{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T18:17:01Z","timestamp":1769969821559,"version":"3.49.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T00:00:00Z","timestamp":1615766400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T00:00:00Z","timestamp":1615766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2022,3]]},"DOI":"10.1007\/s00454-020-00268-y","type":"journal-article","created":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T15:03:40Z","timestamp":1615820620000},"page":"503-524","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Short Simplex Paths in Lattice Polytopes"],"prefix":"10.1007","volume":"67","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8428-3914","authenticated-orcid":false,"given":"Alberto","family":"Del Pia","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4717-816X","authenticated-orcid":false,"given":"Carla","family":"Michini","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,3,15]]},"reference":[{"issue":"2","key":"268_CR1","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1016\/0097-3165(95)90058-6","volume":"69","author":"DM Acketa","year":"1995","unstructured":"Acketa, D.M., \u017duni\u0107, J.D.: On the maximal number of edges of convex digital polygons included into an $$m\\times m$$-grid. J. Combin. Theory Ser. A 69(2), 358\u2013368 (1995)","journal-title":"J. Combin. Theory Ser. A"},{"key":"268_CR2","volume-title":"Network Flows: Theory, Algorithms, and Applications","author":"RK Ahuja","year":"1993","unstructured":"Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Englewood Cliffs (1993)"},{"issue":"1","key":"268_CR3","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1006\/jcta.1997.2780","volume":"79","author":"N Alon","year":"1997","unstructured":"Alon, N., Vu, V.H.: Anti-Hadamard matrices, coin weighing, threshold gates, and indecomposable hypergraphs. J. Combin. Theory Ser. A 79(1), 133\u2013160 (1997)","journal-title":"J. Combin. Theory Ser. A"},{"key":"268_CR4","doi-asserted-by":"crossref","unstructured":"Balog, A., B\u00e1r\u00e1ny, I.: On the convex hull of the integer points in a disc. In: 7th Annual Symposium on Computational Geometry (North Conway 1991), pp. 162\u2013165. ACM, New York (1991)","DOI":"10.1145\/109648.109666"},{"key":"268_CR5","volume-title":"Introduction to Linear Optimization","author":"D Bertsimas","year":"1997","unstructured":"Bertsimas, D., Tsitsiklis, J.N.: Introduction to Linear Optimization. Athena Scientific, Belmont (1997)"},{"key":"268_CR6","doi-asserted-by":"crossref","unstructured":"Blanchard, M., De Loera, J., Louveaux, Q.: On the length of monotone paths in polyhedra (2020). arXiv:2001.09575","DOI":"10.1137\/20M1315646"},{"key":"268_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-11008-0","volume-title":"Integer Programming. Graduate Texts in Mathematics","author":"M Conforti","year":"2014","unstructured":"Conforti, M., Cornu\u00e9jols, G., Zambelli, G.: Integer Programming. Graduate Texts in Mathematics, vol. 271. Springer, Cham (2014)"},{"issue":"3","key":"268_CR8","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1007\/s00454-016-9762-x","volume":"55","author":"A Del Pia","year":"2016","unstructured":"Del Pia, A., Michini, C.: On the diameter of lattice polytopes. Discrete Comput. Geom. 55(3), 681\u2013687 (2016)","journal-title":"Discrete Comput. Geom."},{"issue":"1","key":"268_CR9","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s00454-017-9873-z","volume":"60","author":"A Deza","year":"2018","unstructured":"Deza, A., Manoussakis, G., Onn, S.: Primitive zonotopes. Discrete Comput. Geom. 60(1), 27\u201339 (2018)","journal-title":"Discrete Comput. Geom."},{"issue":"2","key":"268_CR10","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1007\/s10474-017-0777-4","volume":"154","author":"A Deza","year":"2018","unstructured":"Deza, A., Pournin, L.: Improved bounds on the diameter of lattice polytopes. Acta Math. Hungar. 154(2), 457\u2013469 (2018)","journal-title":"Acta Math. Hungar."},{"key":"268_CR11","unstructured":"Deza, A., Pournin, L.: Primitive point packing (2020). arXiv:2006.14228"},{"issue":"8","key":"268_CR12","doi-asserted-by":"publisher","first-page":"3507","DOI":"10.1090\/proc\/14977","volume":"148","author":"A Deza","year":"2020","unstructured":"Deza, A., Pournin, L., Sukegawa, N.: The diameter of lattice zonotopes. Proc. Am. Math. Soc. 148(8), 3507\u20133516 (2020)","journal-title":"Proc. Am. Math. Soc."},{"key":"268_CR13","unstructured":"Dinic, E.A.: An algorithm for the step-by-step decrease of discrepancies, and transport problems. In: Issled. Diskret. Mat., pp. 46\u201357. Nauka, Moscow (1973). (in Russian)"},{"issue":"2","key":"268_CR14","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1145\/321694.321699","volume":"19","author":"J Edmonds","year":"1972","unstructured":"Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. J. Assoc. Comput. Mach. 19(2), 248\u2013264 (1972)","journal-title":"J. Assoc. Comput. Mach."},{"issue":"1","key":"268_CR15","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/BF02579200","volume":"7","author":"A Frank","year":"1987","unstructured":"Frank, A., Tardos, \u00c9.: An application of simultaneous Diophantine approximation in combinatorial optimization. Combinatorica 7(1), 49\u201365 (1987)","journal-title":"Combinatorica"},{"issue":"2","key":"268_CR16","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1016\/0022-0000(85)90039-X","volume":"31","author":"HN Gabow","year":"1985","unstructured":"Gabow, H.N.: Scaling algorithms for network problems. J. Comput. Syst. Sci. 31(2), 148\u2013168 (1985)","journal-title":"J. Comput. Syst. Sci."