{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T22:57:38Z","timestamp":1781305058000,"version":"3.54.1"},"publisher-location":"Cham","reference-count":40,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032286901","type":"print"},{"value":"9783032286918","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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":[[2026]]},"DOI":"10.1007\/978-3-032-28691-8_32","type":"book-chapter","created":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T22:35:51Z","timestamp":1781303751000},"page":"491-506","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Linear Programming Hierarchies Collapse Under Symmetry"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3148-2159","authenticated-orcid":false,"given":"Yuri","family":"Faenza","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0817-7356","authenticated-orcid":false,"given":"Victor","family":"Verdugo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2049-6467","authenticated-orcid":false,"given":"Jos\u00e9","family":"Verschae","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5540-7639","authenticated-orcid":false,"given":"Mat\u00edas","family":"Villagra","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,13]]},"reference":[{"issue":"1","key":"32_CR1","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/BF01581273","volume":"58","author":"E Balas","year":"1993","unstructured":"Balas, E., Ceria, S., Cornu\u00e9jols, G.: A lift-and-project cutting plane algorithm for mixed 0\u20131 programs. Math. Program. 58(1), 295\u2013324 (1993)","journal-title":"Math. Program."},{"issue":"2","key":"32_CR2","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1137\/17M1138236","volume":"48","author":"B Barak","year":"2019","unstructured":"Barak, B., Hopkins, S., Kelner, J., Kothari, P.K., Moitra, A., Potechin, A.: A nearly tight sum-of-squares lower bound for the planted clique problem. SIAM J. Comput. 48(2), 687\u2013735 (2019)","journal-title":"SIAM J. Comput."},{"issue":"2","key":"32_CR3","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1287\/moor.26.2.193.10561","volume":"26","author":"A Ben-Tal","year":"2001","unstructured":"Ben-Tal, A., Nemirovski, A.: On polyhedral approximations of the second-order cone. Math. Oper. Res. 26(2), 193\u2013205 (2001)","journal-title":"Math. Oper. Res."},{"issue":"1","key":"32_CR4","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1137\/S1052623402420346","volume":"15","author":"D Bienstock","year":"2004","unstructured":"Bienstock, D., Zuckerberg, M.: Subset algebra lift operators for 0\u20131 integer programming. SIAM J. Optim. 15(1), 63\u201395 (2004)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"32_CR5","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/s10107-005-0598-z","volume":"105","author":"D Bienstock","year":"2006","unstructured":"Bienstock, D., Zuckerberg, M.: Approximate fixed-rank closures of covering problems. Math. Program. 105(1), 9\u201327 (2006)","journal-title":"Math. Program."},{"issue":"137","key":"32_CR6","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1090\/S0025-5718-1977-0428694-0","volume":"31","author":"JR Bunch","year":"1977","unstructured":"Bunch, J.R., Kaufman, L.: Some stable methods for calculating inertia and solving symmetric linear systems. Math. Comput. 31(137), 163\u2013179 (1977)","journal-title":"Math. Comput."},{"issue":"1","key":"32_CR7","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/s10107-023-02044-1","volume":"206","author":"V Cohen-Addad","year":"2024","unstructured":"Cohen-Addad, V., M\u00f6mke, T., Verdugo, V.: A 2-approximation for the bounded treewidth sparsest cut problem in FPT time. Math. Program. 206(1), 479\u2013495 (2024)","journal-title":"Math. Program."