{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T03:12:43Z","timestamp":1743045163133,"version":"3.40.3"},"publisher-location":"Cham","reference-count":25,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031598340"},{"type":"electronic","value":"9783031598357"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-59835-7_1","type":"book-chapter","created":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T07:05:03Z","timestamp":1716275103000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Sparsity and\u00a0Integrality Gap Transference Bounds for\u00a0Integer Programs"],"prefix":"10.1007","author":[{"given":"Iskander","family":"Aliev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcel","family":"Celaya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Henk","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,22]]},"reference":[{"key":"1_CR1","doi-asserted-by":"crossref","unstructured":"Abdi, A., Cornu\u00e9jols, G., Guenin, B., Tun\u00e7el, L.: Dyadic linear programming and extensions. arXiv:2309.04601 (2023)","DOI":"10.1007\/s10107-024-02146-4"},{"key":"1_CR2","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1007\/s10107-021-01657-8","volume":"192","author":"I Aliev","year":"2022","unstructured":"Aliev, I., Averkov, G., De Loera, J.A., Oertel, T.: Sparse representation of vectors in lattices and semigroups. Math. Program. 192, 519\u2013546 (2022)","journal-title":"Math. Program."},{"issue":"1","key":"1_CR3","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1137\/20M1353228","volume":"31","author":"I Aliev","year":"2021","unstructured":"Aliev, I., Celaya, M., Henk, M., Williams, A.: Distance-sparsity transference for vertices of corner polyhedra. SIAM J. Optim. 31(1), 200\u2013216 (2021)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"1_CR4","doi-asserted-by":"publisher","first-page":"2152","DOI":"10.1137\/17M1162792","volume":"28","author":"I Aliev","year":"2018","unstructured":"Aliev, I., De Loera, J.A., Eisenbrand, F., Oertel, T., Weismantel, R.: The support of integer optimal solutions. SIAM J. Optim. 28(3), 2152\u20132157 (2018)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1_CR5","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1137\/16M1083876","volume":"1","author":"I Aliev","year":"2017","unstructured":"Aliev, I., De Loera, J.A., Oertel, T., O\u2019Neill, C.: Sparse solutions of linear Diophantine equations. SIAM J. Appl. Algebra Geom. 1(1), 239\u2013253 (2017)","journal-title":"SIAM J. Appl. Algebra Geom."},{"issue":"1\u20132","key":"1_CR6","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/s10107-019-01392-1","volume":"182","author":"I Aliev","year":"2020","unstructured":"Aliev, I., Henk, M., Oertel, T.: Distances to lattice points in knapsack polyhedra. Math. Program. 182(1\u20132), 175\u2013198 (2020)","journal-title":"Math. Program."},{"key":"1_CR7","doi-asserted-by":"crossref","unstructured":"Berndt, S., Jansen, K., Klein, K.-M.: New bounds for the vertices of the integer hull. In: Symposium on Simplicity in Algorithms (SOSA), pp. 25\u201336. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2021)","DOI":"10.1137\/1.9781611976496.3"},{"issue":"2","key":"1_CR8","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/0012-365X(77)90028-0","volume":"19","author":"CE Blair","year":"1977","unstructured":"Blair, C.E., Jeroslow, R.G.: The value function of a mixed integer program. I. Discrete Math. 19(2), 121\u2013138 (1977)","journal-title":"I. Discrete Math."},{"issue":"3","key":"1_CR9","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/BF01583794","volume":"23","author":"CE Blair","year":"1982","unstructured":"Blair, C.E., Jeroslow, R.G.: The value function of an integer program. Math. Program. 23(3), 237\u2013273 (1982)","journal-title":"Math. Program."},{"key":"1_CR10","doi-asserted-by":"publisher","unstructured":"Cassels, J.W.S.: An Introduction to the Geometry of Numbers. Classics in Mathematics. Springer, Heidelberg (1996). https:\/\/doi.org\/10.1007\/978-3-642-62035-5","DOI":"10.1007\/978-3-642-62035-5"},{"key":"1_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1007\/978-3-031-06901-7_7","volume-title":"Integer Programming and Combinatorial Optimization","author":"M Celaya","year":"2022","unstructured":"Celaya, M., Kuhlmann, S., Paat, J., Weismantel, R.: Improving the Cook et al. proximity bound given integral valued constraints. In: Aardal, K., Sanit\u00e1, L. (eds.) IPCO 2022. LNCS, vol. 13265, pp. 84\u201397. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-06901-7_7"},{"issue":"1","key":"1_CR12","doi-asserted-by":"publisher","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. Combin. Theory Ser. B 40(1), 63\u201370 (1986)","journal-title":"J. Combin. Theory Ser. B"},{"issue":"3","key":"1_CR13","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/BF01582230","volume":"34","author":"W Cook","year":"1986","unstructured":"Cook, W., Gerards, A.M.H., Schrijver, A., Tardos, \u00c9.: Sensitivity theorems in integer linear programming. Math. Program. 