{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,6]],"date-time":"2024-04-06T00:28:22Z","timestamp":1712363302033},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2010,5,23]],"date-time":"2010-05-23T00:00:00Z","timestamp":1274572800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2012,4]]},"DOI":"10.1007\/s10107-010-0383-5","type":"journal-article","created":{"date-parts":[[2010,5,22]],"date-time":"2010-05-22T02:17:06Z","timestamp":1274494626000},"page":"57-78","source":"Crossref","is-referenced-by-count":3,"title":["Alternatives for testing total dual integrality"],"prefix":"10.1007","volume":"132","author":[{"given":"Edwin","family":"O\u2019Shea","sequence":"first","affiliation":[]},{"given":"Andr\u00e1s","family":"Seb\u00f6","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,5,23]]},"reference":[{"key":"383_CR1","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0167-6377(91)90084-3","volume":"10","author":"D. Applegate","year":"1991","unstructured":"Applegate D., Cook W., McCormick T.: Integral feasibility and testing total dual integrality. Oper. Res. Lett. 10, 37\u201341 (1991)","journal-title":"Oper. Res. Lett."},{"key":"383_CR2","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1090\/S0894-0347-03-00428-4","volume":"16","author":"A. Barvinok","year":"2003","unstructured":"Barvinok A., Woods K.: Short rational generating functions for lattice point problems. J. Am. Math. Soc. 16, 957\u2013979 (2003)","journal-title":"J. Am. Math. Soc."},{"key":"383_CR3","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1515\/crll.1999.045","volume":"510","author":"W. Bruns","year":"1999","unstructured":"Bruns W., Gubeladze J., Henk M., Martin A., Weismantel R.: A counterexample to an integer analogue of Carath\u00e9odory theorem. J. Reine Angew. Math. 510, 179\u2013185 (1999)","journal-title":"J. Reine Angew. Math."},{"key":"383_CR4","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0167-6377(84)90029-4","volume":"3","author":"R. Chandrasekaran","year":"1984","unstructured":"Chandrasekaran R., Tamir A.: On the integrality of an extreme solution to pluperfect graph and balanced systems. Oper. Res. Lett. 3, 215\u2013218 (1984)","journal-title":"Oper. Res. Lett."},{"key":"383_CR5","doi-asserted-by":"crossref","unstructured":"Conti, P., Traverso, C.: Buchberger algorithm and integer programming. In: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Lecture Notes in Computer Science, vol. 539. Springer, Berlin (1991)","DOI":"10.1007\/3-540-54522-0_102"},{"key":"383_CR6","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/0095-8956(86)90064-X","volume":"40","author":"W. Cook","year":"1986","unstructured":"Cook W., Fonlupt J., Schrijver A.: An integer analogue of Carath\u00e9odory\u2019s theorem. J. Comb. Theory (B) 40, 63\u201370 (1986)","journal-title":"J. Comb. Theory (B)"},{"key":"383_CR7","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1007\/BFb0121008","volume":"22","author":"W. Cook","year":"1984","unstructured":"Cook W., Lov\u00e1sz L., Schrijver A.: A polynomial-time test for total dual integrality in fixed dimension. Math. Progr. Study 22, 64\u201369 (1984)","journal-title":"Math. Progr. Study"},{"key":"383_CR8","doi-asserted-by":"crossref","unstructured":"Cornu\u00e9jols, G.: Combinatorial optimization: packing and covering. In: CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 74. SIAM (2001)","DOI":"10.1137\/1.9780898717105"},{"issue":"2","key":"383_CR9","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s00493-005-0012-8","volume":"25","author":"M. Chudnovsky","year":"2005","unstructured":"Chudnovsky M., Cornu\u00e9jols G., Liu X., Seymour P., Vu\u0161kovi\u0107 K.: Recognizing Berge graphs. Combinatorica 25(2), 143\u2013186 (2005)","journal-title":"Combinatorica"},{"issue":"1","key":"383_CR10","doi-asserted-by":"crossref","first-page":"51","DOI":"10.4007\/annals.2006.164.51","volume":"164","author":"M. Chudnovsky","year":"2006","unstructured":"Chudnovsky M., Robertson N., Seymour P., Thomas R.: The strong perfect graph theorem. Ann. Math. 164(1), 51\u2013229 (2006)","journal-title":"Ann. Math."