{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T04:55:51Z","timestamp":1782968151858,"version":"3.54.5"},"publisher-location":"Berlin, Heidelberg","reference-count":30,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540287025","type":"print"},{"value":"9783540318675","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2005]]},"DOI":"10.1007\/11549345_23","type":"book-chapter","created":{"date-parts":[[2005,9,27]],"date-time":"2005-09-27T14:05:47Z","timestamp":1127829947000},"page":"260-270","source":"Crossref","is-referenced-by-count":2,"title":["Basis of Solutions for a System of Linear Inequalities in Integers: Computation and Applications"],"prefix":"10.1007","author":[{"given":"D.","family":"Chubarov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Voronkov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"issue":"1-3","key":"23_CR1","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/S0166-218X(01)00337-7","volume":"123","author":"K. Aardal","year":"2002","unstructured":"Aardal, K., Weismantel, R., Wolsey, L.A.: Non-standard approaches to integer programming. Discrete Applied Mathematics\u00a0123(1-3), 5\u201374 (2002)","journal-title":"Discrete Applied Mathematics"},{"key":"23_CR2","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/S0304-3975(96)00195-8","volume":"173","author":"F. Ajili","year":"1997","unstructured":"Ajili, F., Contejean, E.: Avoiding slack variables in the solving of linear Diophantine equations and inequations. Theoret. Comput. Sci.\u00a0173, 183\u2013208 (1997)","journal-title":"Theoret. Comput. Sci."},{"key":"23_CR3","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1016\/B978-044450813-3\/50014-X","volume-title":"Hanbook of Automated Reasoning, ch.\u00a012","author":"A. Bockmayr","year":"2001","unstructured":"Bockmayr, A., Weispfenning, V.: Solving numerical constraints. In: Robinson, A., Voronkov, A. (eds.) Hanbook of Automated Reasoning, ch.\u00a012, vol.\u00a0I, pp. 751\u2013842. Elsevier Science, Amsterdam (2001)"},{"key":"23_CR4","doi-asserted-by":"publisher","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\u2019s theorem. J. Reine Angew. Math.\u00a0510, 179\u2013185 (1999)","journal-title":"J. Reine Angew. Math."},{"key":"23_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/3-540-54345-7_57","volume-title":"Mathematical Foundations of Computer Science 1991","author":"E. Domenjoud","year":"1991","unstructured":"Domenjoud, E.: Solving systems of linear Diophantine equations: An algebraic approach. In: Tarlecki, A. (ed.) MFCS 1991. LNCS, vol.\u00a0520, pp. 141\u2013150. Springer, Heidelberg (1991)"},{"key":"23_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1007\/3-540-48340-3_9","volume-title":"Mathematical Foundations of Computer Science 1999","author":"A. Durand","year":"1999","unstructured":"Durand, A., Hermann, M., Juban, L.: On the complexity of recognizing the hilbert basis of a linear diophantine system. In: Kutylowski, M., Pacholski, L., Wierzbicki, T. (eds.) MFCS 1999. LNCS, vol.\u00a01672, pp. 92\u2013102. Springer, Heidelberg (1999)"},{"key":"23_CR7","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1006\/jsco.1995.1029","volume":"19","author":"M. Filgueiras","year":"1995","unstructured":"Filgueiras, M., Tom\u00e1s, A.P.: A fast method for finding the basis of nonnegative solutions to a linear Diophantine equation. J. Symbolic Comput.\u00a019, 507\u2013526 (1995)","journal-title":"J. Symbolic Comput."},{"key":"23_CR8","series-title":"Lecture Notes in Computer Science","first-page":"269","volume-title":"Rewriting Techniques and Applications","author":"M. Filgueiras","year":"1997","unstructured":"Filgueiras, M., Tom\u00e1s, A.P.: Solving linear Diophantine equations using the geometric structure of the solution space. In: Comon, H. (ed.) RTA 1997. LNCS, vol.