{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T08:57:41Z","timestamp":1773392261660,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2010,2,23]],"date-time":"2010-02-23T00:00:00Z","timestamp":1266883200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Prog. Comp."],"published-print":{"date-parts":[[2010,3]]},"DOI":"10.1007\/s12532-010-0012-6","type":"journal-article","created":{"date-parts":[[2010,2,22]],"date-time":"2010-02-22T12:03:40Z","timestamp":1266840220000},"page":"59-77","source":"Crossref","is-referenced-by-count":21,"title":["A new relaxation framework for quadratic assignment problems based on matrix splitting"],"prefix":"10.1007","volume":"2","author":[{"given":"Jiming","family":"Peng","sequence":"first","affiliation":[]},{"given":"Hans","family":"Mittelmann","sequence":"additional","affiliation":[]},{"given":"Xiaoxue","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,2,23]]},"reference":[{"key":"12_CR1","doi-asserted-by":"crossref","unstructured":"Adams, W.P., Johnson, T.A.: Improved linear programming-based lower bounds for the quadratic assignment problem. In: Pardalos, P.M., Wolkowicz, H. (eds.) Quadratic Assignment and Related Problems, DIMACS 25 Series in Discrete Mathematics and Theoretical Computer Science, pp. 43\u201375 (1994)","DOI":"10.1090\/dimacs\/016\/02"},{"key":"12_CR2","doi-asserted-by":"crossref","first-page":"1274","DOI":"10.1287\/mnsc.32.10.1274","volume":"32","author":"W.P. Adams","year":"1986","unstructured":"Adams W.P., Sherali H.D.: A tight linearization and an algorithm for zero-one quadrtic programming problems. Manage. Sci. 32, 1274\u20131290 (1986)","journal-title":"Manage. Sci."},{"key":"12_CR3","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/PL00011402","volume":"80","author":"K.M. Anstreicher","year":"2001","unstructured":"Anstreicher K.M., Brixius N.W.: A new bound for the quadratic assignment problem based on convex quadratic programming. Math. Program. 80, 341\u2013357 (2001)","journal-title":"Math. Program."},{"key":"12_CR4","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s101070100255","volume":"91","author":"K.M. Anstreicher","year":"2002","unstructured":"Anstreicher K.M., Brixius N.W., Goux J.-P., Linderoth J.: Solving large quadratic assignment problems on computational grids. Math. Program. 91, 563\u2013588 (2002)","journal-title":"Math. Program."},{"issue":"6","key":"12_CR5","doi-asserted-by":"crossref","first-page":"2227","DOI":"10.1109\/TIT.2005.847750","volume":"51","author":"G. Ben-David","year":"2005","unstructured":"Ben-David G., Malah D.: Bounds on the performance of vector-quantizers under channel errors. IEEE Trans. Inf. Theory 51(6), 2227\u20132235 (2005)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"12_CR6","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1137\/040609574","volume":"16","author":"S. Burer","year":"2006","unstructured":"Burer S., Vandenbussche D.: Solving lift-and-project relaxations of binary integer programs. SIAM J. Optim. 16, 726\u2013750 (2006)","journal-title":"SIAM J. Optim."},{"key":"12_CR7","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1023\/A:1008293323270","volume":"10","author":"R.E. Burkard","year":"1997","unstructured":"Burkard R.E., Ela E., Karisch S.E., Rendl F.: QAPLIB-A quadratic assignment problem library. J. Glob. Optim. 10, 391\u2013403 (1997)","journal-title":"J. Glob. Optim."},{"key":"12_CR8","unstructured":"Ding, Y., Wolkowicz, H.: A matrix-lifting semidefinite relaxation for the quadratic assignment problem. Technical report CORR 06-22, University of Waterloo, Ontario, Canada, October (2006)"},{"key":"12_CR9","doi-asserted-by":"crossref","unstructured":"Fiedler, M.: Algebraic connectivity of graphs. Czechoslovak Math. J. 23(98) (1973)","DOI":"10.21136\/CMJ.1973.101168"},{"key":"12_CR10","first-page":"57","volume":"25","author":"M. Fiedler","year":"1989","unstructured":"Fiedler M.: Laplacian of graphs and algebraic connectivity. Comb. Graph Theory 25, 57\u201370 (1989)","journal-title":"Comb. Graph Theory"},{"key":"12_CR11","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1137\/0110022","volume":"10","author":"P.C. Gilmore","year":"1962","unstructured":"Gilmore P.C.: Optimal and suboptimal algorithms for the quadratic assignment problem. SIAM J. Appl. Math. 10, 305\u2013313 (1962)","journal-title":"SIAM J. Appl. Math."},{"key":"12_CR12","volume-title":"Matix Computation","author":"G. Golub","year":"1996","unstructured":"Golub G., Loan C.V.: Matix Computation. John Hopkins University Press, Baltimore (1996)"},{"key":"12_CR13","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1287\/moor.17.3.727","volume":"17","author":"S.W. Hadley","year":"1992","unstructured":"Hadley S.W., Rendl F., Wolkowicz H.: A new lower bound via projection for the quadratic assignment problem. Math. Oper. Res. 17, 727\u2013739 (1992)","journal-title":"Math. Oper. Res."},{"key":"12_CR14","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1287\/opre.46.6.912","volume":"46","author":"P. Hahn","year":"1998","unstructured":"Hahn P., Grant T.: Lower bounds for the quadratic assignment problem based upon a dual formulation. Oper. Res. 46, 912\u2013922 (1998)","journal-title":"Oper. Res."