},{"key":"383_CR11","volume-title":"Ideals, Varieties and Algorithms","author":"D. Cox","year":"1996","unstructured":"Cox D., Little J., O\u2019Shea D.: Ideals, Varieties and Algorithms, 2nd edn. Springer-Verlag, New York (1996)","edition":"2"},{"key":"383_CR12","doi-asserted-by":"crossref","unstructured":"De Loera, J.A., Lee, J., Malkin, P., Margulies, S.: Hilbert\u2019s Nullstellensatz and an algorithm for proving combinatorial infeasibility. In: ISSAC 21: Proceedings of the Twenty-First International Symposium on Symbolic and Algebraic Computation, pp. 197\u2013206. ACM, New York (2008)","DOI":"10.1145\/1390768.1390797"},{"key":"383_CR13","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s10107-007-0103-y","volume":"114","author":"G. Ding","year":"2008","unstructured":"Ding G., Feng L., Zang W.: The complexity of recognizing linear systems with certain integrality properties. Math. Progr. 114, 321\u2013334 (2008)","journal-title":"Math. Progr."},{"key":"383_CR14","doi-asserted-by":"crossref","first-page":"1636","DOI":"10.1016\/j.jpaa.2008.11.045","volume":"213","author":"P. Dueck","year":"2009","unstructured":"Dueck P., Ho\u015ften S., Sturmfels B.: Normal Toric ideals of low codimension. J. Pure Appl. Algebra 213, 1636\u20131641 (2009)","journal-title":"J. Pure Appl. Algebra"},{"key":"383_CR15","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1287\/moor.1080.0320","volume":"33","author":"F. Eisenbrand","year":"2008","unstructured":"Eisenbrand F., Shmonin G.: Parametric integer programming in fixed dimension. Math. Oper. Res. 33, 839\u2013850 (2008)","journal-title":"Math. Oper. Res."},{"key":"383_CR16","unstructured":"Eisenbrand, F., Seb\u0151, A., Shmonin, G.: Testing Hilbert bases. August 2007 (manuscript)"},{"key":"383_CR17","unstructured":"Fukuda, K.: cdd+ reference manual. Institute for Operations Research, Swiss Federal Institute of Technology, Zurich, Switzerland. http:\/\/www.ifor.math.ethz.ch\/~fukuda\/cdd_home\/cdd.html (1995)"},{"key":"383_CR18","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/0095-8956(72)90032-9","volume":"12","author":"D.R. Fulkerson","year":"1972","unstructured":"Fulkerson D.R.: Anti-blocking polyhedra. J. Comb. Theory (B) 12, 50\u201371 (1972)","journal-title":"J. Comb. Theory (B)"},{"key":"383_CR19","doi-asserted-by":"crossref","unstructured":"Gawrilow, E., Joswig, M.: Polymake: a framework for analyzing convex polytopes. In: Polytopes\u2014Combinatorics and Computation (Oberwolfach, 1997), pp. 43\u201373. DMV Sem. 29. Birkh\u00e4user, Basel (2000)","DOI":"10.1007\/978-3-0348-8438-9_2"},{"key":"383_CR20","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/BF02591852","volume":"38","author":"A. Gerards","year":"1987","unstructured":"Gerards A., Seb\u0151 A.: Total dual integrality implies local strong unimodularity. Math. Progr. 38, 69\u201373 (1987)","journal-title":"Math. Progr."},{"key":"383_CR21","volume-title":"Algorithmic Graph Theory and Perfect Graphs","author":"M.C. Golumbic","year":"1980","unstructured":"Golumbic M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York (1980)"},{"key":"383_CR22","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF01681344","volume":"8","author":"J. Graver","year":"1975","unstructured":"Graver J.: On the foundations of linear and integer programming I. Math. Progr. 8, 207\u2013226 (1975)","journal-title":"Math. Progr."