34(3), 251\u2013264 (1986)","journal-title":"Math. Program."},{"key":"1_CR14","unstructured":"Dubey, Y., Liu, S.: A short proof of tight bounds on the smallest support size of integer solutions to linear equations. arXiv:2307.08826 (2023)"},{"issue":"5","key":"1_CR15","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1016\/j.orl.2005.09.008","volume":"34","author":"F Eisenbrand","year":"2006","unstructured":"Eisenbrand, F., Shmonin, G.: Carath\u00e9odory bounds for integer cones. Oper. Res. Lett. 34(5), 564\u2013568 (2006)","journal-title":"Oper. Res. Lett."},{"key":"1_CR16","doi-asserted-by":"crossref","unstructured":"Eisenbrand, F., Weismantel, R.: Proximity results and faster algorithms for integer programming using the Steinitz lemma. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 808\u2013816. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2018)","DOI":"10.1137\/1.9781611975031.52"},{"key":"1_CR17","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1073\/pnas.53.2.260","volume":"53","author":"RE Gomory","year":"1965","unstructured":"Gomory, R.E.: On the relation between integer and noninteger solutions to linear programs. Proc. Nat. Acad. Sci. U.S.A. 53, 260\u2013265 (1965)","journal-title":"Proc. Nat. Acad. Sci. U.S.A."},{"key":"1_CR18","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1016\/0024-3795(69)90017-2","volume":"2","author":"RE Gomory","year":"1969","unstructured":"Gomory, R.E.: Some polyhedra related to combinatorial problems. Linear Algebra Appl. 2, 451\u2013558 (1969)","journal-title":"Linear Algebra Appl."},{"key":"1_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/978-3-030-53262-8_10","volume-title":"Combinatorial Optimization","author":"J Lee","year":"2020","unstructured":"Lee, J., Paat, J., Stallknecht, I., Xu, L.: Improving proximity bounds using sparsity. In: Ba\u00efou, M., Gendron, B., G\u00fcnl\u00fck, O., Mahjoub, A.R. (eds.) ISCO 2020. LNCS, vol. 12176, pp. 115\u2013127. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-53262-8_10"},{"key":"1_CR20","first-page":"2267","volume":"48","author":"J Lee","year":"2023","unstructured":"Lee, J., Paat, J., Stallknecht, I., Xu, L.: Polynomial upper bounds on the number of differing columns of $$\\varDelta $$-modular integer programs. Math. Oper. Res. 48, 2267\u20132286 (2023)","journal-title":"Math. Oper. Res."},{"issue":"3","key":"1_CR21","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1137\/19M1275954","volume":"4","author":"T Oertel","year":"2020","unstructured":"Oertel, T., Paat, J., Weismantel, R.: The distributions of functions related to parametric integer optimization. SIAM J. Appl. Algebra Geom. 4(3), 422\u2013440 (2020)","journal-title":"SIAM J. Appl. Algebra Geom."},{"issue":"1\u20132","key":"1_CR22","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/s10107-018-1323-z","volume":"179","author":"J Paat","year":"2020","unstructured":"Paat, J., Weismantel, R., Weltge, S.: Distances between optimal solutions of mixed-integer programs. Math. Program. 179(1\u20132), 455\u2013468 (2020)","journal-title":"Math. Program."},{"key":"1_CR23","unstructured":"Seb\u0151, A.: Hilbert bases, Carath\u00e9odory\u2019s theorem and combinatorial optimization. In: Proceedings of the 1st Integer Programming and Combinatorial Optimization Conference, pp. 431\u2013455. University of Waterloo Press (1990)"},{"key":"1_CR24","unstructured":"Skolem, T.: Diophantische Gleichungen. Ergebnisse der Mathematik, vol 5. Springer, Berlin (1938)"},{"issue":"2","key":"1_CR25","doi-asserted-by":"publisher","first-page":"543","DOI":"10.2140\/pjm.1979.83.543","volume":"83","author":"JD Vaaler","year":"1979","unstructured":"Vaaler, J.D.: A geometric inequality with applications to linear forms. Pacific J. Math. 83(2), 543\u2013553 (1979)","journal-title":"Pacific J. Math."}],"container-title":["Lecture Notes in Computer Science","Integer Programming and Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-59835-7_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T14:31:13Z","timestamp":1732026673000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-59835-7_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031598340","9783031598357"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-59835-7_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"22 May 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"IPCO","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Integer Programming and Combinatorial Optimization","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Wroc\u0142aw","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Poland","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"3 July 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5 July 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ipco2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ipco2024.ii.uni.wroc.pl\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}