{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T08:29:04Z","timestamp":1750235344367,"version":"3.37.3"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,1,27]],"date-time":"2018-01-27T00:00:00Z","timestamp":1517011200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11501412"],"award-info":[{"award-number":["11501412"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Paul and Heidi Brown Preeminent Professorship at ISE, University of Florida"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11531014","61222201"],"award-info":[{"award-number":["11531014","61222201"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11531011"],"award-info":[{"award-number":["11531011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2018,5]]},"DOI":"10.1007\/s10107-018-1242-z","type":"journal-article","created":{"date-parts":[[2018,1,27]],"date-time":"2018-01-27T01:30:23Z","timestamp":1517016623000},"page":"255-275","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Solving the degree-concentrated fault-tolerant spanning subgraph problem by DC programming"],"prefix":"10.1007","volume":"169","author":[{"given":"Chenchen","family":"Wu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yishui","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zaixin","family":"Lu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Panos M.","family":"Pardalos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dachuan","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ding-Zhu","family":"Du","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,1,27]]},"reference":[{"key":"1242_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5","volume-title":"Graph Theory","author":"JA Bondy","year":"2008","unstructured":"Bondy, J.A., Murty, U.S.R.: Graph Theory. Springer, New York (2008)"},{"key":"1242_CR2","doi-asserted-by":"crossref","unstructured":"Boros, E., Borys, K., Elbassioni, K., Gurvich, V., Makino, K., Rudolf, G.: Generating minimal \n                    \n                      \n                    \n                    $$k$$\n                    \n                      \n                        k\n                      \n                    \n                  -vertex connected spanning subgraphs. In: Proceedings of the 13th International Computing and Combinatorics Conference, pp. 222\u2013231 (2007)","DOI":"10.1007\/978-3-540-73545-8_23"},{"issue":"1","key":"1242_CR3","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1145\/2432622.2432628","volume":"60","author":"J Byrka","year":"2013","unstructured":"Byrka, J., Grandoni, F., Rothvoss, T., Sanit\u00e1, L.: Steiner tree approximation via iterative randomized rounding. J. ACM 60(1), 6 (2013)","journal-title":"J. ACM"},{"key":"1242_CR4","doi-asserted-by":"crossref","unstructured":"Chakraborty, T., Chuzhoy, J., Khanna, S.: Network design for vertex connectivity. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 167\u2013176 (2008)","DOI":"10.1145\/1374376.1374403"},{"key":"1242_CR5","doi-asserted-by":"crossref","unstructured":"Cornaz, D., Magnouche, Y.: On minimal two-edge-connected graphs. In: Proceedings of 2014 International Conference on Control, Decision and Information Technologies, pp. 251\u2013256 (2014)","DOI":"10.1109\/CoDIT.2014.6996902"},{"key":"1242_CR6","volume-title":"The Combinatorics of Network Reliability","author":"CJ Coulbourn","year":"1987","unstructured":"Coulbourn, C.J.: The Combinatorics of Network Reliability. Oxford University Press, Oxford (1987)"},{"key":"1242_CR7","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1109\/TNET.2011.2170849","volume":"20","author":"TN Dinh","year":"2011","unstructured":"Dinh, T.N., Xuan, Y., Thai, M.T., Pardalos, P.M., Znati, T.: On new approaches of assessing network vulnerability: hardness and approximation. IEEE ACM Trans. Netw. 20, 609\u2013619 (2011)","journal-title":"IEEE ACM Trans. Netw."},{"key":"1242_CR8","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1007\/s101070050040","volume":"84","author":"A Frank","year":"1999","unstructured":"Frank, A.: Increasing the rooted-connectivity of a digraph by one. Math. Program. Ser. B 84, 565\u2013576 (1999)","journal-title":"Math. Program. Ser. B"},{"key":"1242_CR9","volume-title":"Computers and Intractability\u2014A Guide to the Theory of NP-Completeness","author":"MR Garey","year":"1979","unstructured":"Garey, M.R., Johnson, D.S.: Computers and Intractability\u2014A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)"},{"key":"1242_CR10","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1145\/227683.227684","volume":"42","author":"MX Goemans","year":"1995","unstructured":"Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42, 1115\u20131145 (1995)","journal-title":"J. ACM"},{"key":"1242_CR11","first-page":"236","volume-title":"Approximation Algorithms for NP-Hard Problems","author":"S Khuller","year":"1997","unstructured":"Khuller, S.: Approximation algorithms for finding highly connected subgraphs. In: Hochbaum, D.S. (ed.) Approximation Algorithms for NP-Hard Problems, pp. 236\u2013265. PWS Publishing Company, Boston, MA (1997)"},{"key":"1242_CR12","unstructured":"Kobayashi, Y.: The complexity of maximizing the difference of two matorid rank functions. METR2014-42, University of Tokyo (2014)"},{"key":"1242_CR13","volume-title":"Handbook on Approximation Algorithms and Metaheuristics","author":"G Kortsarz","year":"2007","unstructured":"Kortsarz, G., Nutov, Z.: Chapter 58: Approximating minimum cost connectivity problems. In: Gonzalez, T.F. (ed.) Handbook on Approximation Algorithms and Metaheuristics. Chapman Hall, Santa Barbara (2007)"},{"key":"1242_CR14","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s101070050003","volume":"87","author":"HA Thi Le","year":"2000","unstructured":"Le Thi, H.A.: An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints. Math. Program. Ser. A 87, 401\u2013426 (2000)","journal-title":"Math. Program. Ser. A"},{"key":"1242_CR15","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1023\/A:1008288411710","volume":"11","author":"HA Thi Le","year":"1997","unstructured":"Le Thi, H.A., Pham Dinh, T.: Solving a class of linearly constrained indefinite quadratic problems by D.C. algorithms. J. Glob. Optim. 