\u00a01232, pp. 269\u2013283. Springer, Heidelberg (1997)"},{"key":"23_CR9","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0024-3795(79)90018-1","volume":"25","author":"R. Giles","year":"1979","unstructured":"Giles, R., Pulleyblank, W.R.: Total dual integrality and integer polyhedra. Linear Algebra and Appl.\u00a025, 191\u2013196 (1979)","journal-title":"Linear Algebra and Appl."},{"key":"23_CR10","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/BF01442864","volume":"6","author":"P. Gordan","year":"1873","unstructured":"Gordan, P.: \u00dcber die aufl\u00f6sung linearer gleichungen mit reellen coefficienten. Math. Ann.\u00a06, 23\u201328 (1873)","journal-title":"Math. Ann."},{"key":"23_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/3-540-56922-7_28","volume-title":"Computer Aided Verification","author":"N. Halbwachs","year":"1993","unstructured":"Halbwachs, N.: Delay analysis in synchronous programs. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol.\u00a0697, pp. 333\u2013346. Springer, Heidelberg (1993)"},{"key":"23_CR12","doi-asserted-by":"crossref","unstructured":"Hemmecke, R.: On the computation of Hilbert bases and extreme rays of cones. E-print arXiv:math.CO\/0203105 (March 2002)","DOI":"10.1142\/9789812777171_0032"},{"issue":"1","key":"23_CR13","first-page":"49","volume":"41","author":"M. Henk","year":"2000","unstructured":"Henk, M., Weismantel, R.: On minimal solutions of linear diophantine equations. Contrib. Algebra and Geometry\u00a041(1), 49\u201355 (2000)","journal-title":"Contrib. Algebra and Geometry"},{"key":"23_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1007\/3-540-63166-6_48","volume-title":"Computer Aided Verification","author":"T. Henzinger","year":"1997","unstructured":"Henzinger, T., Ho, P.-H., Wong-Toi, H.: HyTech: A model checker for hybrid systems. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol.\u00a01254, pp. 460\u2013463. Springer, Heidelberg (1997)"},{"key":"23_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1007\/3-540-48242-3_2","volume-title":"Logic Programming and Automated Reasoning","author":"M. Hermann","year":"1999","unstructured":"Hermann, M., Juban, L., Kolaitis, P.G.: On the complexity of counting the hilbert basis of a linear diophnatine system. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS, vol.\u00a01705, pp. 13\u201332. Springer, Heidelberg (1999)"},{"key":"23_CR16","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/BF01443852","volume":"33","author":"D. Hilbert","year":"1888","unstructured":"Hilbert, D.: \u00dcber die endlichkeit des invariantensystems f\u00fcr bin\u00e4re grundformen. Math. Ann.\u00a033, 223\u2013226 (1888) (In German)","journal-title":"Math. Ann."},{"key":"23_CR17","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1016\/0020-0190(78)90078-9","volume":"7","author":"G.P. Huet","year":"1978","unstructured":"Huet, G.P.: An algorithm to generate the basis of solutions to homogeneous linear Diophantine equations. Inform. Process. Lett.\u00a07, 144\u2013147 (1978)","journal-title":"Inform. Process. Lett."},{"key":"23_CR18","first-page":"39","volume":"305","author":"J. Lambert","year":"1987","unstructured":"Lambert, J.: Une borne pour g\u00e9n\u00e9rateurs des solutions enti\u00e8re positives d\u2019une \u00e9quation diophantienne lin\u00e9aire (A bound for the minimal positive integer solutions of a linear diophantine equation) (in French). C. R. Acad. Sci. Paris S\u00e9r. I Math.\u00a0305, 39\u201340 (1987)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. I Math."