},{"issue":"3","key":"268_CR17","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1016\/j.orl.2012.01.004","volume":"40","author":"T Kitahara","year":"2012","unstructured":"Kitahara, T., Mizuno, S.: On the number of solutions generated by the dual simplex method. Oper. Res. Lett. 40(3), 172\u2013174 (2012)","journal-title":"Oper. Res. Lett."},{"issue":"1\u20132","key":"268_CR18","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1007\/s10107-011-0482-y","volume":"137","author":"T Kitahara","year":"2013","unstructured":"Kitahara, T., Mizuno, S.: A bound for the number of different basic solutions generated by the simplex method. Math. Program. Ser. A 137(1\u20132), 579\u2013586 (2013)","journal-title":"Math. Program. Ser. A"},{"issue":"1","key":"268_CR19","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/0012-365X(92)90349-K","volume":"102","author":"P Kleinschmidt","year":"1992","unstructured":"Kleinschmidt, P., Onn, S.: On the diameter of convex polytopes. Discrete Math. 102(1), 75\u201377 (1992)","journal-title":"Discrete Math."},{"key":"268_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.disopt.2017.08.004","volume":"27","author":"P Le Bodic","year":"2018","unstructured":"Le Bodic, P., Pavelka, J.W., Pfetsch, M.E., Pokutta, S.: Solving MIPs via scaling-based augmentation. Discrete Optim. 27, 1\u201325 (2018)","journal-title":"Discrete Optim."},{"issue":"4","key":"268_CR21","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/BF01457454","volume":"261","author":"AK Lenstra","year":"1982","unstructured":"Lenstra, A.K., Lenstra Jr., H.W., Lov\u00e1sz, L.: Factoring polynomials with rational coefficients. Math. Ann. 261(4), 515\u2013534 (1982)","journal-title":"Math. Ann."},{"issue":"6","key":"268_CR22","doi-asserted-by":"publisher","first-page":"1298","DOI":"10.1080\/10556788.2016.1208748","volume":"31","author":"S Mizuno","year":"2016","unstructured":"Mizuno, S.: The simplex method using Tardos\u2019 basic algorithm is strongly polynomial for totally unimodular LP under nondegeneracy assumption. Optim. Methods Softw. 31(6), 1298\u20131304 (2016)","journal-title":"Optim. Methods Softw."},{"issue":"1","key":"268_CR23","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/BF01589099","volume":"45","author":"D Naddef","year":"1989","unstructured":"Naddef, D.: The Hirsch conjecture is true for $$(0,1)$$-polytopes. Math. Program. 45(1), 109\u2013110 (1989)","journal-title":"Math. Program."},{"key":"268_CR24","doi-asserted-by":"crossref","unstructured":"Pokutta, S.: Restarting algorithms: sometimes there is free lunch. In: International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research (Vienna 2020), pp. 22\u201338. Springer, Cham (2020)","DOI":"10.1007\/978-3-030-58942-4_2"},{"key":"268_CR25","volume-title":"Theory of Linear and Integer Programming","author":"A Schrijver","year":"1986","unstructured":"Schrijver, A.: Theory of Linear and Integer Programming. Wiley-Interscience Series in Discrete Mathematics. Wiley, Chichester (1986)"},{"key":"268_CR26","volume-title":"Combinatorial Optimization. Polyhedra and Efficiency","author":"A Schrijver","year":"2003","unstructured":"Schrijver, A.: Combinatorial Optimization. Polyhedra and Efficiency. Springer, Berlin (2003)"},{"key":"268_CR27","doi-asserted-by":"crossref","unstructured":"Schulz, A.S., Weismantel, R., Ziegler, G.M.: $$0\/1$$-Integer programming: optimization and augmentation are equivalent. In: Algorithms\u2014ESA\u00a0\u201995 (Corfu 1995). Lecture Notes in Comput. Sci., vol. 979, pp. 473\u2013483. Springer, Berlin (1995)","DOI":"10.1007\/3-540-60313-1_164"},{"issue":"2","key":"268_CR28","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1287\/opre.34.2.250","volume":"34","author":"\u00c9 Tardos","year":"1986","unstructured":"Tardos, \u00c9.: A strongly polynomial algorithm to solve combinatorial linear programs. Oper. Res. 34(2), 250\u2013256 (1986)","journal-title":"Oper. Res."},{"key":"268_CR29","unstructured":"Thiele, T.: Extremalprobleme f\u00fcr Punktmengen. PhD thesis, Freie Universit\u00e4t Berlin (1991)"},{"key":"268_CR30","doi-asserted-by":"crossref","unstructured":"Ziegler, G.M.: Lectures on $$0\/1$$-polytopes. In: Polytopes\u2014Combinatorics and Computation (Oberwolfach 1997). DMV Sem., vol. 29, pp. 1\u201341. Birkh\u00e4user, Basel (2000)","DOI":"10.1007\/978-3-0348-8438-9_1"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00268-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-020-00268-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00268-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T05:21:26Z","timestamp":1698038486000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-020-00268-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,15]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["268"],"URL":"https:\/\/doi.org\/10.1007\/s00454-020-00268-y","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,15]]},"assertion":[{"value":"21 March 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 November 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 December 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 March 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}