},{"key":"383_CR23","unstructured":"Grayson, D., Stillman, M.: Macaulay 2, a software system for research in algebraic geometry. http:\/\/www.math.uiuc.edu\/Macaulay2\/"},{"key":"383_CR24","volume-title":"Geometric Algorithms and Combinatorial Optimization","author":"M. Gr\u00f6tschel","year":"1984","unstructured":"Gr\u00f6tschel M., Lov\u00e1sz L., Schrijver A.: Geometric Algorithms and Combinatorial Optimization. Springer, Berlin (1984)"},{"key":"383_CR25","doi-asserted-by":"crossref","unstructured":"Hemmecke, R., Onn, S., Weismantel, R.: A polynomial oracle-time algorithm for convex integer minimization. Math. Progr. A. doi: 10.1007\/s10107-009-0276-7","DOI":"10.1007\/s10107-009-0276-7"},{"key":"383_CR26","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/s00493-007-2057-3","volume":"27","author":"S. Ho\u015ften","year":"2007","unstructured":"Ho\u015ften S., Sturmfels B.: Computing the integer programming gap. Combinatorica 27, 367\u2013382 (2007)","journal-title":"Combinatorica"},{"key":"383_CR27","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1090\/dimacs\/004\/35","volume":"4","author":"C.W. Lee","year":"1991","unstructured":"Lee C.W.: Regular triangulations of convex polytopes. DIMACS Series Discrete Math. Theor. Comput. Sci. 4, 443\u2013456 (1991)","journal-title":"DIMACS Series Discrete Math. Theor. Comput. Sci."},{"key":"383_CR28","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1287\/moor.8.4.538","volume":"8","author":"H.W. Lenstra Jr.","year":"1983","unstructured":"Lenstra H.W. Jr.: Integer programming with a fixed number of variables. Math. Oper. Res. 8, 538\u2013548 (1983)","journal-title":"Math. Oper. Res."},{"key":"383_CR29","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/0012-365X(72)90006-4","volume":"2","author":"L. Lov\u00e1sz","year":"1972","unstructured":"Lov\u00e1sz L.: Normal hypergraphs and the perfect graph conjecture. Discrete Math. 2, 253\u2013267 (1972)","journal-title":"Discrete Math."},{"key":"383_CR30","unstructured":"Lueker, G.S.: Structured Breadth First Search and Chordal Graphs. Princeton Univ. Tech. Rep. TR-158"},{"key":"383_CR31","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/0001-8708(82)90048-2","volume":"46","author":"E.W. Mayr","year":"1982","unstructured":"Mayr E.W., Meyer A.: The complexity of the word problems for commutative semigroups and polynomial ideals. Adv. Math. 46, 305\u2013329 (1982)","journal-title":"Adv. Math."},{"key":"383_CR32","doi-asserted-by":"crossref","first-page":"2541","DOI":"10.1090\/S0002-9939-01-05853-1","volume":"129","author":"H. Ohsugi","year":"2001","unstructured":"Ohsugi H., Hibi T.: Convex polytopes all of whose reverse lexicographic initial ideals are squarefree. Proc. A.M.S. 129, 2541\u20132546 (2001)","journal-title":"Proc. A.M.S."},{"key":"383_CR33","unstructured":"O\u2019Shea, E.: Toric algebra and the weak perfect graph theorem. Ph.D. dissertation, University of Washington (2006)"},{"key":"383_CR34","doi-asserted-by":"crossref","unstructured":"O\u2019Shea, E., Seb\u0151, A.: Characterizations of total dual integrality. In: Fischetti, M., Williamson, D. (eds.) Integer Programming and Combinatorial Optimization, vol. 12. LNCS (2007)","DOI":"10.1007\/978-3-540-72792-7_29"},{"key":"383_CR35","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1007\/BF01580235","volume":"6","author":"M. Padberg","year":"1974","unstructured":"Padberg M.: Perfect zero-one matrices. Math. Progr. 6, 180\u2013196 (1974)","journal-title":"Math. Progr."