},{"issue":"1","key":"32_CR8","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1287\/moor.26.1.19.10593","volume":"26","author":"W Cook","year":"2001","unstructured":"Cook, W., Dash, S.: On the matrix-cut rank of polyhedra. Math. Oper. Res. 26(1), 19\u201330 (2001)","journal-title":"Math. Oper. Res."},{"key":"32_CR9","series-title":"Encyclopaedia of Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-04958-7","volume-title":"Computational Invariant Theory","author":"H Derksen","year":"2002","unstructured":"Derksen, H., Kemper, G.: Computational Invariant Theory. Encyclopaedia of Mathematical Sciences, vol. 130. Springer, Berlin (2002)"},{"key":"32_CR10","doi-asserted-by":"crossref","unstructured":"Dixon, J., Mortimer, B.: Permutation Groups. Springer, Cham (1996)","DOI":"10.1007\/978-1-4612-0731-3"},{"issue":"1","key":"32_CR11","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s10107-024-02102-2","volume":"212","author":"J van Doornmalen","year":"2025","unstructured":"van Doornmalen, J., Hojny, C.: A unified framework for symmetry handling. Math. Program. 212(1), 217\u2013271 (2025)","journal-title":"Math. Program."},{"issue":"2","key":"32_CR12","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/0167-6377(89)90002-3","volume":"8","author":"TA Feo","year":"1989","unstructured":"Feo, T.A., Resende, M.G.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8(2), 67\u201371 (1989)","journal-title":"Oper. Res. Lett."},{"issue":"1\u20132","key":"32_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/0400000086","volume":"14","author":"N Fleming","year":"2019","unstructured":"Fleming, N., Kothari, P., Pitassi, T.: Semialgebraic proofs and efficient algorithm design. Found. Trends Theor. Comput. Sci. 14(1\u20132), 1\u2013221 (2019)","journal-title":"Found. Trends Theor. Comput. Sci."},{"key":"32_CR14","doi-asserted-by":"crossref","unstructured":"Fulkerson, D., Nemhauser, G.L., Trotter, L.E.: Two computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of steiner triple systems. In: Approaches to Integer Programming, pp. 72\u201381. Springer (2009)","DOI":"10.1007\/BFb0120689"},{"issue":"1\u20133","key":"32_CR15","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.jpaa.2003.12.011","volume":"192","author":"K Gatermann","year":"2004","unstructured":"Gatermann, K., Parrilo, P.A.: Symmetry groups, semidefinite programs, and sums of squares. J. Pure Appl. Algebra 192(1\u20133), 95\u2013128 (2004)","journal-title":"J. Pure Appl. Algebra"},{"issue":"8","key":"32_CR16","doi-asserted-by":"publisher","first-page":"3553","DOI":"10.1137\/080721479","volume":"39","author":"K Georgiou","year":"2010","unstructured":"Georgiou, K., Magen, A., Pitassi, T., Tourlakis, I.: Integrality gaps of 2-o(1) for vertex cover SDPs in the Lov\u00e1sz-Schrijver hierarchy. SIAM J. Comput. 39(8), 3553\u20133570 (2010)","journal-title":"SIAM J. Comput."},{"issue":"4","key":"32_CR17","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1287\/moor.26.4.796.10012","volume":"26","author":"M Goemans","year":"2001","unstructured":"Goemans, M., Tun\u00e7el, L.: When does the positive semidefiniteness constraint help in lifting procedures. Math. Oper. Res. 26(4), 769\u2013815 (2001)","journal-title":"Math. Oper. Res."},{"key":"32_CR18","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s00037-001-8192-0","volume":"10","author":"D Grigoriev","year":"2001","unstructured":"Grigoriev, D.: Complexity of positivstellensatz proofs for the knapsack. Comput. Complex. 10, 139\u2013154 (2001)","journal-title":"Comput. Complex."},{"key":"32_CR19","doi-asserted-by":"crossref","unstructured":"Gupta, A., Talwar, K., Witmer, D.: Sparsest cut on bounded treewidth graphs: algorithms and hardness results. In: ACM Symposium on Theory of Computing (STOC), pp. 281\u2013290 (2013)","DOI":"10.1145\/2488608.2488644"},{"issue":"5","key":"32_CR20","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1147\/rd.45.0460","volume":"4","author":"M Hall","year":"1960","unstructured":"Hall, M.: Automorphisms of steiner triple systems. IBM J. Res. Dev. 4(5), 460\u2013472 (1960)","journal-title":"IBM J. Res. Dev."