},{"issue":"3","key":"23_CR19","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1006\/jcom.1997.0447","volume":"13","author":"E.W. Mayr","year":"1997","unstructured":"Mayr, E.W.: Some complexity results for polynomial ideals. J. Complexity\u00a013(3), 303\u2013325 (1997)","journal-title":"J. Complexity"},{"key":"23_CR20","first-page":"231","volume-title":"proceedings ISAAC 2001","author":"D. Micciancio","year":"2001","unstructured":"Micciancio, D., Warinschi, B.: A linear space algorithm for computing the Hermite normal form. In: proceedings ISAAC 2001, pp. 231\u2013236. ACM, New York (2001)"},{"issue":"4","key":"23_CR21","doi-asserted-by":"publisher","first-page":"765","DOI":"10.1145\/322276.322287","volume":"28","author":"C.H. Papadimitriou","year":"1981","unstructured":"Papadimitriou, C.H.: On the complexity of integer programming. J. ACM\u00a028(4), 765\u2013768 (1981)","journal-title":"J. ACM"},{"key":"23_CR22","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/S0304-3975(00)00229-2","volume":"263","author":"D.V. Pasechnik","year":"2001","unstructured":"Pasechnik, D.V.: On computing Hilbert bases via the Elliot\u2013MacMahon algorithm. Theoret. Comput. Sci.\u00a0263, 37\u201346 (2001)","journal-title":"Theoret. Comput. Sci."},{"key":"23_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1007\/3-540-53904-2_94","volume-title":"Rewriting Techniques and Applications","author":"L. Pottier","year":"1991","unstructured":"Pottier, L.: Minimal solutions of linear diophantine systems: Bounds and algorithms. In: Book, R.V. (ed.) RTA 1991. LNCS, vol.\u00a0488, pp. 162\u2013173. Springer, Heidelberg (1991)"},{"key":"23_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1007\/3-540-45657-0_32","volume-title":"Computer Aided Verification","author":"T. Rybina","year":"2002","unstructured":"Rybina, T., Voronkov, A.: Using canonical representations of solutions to speed up infinite-state model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol.\u00a02404, pp. 386\u2013400. Springer, Heidelberg (2002)"},{"key":"23_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"546","DOI":"10.1007\/978-3-540-45220-1_46","volume-title":"Computer Science Logic","author":"T. Rybina","year":"2003","unstructured":"Rybina, T., Voronkov, A.: Fast infinite-state model checking in integer-based systems. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol.\u00a02803, pp. 546\u2013573. Springer, Heidelberg (2003)"},{"key":"23_CR26","volume-title":"Theory of Linear and Integer Programming","author":"A. Schrijver","year":"1998","unstructured":"Schrijver, A.: Theory of Linear and Integer Programming. John Wiley, Chichester (1998)"},{"key":"23_CR27","unstructured":"Schulz, A., Weismantel, R.: An oracle-polynomial time augmentation algorithm for integer programming. In: proceedings ACM\u2013SIAM SODA 1999, pp. 967\u2013968 (1999)"},{"key":"23_CR28","unstructured":"Seb\u0151, A.: Hilbert bases, Caratheodory\u2019s theorem and combinatorial optimization. In: Kannan, R., Pulleyblank, W.R. (eds.) Proceedings IPCO 1990, pp. 431\u2013455. University of Waterloo Press (1990)"},{"key":"23_CR29","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1145\/322261.322262","volume":"28","author":"M.E. Stickel","year":"1981","unstructured":"Stickel, M.E.: A unification algorithm for associative-commutative functions. J. ACM\u00a028, 423\u2013434 (1981)","journal-title":"J. ACM"},{"key":"23_CR30","first-page":"368","volume":"34","author":"J.G. Corput van der","year":"1931","unstructured":"van der Corput, J.G.: \u00dcber systeme von linear-homogenen Gleichungen und Ungleichungen. Proc. Roy. Acad. Amsterdam\u00a034, 368\u2013371 (1931) (in German)","journal-title":"Proc. Roy. Acad. Amsterdam"}],"container-title":["Lecture Notes in Computer Science","Mathematical Foundations of Computer Science 2005"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11549345_23.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T19:41:13Z","timestamp":1605642073000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11549345_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005]]},"ISBN":["9783540287025","9783540318675"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/11549345_23","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005]]}}}