},{"key":"383_CR36","doi-asserted-by":"crossref","unstructured":"Pap, J.: Recognizing conic TDI systems is hard. EGRES Technical Report TR-2008-15. Mathematical Programming. doi: 10.1007\/s10107-009-0294-5","DOI":"10.1007\/s10107-009-0294-5"},{"key":"383_CR37","unstructured":"Rambau, J.: TOPCOM (Triangulations of Point Configurations and Oriented Matroids). http:\/\/www.uni-bayreuth.de\/departments\/wirtschaftsmathematik\/rambau\/TOPCOM\/"},{"key":"383_CR38","doi-asserted-by":"crossref","unstructured":"Rose, D.J., Tarjan, R.E.: Algorithmic aspects of vertex elimination. In: Proc. 7. Ann. ACM Symp., Theory Comput, pp. 245\u2013254 (1975)","DOI":"10.1145\/800116.803775"},{"key":"383_CR39","doi-asserted-by":"crossref","unstructured":"Saito, M., Sturmfels, B., Takayama, N.: Gr\u00f6bner deformations of hypergeometric differential equations. In: Algorithms and Computation in Mathematics, vol. 6. Springer-Verlag, Berlin (2000)","DOI":"10.1007\/978-3-662-04112-3"},{"key":"383_CR40","volume-title":"Theory of Linear and Integer Programming","author":"A. Schrijver","year":"1986","unstructured":"Schrijver A.: Theory of Linear and Integer Programming. Wiley, New York (1986)"},{"key":"383_CR41","volume-title":"Integer Programming and Combinatorial Optimization","author":"A. Seb\u0151","year":"1990","unstructured":"Seb\u0151 A.: Hilbert bases, Caratheodory\u2019s theorem and combinatorial optimization. In: Kannan, R., Pulleyblank, W. (eds) Integer Programming and Combinatorial Optimization, Mathematical Programming Society, University of Waterloo Press, Waterloo (1990)"},{"key":"383_CR42","unstructured":"Seb\u0151, A.: Problem A.6, \u201cTDI Matrices\u201d. In: Open Problems Workshop on \u201cThe Perfect Graph Conjecture\u201d. http:\/\/www.aimath.org\/pastworkshops\/perfectgraph.html (2002)"},{"key":"383_CR43","doi-asserted-by":"crossref","first-page":"249","DOI":"10.2748\/tmj\/1178227496","volume":"43","author":"B. Sturmfels","year":"1991","unstructured":"Sturmfels B.: Gr\u00f6bner bases of toric varieties. Tohoku Math. J. 43, 249\u2013261 (1991)","journal-title":"Tohoku Math. J."},{"key":"383_CR44","first-page":"281","volume":"36","author":"B. Sturmfels","year":"1995","unstructured":"Sturmfels B., Weismantel R., Ziegler G.M.: Gr\u00f6bner bases of lattices, corner polyhedra, and integer programming. Beitr\u00e4ge Algebra Geom. 36, 281\u2013298 (1995)","journal-title":"Beitr\u00e4ge Algebra Geom."},{"key":"383_CR45","doi-asserted-by":"crossref","unstructured":"Sturmfels, B.: Gr\u00f6bner bases and convex polytopes. University Lecture Series, vol. 8. American Mathematical Society, Providence (1996)","DOI":"10.1090\/ulect\/008"},{"key":"383_CR46","doi-asserted-by":"crossref","unstructured":"Sturmfels, B.: Algebraic recipes for integer programming. AMS Shortcourse: Trends in Optimization. In: Ho\u015ften, S., Lee, J., Thomas, R.R. (eds.) Proceedings of Symposia in Applied Mathematics, vol. 61. American Mathematical Society, Providence (2004)","DOI":"10.1090\/psapm\/061\/2104733"},{"key":"383_CR47","first-page":"357","volume":"77","author":"B. Sturmfels","year":"1997","unstructured":"Sturmfels B., Thomas R.R.: Variations of cost functions in integer programming. Math. Progr. 77, 357\u2013387 (1997)","journal-title":"Math. Progr."},{"key":"383_CR48","volume-title":"Encyclopedia of Optimization","author":"R.R. Thomas","year":"2001","unstructured":"Thomas R.R.: Algebraic methods in integer programming. In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization, Kluwer Academic Publishers, Dordrecht (2001)"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-010-0383-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-010-0383-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-010-0383-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T10:38:11Z","timestamp":1559126291000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-010-0383-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,5,23]]},"references-count":48,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,4]]}},"alternative-id":["383"],"URL":"https:\/\/doi.org\/10.1007\/s10107-010-0383-5","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,5,23]]}}}