},{"key":"32_CR21","doi-asserted-by":"crossref","unstructured":"Karlin, A.R., Mathieu, C., Nguyen, C.T.: Integrality gaps of linear and semi-definite programming relaxations for knapsack. In: Integer Programming and Combinatorial Optimization (IPCO), pp. 301\u2013314 (2011)","DOI":"10.1007\/978-3-642-20807-2_24"},{"issue":"3","key":"32_CR22","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1007\/s10878-017-0169-2","volume":"36","author":"A Kurpisz","year":"2018","unstructured":"Kurpisz, A., Lepp\u00e4nen, S., Mastrolilli, M.: Sum-of-squares rank upper bounds for matching problems. J. Comb. Optim. 36(3), 831\u2013844 (2018)","journal-title":"J. Comb. Optim."},{"key":"32_CR23","doi-asserted-by":"crossref","unstructured":"Kurpisz, A., Lepp\u00e4nen, S., Mastrolilli, M.: Sum-of-squares hierarchy lower bounds for symmetric formulations. In: Integer Programming and Combinatorial Optimization (IPCO). Lecture Notes in Computer Science, pp. 362\u2013374 (2016)","DOI":"10.1007\/978-3-319-33461-5_30"},{"issue":"1","key":"32_CR24","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1007\/s10107-019-01398-9","volume":"182","author":"A Kurpisz","year":"2020","unstructured":"Kurpisz, A., Lepp\u00e4nen, S., Mastrolilli, M.: Sum-of-squares hierarchy lower bounds for symmetric formulations. Math. Program. 182(1), 369\u2013397 (2020)","journal-title":"Math. Program."},{"issue":"1","key":"32_CR25","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s10107-017-1152-5","volume":"172","author":"A Kurpisz","year":"2018","unstructured":"Kurpisz, A., Mastrolilli, M., Mathieu, C., M\u00f6mke, T., Verdugo, V., Wiese, A.: Semidefinite and linear programming integrality gaps for scheduling identical machines. Math. Program. 172(1), 231\u2013248 (2018)","journal-title":"Math. Program."},{"issue":"3","key":"32_CR26","doi-asserted-by":"publisher","first-page":"796","DOI":"10.1137\/S1052623400366802","volume":"11","author":"JB Lasserre","year":"2001","unstructured":"Lasserre, J.B.: Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11(3), 796\u2013817 (2001)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"32_CR27","doi-asserted-by":"publisher","first-page":"470","DOI":"10.1287\/moor.28.3.470.16391","volume":"28","author":"M Laurent","year":"2003","unstructured":"Laurent, M.: A comparison of the Sherali-Adams, Lov\u00e1sz-Schrijver, and Lasserre relaxations for 0\u20131 programming. Math. Oper. Res. 28(3), 470\u2013496 (2003)","journal-title":"Math. Oper. Res."},{"issue":"4","key":"32_CR28","doi-asserted-by":"publisher","first-page":"871","DOI":"10.1287\/moor.28.4.871.20508","volume":"28","author":"M Laurent","year":"2003","unstructured":"Laurent, M.: Lower bound for the number of iterations in semidefinite hierarchies for the cut polytope. Math. Oper. Res. 28(4), 871\u2013883 (2003)","journal-title":"Math. Oper. Res."},{"issue":"2","key":"32_CR29","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1137\/0801013","volume":"1","author":"L Lov\u00e1sz","year":"1991","unstructured":"Lov\u00e1sz, L., Schrijver, A.: Cones of matrices and set-functions and 0\u20131 optimization. SIAM J. Optim. 1(2), 166\u2013190 (1991)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"32_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0167-6377(95)00034-H","volume":"18","author":"C Mannino","year":"1995","unstructured":"Mannino, C., Sassano, A.: Solving hard set covering problems. Oper. Res. Lett. 18(1), 1\u20136 (1995)","journal-title":"Oper. Res. Lett."