":"DMV Sem.","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/978-3-0348-8438-9_2","volume-title":"Polytopes\u2013combinatorics and computation (Oberwolfach, 1997)","author":"E Gawrilow","year":"2000","unstructured":"Gawrilow, E., Joswig, M.: polymake: a framework for analyzing convex polytopes. In: Kalai, G., Ziegler, G.M. (eds.) Polytopes\u2013combinatorics and computation (Oberwolfach, 1997). DMV Sem., pp. 43\u201373. Birkh\u00e4user, Basel (2000)"},{"issue":"4","key":"37_CR15","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1016\/0166-218X(79)90004-0","volume":"1","author":"D Goldfarb","year":"1979","unstructured":"Goldfarb, D., Sit, W.Y.: Worst case behavior of the steepest edge simplex method. Discrete Appl. Math. 1(4), 277\u2013285 (1979). http:\/\/dx.doi.org\/10.1016\/0166-218X(79)90004-0","journal-title":"Discrete Appl. Math."},{"issue":"5","key":"37_CR16","doi-asserted-by":"publisher","first-page":"1128","DOI":"10.1287\/opre.21.5.1128","volume":"21","author":"RG Jeroslow","year":"1973","unstructured":"Jeroslow, R.G.: Asymptotic linear programming. Oper. Res. 21(5), 1128\u20131141 (1973). http:\/\/dx.doi.org\/10.1287\/opre.21.5.1128","journal-title":"Oper. Res."},{"issue":"2","key":"37_CR17","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/s10957-008-9384-4","volume":"138","author":"CN Jones","year":"2008","unstructured":"Jones, C.N., Kerrigan, E.C., Maciejowski, J.M.: On polyhedral projection and parametric programming. J. Optim. Theor. Appl. 138(2), 207\u2013220 (2008). http:\/\/dx.doi.org\/10.1007\/s10957-008-9384-4","journal-title":"J. Optim. Theor. Appl."},{"key":"37_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-662-05148-1_1","volume-title":"Algebra, Geometry, and Software Systems","author":"M Joswig","year":"2003","unstructured":"Joswig, M.: Beneath-and-beyond revisited. In: Joswig, M., Takayama, N. (eds.) Algebra, Geometry, and Software Systems, pp. 1\u201321. Springer, Berlin (2003)"},{"key":"37_CR19","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1090\/conm\/495\/09698","volume-title":"Tropical and Idempotent Mathematics, Contemporary Mathematics","author":"M Joswig","year":"2009","unstructured":"Joswig, M.: Tropical convex hull computations. In: Litvinov, G.L., Sergeev, S.N. (eds.) Tropical and Idempotent Mathematics, Contemporary Mathematics, vol. 495, pp. 193\u2013212. American Mathematical Society, Providence (2009)"},{"key":"#cr-split#-37_CR20.1","unstructured":"Klee, V., Minty, G.J.: How good is the simplex algorithm? In: Inequalities, III (Proceedings of Third Symposium, University of California, Los Angeles, California, 1969"},{"key":"#cr-split#-37_CR20.2","unstructured":"dedicated to the memory of Theodore S. Motzkin), pp. 159-175. Academic Press, New York (1972)"},{"key":"37_CR21","doi-asserted-by":"crossref","DOI":"10.1090\/gsm\/161","volume-title":"Introduction to Tropical Geometry, Graduate Studies in Mathematics","author":"D Maclagan","year":"2015","unstructured":"Maclagan, D., Sturmfels, B.: Introduction to Tropical Geometry, Graduate Studies in Mathematics, vol. 161. American Mathematical Society, Providence, RI (2015)"},{"key":"37_CR22","first-page":"22","volume":"5","author":"B Mannaa","year":"2013","unstructured":"Mannaa, B., Coquand, T.: Dynamic Newton-Puiseux theorem. J. Log. Anal. 5, 22 (2013). Paper 5","journal-title":"J. Log. Anal."},{"issue":"1","key":"37_CR23","first-page":"79","volume":"68","author":"T Markwig","year":"2010","unstructured":"Markwig, T.: A field of generalised Puiseux series for tropical geometry. Rend. Semin. Mat. Univ. Politec. Torino 68(1), 79\u201392 (2010)","journal-title":"Rend. Semin. Mat. Univ. Politec. Torino"},{"key":"37_CR24","unstructured":"Maslov, V.P.: On a new superposition principle for optimization problem. In: S\u00e9minaire sur les \u00e9quations aux d\u00e9riv\u00e9es partielles, pp. 1985\u20131986, Exp. No. XXIV, 14. \u00c9cole Polytech., Palaiseau (1986)"},{"key":"37_CR25","unstructured":"Opfer, T.: Entwicklung eines exakten rationalen dualen Simplex-L\u00f6sers. Master\u2019s thesis, TU Darmstadt (2011)"},{"key":"37_CR26","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534938.001.0001","volume-title":"Analytic Theory of Polynomials, London Mathematical Society Monographs. New Series","author":"QI Rahman","year":"2002","unstructured":"Rahman, Q.I., Schmeisser, G.: Analytic Theory of Polynomials, London Mathematical Society Monographs. New Series, vol. 26. The University Press, Clarendon Press, Oxford (2002)"},{"key":"37_CR27","volume-title":"The classical fields, Encyclopedia of Mathematics and its Applications","author":"H Salzmann","year":"2007","unstructured":"Salzmann, H., Grundh\u00f6fer, T., H\u00e4hl, H., L\u00f6wen, R.: The classical fields, Encyclopedia of Mathematics and its Applications, vol. 112. Cambridge University Press, Cambridge (2007). http:\/\/dx.doi.org\/10.1017\/CBO9780511721502"},{"key":"37_CR28","volume-title":"A Decision Method for Elementary Algebra and Geometry","author":"A Tarski","year":"1948","unstructured":"Tarski, A.: A Decision Method for Elementary Algebra and Geometry. RAND Corporation, Santa Monica, California (1948)"},{"key":"37_CR29","unstructured":"The MathWorks Inc.: MATLAB, version 8.4.0.150421 (R2014b). Natick, Massachusetts (2014)"},{"key":"37_CR30","volume-title":"Algebra II. Unter Benutzung von Vorlesungen von E. Artin und E. Noether","author":"BL van der Waerden","year":"1993","unstructured":"van der Waerden, B.L.: Algebra II. Unter Benutzung von Vorlesungen von E. Artin und E. Noether, 6th edn. Springer, Berlin (1993). Mit einem Geleitwort von J\u00fcrgen Neukirch","edition":"6"},{"key":"37_CR31","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8431-1","volume-title":"Lectures on Polytopes","author":"GM Ziegler","year":"1995","unstructured":"Ziegler, G.M.: Lectures on Polytopes. Graduate Texts in Mathematics, vol. 152. Springer-Verlag, New York (1995)"}],"container-title":["Lecture Notes in Computer Science","Mathematical Aspects of Computer and Information Sciences"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-32859-1_37","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,15]],"date-time":"2024-06-15T20:00:17Z","timestamp":1718481617000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-32859-1_37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319328584","9783319328591"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-32859-1_37","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]}}}