{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T23:53:44Z","timestamp":1775001224186,"version":"3.50.1"},"publisher-location":"Cham","reference-count":23,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032157904","type":"print"},{"value":"9783032157911","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\/978-3-032-15791-1_13","type":"book-chapter","created":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T22:54:37Z","timestamp":1774997677000},"page":"185-198","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Implementation and\u00a0Numerical Evaluation of\u00a0Traub and\u00a0Vygen Algorithm for\u00a0the\u00a0Subtour Cover Problem"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7508-4833","authenticated-orcid":false,"given":"Ksenia","family":"Rizhenko","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9276-4128","authenticated-orcid":false,"given":"Daniil","family":"Khachai","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2122-0446","authenticated-orcid":false,"given":"Katherine","family":"Neznakhina","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3555-0080","authenticated-orcid":false,"given":"Michael","family":"Khachay","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,4,1]]},"reference":[{"key":"13_CR1","unstructured":"Cirasella ATSP instances. https:\/\/sites.google.com\/site\/atspinstances\/cirasella-instances"},{"key":"13_CR2","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1145\/290179.290180","volume":"45","author":"S Arora","year":"1998","unstructured":"Arora, S.: Polynomial time approximation schemes for euclidean traveling salesman and other geometric problems. J. ACM 45, 753\u2013782 (1998)","journal-title":"J. ACM"},{"issue":"4","key":"13_CR3","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1287\/opre.2017.1603","volume":"65","author":"A Asadpour","year":"2017","unstructured":"Asadpour, A., Goemans, M.X., M\u0105dry, A., Gharan, S.O., Saberi, A.: An O(log n\/log log n)-approximation algorithm for the Asymmetric Traveling Salesman Problem. Oper. Res. 65(4), 1043\u20131061 (2017). https:\/\/doi.org\/10.1287\/opre.2017.1603","journal-title":"Oper. Res."},{"issue":"4","key":"13_CR4","doi-asserted-by":"publisher","first-page":"1563","DOI":"10.1137\/130913328","volume":"45","author":"Y Bartal","year":"2016","unstructured":"Bartal, Y., Gottlieb, L.A., Krauthgamer, R.: The Traveling Salesman Problem: Low-dimensionality implies a polynomial time approximation scheme. SIAM J. Comput. 45(4), 1563\u20131581 (2016). https:\/\/doi.org\/10.1137\/130913328","journal-title":"SIAM J. Comput."},{"key":"13_CR5","unstructured":"Christofides, N.: Worst-case analysis of a new heuristic for the traveling salesman problem. In: Symposium on New Directions and Recent Results in Algorithms and Complexity, p.\u00a0441 (1975)"},{"issue":"4","key":"13_CR6","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1287\/opre.2.4.393","volume":"2","author":"G Dantzig","year":"1954","unstructured":"Dantzig, G., Fulkerson, R., Johnson, S.: Solution of a large-scale traveling-salesman problem. J. Oper. Res. Soc. Am. 2(4), 393\u2013410 (1954). https:\/\/doi.org\/10.1287\/opre.2.4.393","journal-title":"J. Oper. Res. Soc. Am."},{"issue":"1","key":"13_CR7","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1287\/mnsc.6.1.80","volume":"6","author":"GB Dantzig","year":"1959","unstructured":"Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manage. Sci. 6(1), 80\u201391 (1959)","journal-title":"Manage. Sci."