},{"key":"32_CR31","doi-asserted-by":"crossref","unstructured":"Margot, F.: Symmetry in integer linear programming. In: 50 Years of Integer Programming 1958-2008, pp. 647\u2013686. Springer, Heidelberg (2010)","DOI":"10.1007\/978-3-540-68279-0_17"},{"key":"32_CR32","doi-asserted-by":"crossref","unstructured":"Mathieu, C., Sinclair, A.: Sherali-Adams relaxations of the matching polytope. In: ACM Symposium on Theory of Computing (STOC), pp. 293\u2013302 (2009)","DOI":"10.1145\/1536414.1536456"},{"key":"32_CR33","doi-asserted-by":"crossref","unstructured":"Meka, R., Potechin, A., Wigderson, A.: Sum-of-squares lower bounds for Planted Clique. In: ACM Symposium on Theory of Computing (STOC), pp. 87\u201396 (2015)","DOI":"10.1145\/2746539.2746600"},{"issue":"4","key":"32_CR34","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1007\/s12532-014-0072-0","volume":"6","author":"J Ostrowski","year":"2014","unstructured":"Ostrowski, J.: Using symmetry to optimize over the Sherali-Adams relaxation. Math. Program. Comput. 6(4), 405\u2013428 (2014)","journal-title":"Math. Program. Comput."},{"issue":"2","key":"32_CR35","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/j.orl.2011.02.001","volume":"39","author":"J Ostrowski","year":"2011","unstructured":"Ostrowski, J., Linderoth, J., Rossi, F., Smriglio, S.: Solving large steiner triple covering problems. Oper. Res. Lett. 39(2), 127\u2013131 (2011)","journal-title":"Oper. Res. Lett."},{"issue":"1","key":"32_CR36","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s12532-018-0140-y","volume":"11","author":"M Pfetsch","year":"2019","unstructured":"Pfetsch, M., Rehn, T.: A computational comparison of symmetry handling methods for mixed integer programs. Math. Program. Comput. 11(1), 37\u201393 (2019)","journal-title":"Math. Program. Comput."},{"issue":"3","key":"32_CR37","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1137\/0403036","volume":"3","author":"HD Sherali","year":"1990","unstructured":"Sherali, H.D., Adams, W.P.: A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Discret. Math. 3(3), 411\u2013430 (1990)","journal-title":"SIAM J. Discret. Math."},{"issue":"3","key":"32_CR38","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1137\/0403036","volume":"3","author":"H Sherali","year":"1990","unstructured":"Sherali, H., Adams, W.: A hierarchy of relaxations between the continuous and convex hull representations for zero one programming problems. SIAM J. Discret. Math. 3(3), 411\u2013430 (1990)","journal-title":"SIAM J. Discret. Math."},{"key":"32_CR39","doi-asserted-by":"publisher","unstructured":"Verdugo, V., Verschae, J., Wiese, A.: Breaking symmetries to rescue sum of squares in the case of makespan scheduling. Math. Program. (1), 583\u2013618 (2020). https:\/\/doi.org\/10.1007\/s10107-020-01511-3","DOI":"10.1007\/s10107-020-01511-3"},{"key":"32_CR40","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1016\/0022-0000(91)90024-Y","volume":"43","author":"M Yannakakis","year":"1991","unstructured":"Yannakakis, M.: Expressing combinatorial optimization problems by linear programs. J. Comput. Syst. Sci. 43, 441\u2013466 (1991)","journal-title":"J. Comput. Syst. Sci."}],"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\/978-3-032-28691-8_32","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T22:35:53Z","timestamp":1781303753000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-28691-8_32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032286901","9783032286918"],"references-count":40,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-28691-8_32","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"13 June 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"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":"Padua","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 June 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 June 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ipco2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/events.math.unipd.it\/ipco2026\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}