},{"key":"12_CR15","first-page":"213","volume-title":"Design Automation of Digital Systems: Theory and Techniques, vol. 1","author":"M. Hannan","year":"1972","unstructured":"Hannan M., Kurtzberg J.M.: Placement techniques. In: Breuer, M.A. (eds) Design Automation of Digital Systems: Theory and Techniques, vol. 1, pp. 213\u2013282. Prentice-hall, Englewood Cliffs (1972)"},{"key":"12_CR16","first-page":"188","volume":"46","author":"C. Jansson","year":"2007","unstructured":"Jansson C., Keil C.: Rigorous error bounds for the optimal value in semidefinite programming. SIAM J. Numer. Anal. 46, 188\u2013200 (2007)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"12_CR17","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s10107-008-0246-5","volume":"122","author":"E. de Klerk","year":"2010","unstructured":"de Klerk E., Sotirov R.: Exploring group summetry in semidefinite programming relaxations of the quadratic assignment problem. Math. Program. 122(2), 225\u2013246 (2010)","journal-title":"Math. Program."},{"key":"12_CR18","doi-asserted-by":"crossref","first-page":"53","DOI":"10.2307\/1907742","volume":"25","author":"T. Koopmans","year":"1957","unstructured":"Koopmans T., Beckmann M.: Assignment problems and the location of economic activities. Econometrica 25, 53\u201376 (1957)","journal-title":"Econometrica"},{"key":"12_CR19","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1287\/mnsc.9.4.586","volume":"9","author":"E. Lawler","year":"1963","unstructured":"Lawler E.: The quadratic assignment problem. Manage. Sci. 9, 586\u2013599 (1963)","journal-title":"Manage. Sci."},{"issue":"2","key":"12_CR20","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1016\/j.ejor.2005.09.032","volume":"176","author":"E.M. Loiola","year":"2007","unstructured":"Loiola E.M., Maiade Abreu N.M., Boaventura-Netto P.O., Hahn P., Querido T.: A survey for the quadratic assignment problem. Eur. J. Oper. Res. 176(2), 657\u2013690 (2007)","journal-title":"Eur. J. Oper. Res."},{"key":"12_CR21","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534891.001.0001","volume-title":"Symmetric Functions and Hall Polynomials","author":"I.G. Macdonald","year":"1995","unstructured":"Macdonald I.G.: Symmetric Functions and Hall Polynomials. The Clarendon Press, Oxford University Press, New York (1995)"},{"key":"12_CR22","unstructured":"Mittelmann, H., Peng, J., Wu, X.: Graph modeling for quadratic assignment problem associated with the hypercube. Technical Report. University of Illinois at Urbana-Champaign. http:\/\/www.optimization-online.org\/DB_HTML\/2007\/06\/1674.html (2007)"},{"key":"12_CR23","unstructured":"Mittelmann, H., Peng, J.: Estimating bounds for quadratic assignment problems associated with hamming and manhattan distance matrices based on semidefinite programming. Technical Report. University of Illinois at Urbana-Champaign. http:\/\/www.optimization-online.org\/DB_HTML\/2008\/05\/1980.html (2008)"},{"key":"12_CR24","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1287\/opre.16.1.150","volume":"16","author":"C.E. Nugent","year":"1968","unstructured":"Nugent C.E., Vollman T.E., Ruml J.: An experimental comparison of techniques for the assignment of facilities to locations. Oper. Res. 16, 150\u2013173 (1968)","journal-title":"Oper. Res."},{"issue":"2\/3\/4","key":"12_CR25","doi-asserted-by":"crossref","first-page":"804","DOI":"10.1109\/26.380112","volume":"43","author":"L.C. Potter","year":"1995","unstructured":"Potter L.C., Chiang D.M.: Minimax nonredundant channel coding. IEEE Trans. Commun. 43(2\/3\/4), 804\u2013811 (1995)","journal-title":"IEEE Trans. Commun."},{"issue":"2\u20133","key":"12_CR26","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1007\/s10107-006-0038-8","volume":"109","author":"F. Rendl","year":"2007","unstructured":"Rendl F., Sotirov R.: Bounds for the quadrtic assignment problem using bundle method. Math. Program. Series B 109(2\u20133), 505\u2013524 (2007)","journal-title":"Math. Program. Series B"},{"issue":"1","key":"12_CR27","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/BF01585694","volume":"53","author":"F. Rendl","year":"1992","unstructured":"Rendl F., Wolkowicz H.: Applications of pasrametric programming and eigenvalue maximization to the quadratic assignment problem. Math. Program. Series A 53(1), 63\u201378 (1992)","journal-title":"Math. Program. Series A"},{"key":"12_CR28","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0966-8349(95)00008-6","volume":"3","author":"E.D. Taillard","year":"1995","unstructured":"Taillard E.D.: Comparison of iterative searches for the quadratic assingnment problem. Location Sci. 3, 87\u2013105 (1995)","journal-title":"Location Sci."},{"key":"12_CR29","unstructured":"Toh, K.C.: Private communication (2009)"},{"key":"12_CR30","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1023\/A:1009795911987","volume":"2","author":"Q. Zhao","year":"1998","unstructured":"Zhao Q., Karisch S.E., Rendl F., Wolkowicz H.: Semidefinite programming relaxations for the quadratic assignment problem. J. Comb. Optim. 2, 71\u2013109 (1998)","journal-title":"J. Comb. Optim."}],"container-title":["Mathematical Programming Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-010-0012-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12532-010-0012-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-010-0012-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,24]],"date-time":"2024-03-24T07:20:23Z","timestamp":1711264823000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12532-010-0012-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2,23]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["12"],"URL":"https:\/\/doi.org\/10.1007\/s12532-010-0012-6","relation":{},"ISSN":["1867-2949","1867-2957"],"issn-type":[{"value":"1867-2949","type":"print"},{"value":"1867-2957","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,2,23]]}}}