11, 253\u2013285 (1997)","journal-title":"J. Glob. Optim."},{"key":"1242_CR16","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s10479-004-5022-1","volume":"133","author":"HA Thi Le","year":"2005","unstructured":"Le Thi, H.A., Pham Dinh, T.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133, 23\u201346 (2005)","journal-title":"Ann. Oper. Res."},{"key":"1242_CR17","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1007\/s10898-010-9573-1","volume":"49","author":"HA Thi Le","year":"2011","unstructured":"Le Thi, H.A., Pham Dinh, T., Yen, N.D.: Properties of two DC algorithms in quadratic programming. J. Glob. Optim. 49, 481\u2013495 (2011)","journal-title":"J. Glob. Optim."},{"key":"1242_CR18","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1007\/s10898-011-9765-3","volume":"52","author":"HA Thi Le","year":"2012","unstructured":"Le Thi, H.A., Pham Dinh, T., Ngai, H.V.: Exact penalty and error bounds in DC programming. J. Glob. Optim. 52, 509\u2013535 (2012)","journal-title":"J. Glob. Optim."},{"key":"1242_CR19","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/BF01585745","volume":"46","author":"JK Lenstra","year":"1990","unstructured":"Lenstra, J.K., Shmoys, D.B., Tardos, E.: Approximation algorithms for scheduling unrelated parallel machines. Math. Program. 46, 259\u2013271 (1990)","journal-title":"Math. Program."},{"key":"1242_CR20","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.ic.2012.01.007","volume":"222","author":"S Li","year":"2013","unstructured":"Li, S.: A 1.488 approximation algorithm for the uncapacitated facility location problem. Inf. Comput. 222, 45\u201358 (2013)","journal-title":"Inf. Comput."},{"key":"1242_CR21","doi-asserted-by":"crossref","unstructured":"Maehara, T., Marumo, N., Murota, K.: Continuous relaxation for discrete DC programming. In: Proceedings of the 3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences, pp. 181\u2013190 (2015)","DOI":"10.1007\/978-3-319-18161-5_16"},{"key":"1242_CR22","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1007\/s10107-014-0792-y","volume":"152","author":"T Maehara","year":"2015","unstructured":"Maehara, T., Murota, K.: A framework of discrete DC programming by discrete convex analysis. Math. Program. Ser. A 152, 435\u2013466 (2015)","journal-title":"Math. Program. Ser. A"},{"key":"1242_CR23","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718508","volume-title":"Discrete Convex Analysis","author":"K Murota","year":"2003","unstructured":"Murota, K.: Discrete Convex Analysis. Society for Industrial and Applied Mathematics, Philadelphia (2003)"},{"key":"1242_CR24","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/S0304-0208(08)72402-2","volume-title":"Fermat Days 85: Mathematics for Optimization, North-Holland Mathematics Studies","author":"T Pham Dinh","year":"1986","unstructured":"Pham Dinh, T., Souad, E.B.: Algorithms for solving a class of nonconvex optimization problems: methods of subgradients. In: Hiriart-Urruty, J.B. (ed.) Fermat Days 85: Mathematics for Optimization, North-Holland Mathematics Studies, vol. 129, pp. 249\u2013271. North-Holland, Amsterdam (1986)"},{"key":"1242_CR25","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/s10898-009-9507-y","volume":"48","author":"T Pham Dinh","year":"2010","unstructured":"Pham Dinh, T., Canh, N.N., Le Thi, H.A.: An efficient combined DCA and B&B using DC\/SDP relaxation for globally solving binary quadratic programs. J. Glob. Optim. 48, 595\u2013632 (2010)","journal-title":"J. Glob. Optim."},{"key":"1242_CR26","first-page":"73","volume":"255","author":"AS Strekalovsky","year":"2015","unstructured":"Strekalovsky, A.S.: On local search in D.C. optimization problems. Appl. Math. Comput. 255, 73\u201383 (2015)","journal-title":"Appl. Math. Comput."},{"key":"1242_CR27","volume-title":"Computer Networks","author":"AS Tanenbaum","year":"2010","unstructured":"Tanenbaum, A.S.: Computer Networks, 5th edn. Prentice Hall, Upper Saddle River (2010)","edition":"5"},{"issue":"1","key":"1242_CR28","first-page":"289","volume":"22","author":"PD Tao","year":"1997","unstructured":"Tao, P.D., An, L.T.E.: Convex analysis approach to D.C. programming: theory, algorithm and applications. Acta Math. Vietnam. 22(1), 289\u2013355 (1997)","journal-title":"Acta Math. Vietnam."},{"key":"1242_CR29","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1137\/0201010","volume":"1","author":"R Tarjan","year":"1972","unstructured":"Tarjan, R.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1, 146\u2013160 (1972)","journal-title":"SIAM J. Comput."},{"key":"1242_CR30","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511921735","volume-title":"The Design of Approximation Algorithms","author":"DP Williamson","year":"2011","unstructured":"Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms. Cambridge University Press, Cambridge (2011)"},{"key":"1242_CR31","volume-title":"Combinatorial Theory in Networks","author":"JM Xu","year":"2013","unstructured":"Xu, J.M.: Combinatorial Theory in Networks. Academic Press, Cambridge (2013)"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-018-1242-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-018-1242-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-018-1242-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,1,26]],"date-time":"2019-01-26T19:55:53Z","timestamp":1548532553000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-018-1242-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,27]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,5]]}},"alternative-id":["1242"],"URL":"https:\/\/doi.org\/10.1007\/s10107-018-1242-z","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"type":"print","value":"0025-5610"},{"type":"electronic","value":"1436-4646"}],"subject":[],"published":{"date-parts":[[2018,1,27]]},"assertion":[{"value":"28 August 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 January 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}