},{"issue":"1","key":"13_CR8","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1002\/net.3230120103","volume":"12","author":"AM Frieze","year":"1982","unstructured":"Frieze, A.M., Galbiati, G., Maffioli, F.: On the worst-case performance of some algorithms for the asymmetric traveling salesman problem. Networks 12(1), 23\u201339 (1982). https:\/\/doi.org\/10.1002\/net.3230120103","journal-title":"Networks"},{"key":"13_CR9","unstructured":"Gallai, T.: Gr\u00e1fokkal kapcsolatos maximum\u2014minimum t\u00e9telek (ii. r\u00e9sz). A Magyar Tudomanyos Akademia Matematikai Es Fizikai Tudomanyok Osztalyanak Kozlemenyei 8, 1\u201340"},{"key":"13_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/b101971","volume-title":"The Traveling Salesman Problem and Its Variations","author":"G Gutin","year":"2007","unstructured":"Gutin, G., Punnen, A.P.: The Traveling Salesman Problem and Its Variations. Springer, US, Boston, MA (2007)"},{"key":"13_CR11","doi-asserted-by":"publisher","unstructured":"Hubert\u00a0Chan, T.H., Jiang, H., Jiang, S.H.C.: A unified PTAS for prize collecting TSP and Steiner tree problem in doubling metrics. ACM Trans. Algorithms 16(2), 1\u201323 (2020).https:\/\/doi.org\/10.1145\/3378571","DOI":"10.1145\/3378571"},{"key":"13_CR12","doi-asserted-by":"publisher","first-page":"S140","DOI":"10.1134\/S0081543822060128","volume":"319","author":"MY Khachay","year":"2022","unstructured":"Khachay, M.Y., Neznakhina, E., Ryzhenko, K.: Constant-factor approximation algorithms for a series of combinatorial routing problems based on the reduction to the Asymmetric Traveling Salesman Problem. Proc. Steklov Inst. Math. 319, S140\u2013S155 (2022). https:\/\/doi.org\/10.1134\/S0081543822060128","journal-title":"Proc. Steklov Inst. Math."},{"issue":"3","key":"13_CR13","doi-asserted-by":"publisher","first-page":"679","DOI":"10.1007\/s10898-020-00990-0","volume":"80","author":"M Khachay","year":"2021","unstructured":"Khachay, M., Ogorodnikov, Y., Khachay, D.: Efficient approximation of the metric CVRP in spaces of fixed doubling dimension. J. Global Optim. 80(3), 679\u2013710 (2021). https:\/\/doi.org\/10.1007\/s10898-020-00990-0","journal-title":"J. Global Optim."},{"key":"13_CR14","doi-asserted-by":"crossref","unstructured":"Mitchell, J.S.: Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric tsp, k-mst, and related problems. SIAM J. Comput. 28(4), 1298\u20131309 (1999). https:\/\/doi.org\/10.1137\/S0097539796309764","DOI":"10.1137\/S0097539796309764"},{"issue":"3","key":"13_CR15","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1134\/S1064562423701454","volume":"108","author":"E Neznakhina","year":"2023","unstructured":"Neznakhina, E., Ogorodnikov, Y.Y., Rizhenko, K., Khachay, M.Y.: Approximation algorithms with constant factors for a series of asymmetric routing problems. Dokl. Math. 108(3), 499\u2013505 (2023). https:\/\/doi.org\/10.1134\/S1064562423701454","journal-title":"Dokl. Math."},{"key":"13_CR16","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/0304-3975(77)90012-3","volume":"4","author":"C Papadimitriou","year":"1977","unstructured":"Papadimitriou, C.: Euclidean TSP is NP-complete. Theoret. Comput. Sci. 4, 237\u2013244 (1977)","journal-title":"Theoret. Comput. Sci."},{"key":"13_CR17","doi-asserted-by":"publisher","unstructured":"Rizhenko, K., Neznakhina, K., Khachay, M.: Fixed ratio polynomial time approximation algorithm for the prize-collecting asymmetric traveling salesman problem. Ural Math. J. 9(1), 135\u2013146 (2023). https:\/\/doi.org\/10.15826\/umj.2023.1.012","DOI":"10.15826\/umj.2023.1.012"},{"key":"13_CR18","volume-title":"Combinatorial Optimization - Polyhedra and Efficiency","author":"A Schrijver","year":"2003","unstructured":"Schrijver, A.: Combinatorial Optimization - Polyhedra and Efficiency. Springer, Berlin (2003)"},{"key":"13_CR19","first-page":"76","volume":"17","author":"A Serdyukov","year":"1978","unstructured":"Serdyukov, A.: On some extremal routes in graphs. Upravl. Sist. 17, 76\u201379 (1978)","journal-title":"Upravl. Sist."},{"key":"13_CR20","doi-asserted-by":"publisher","unstructured":"Svensson, O., Tarnawski, J., V\u00e9gh, L.A.: A constant-factor approximation algorithm for the asymmetric traveling salesman problem. In: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, pp. 204\u2013213. STOC 2018, Association for Computing Machinery, New York, NY, USA (2018). https:\/\/doi.org\/10.1145\/3188745.3188824","DOI":"10.1145\/3188745.3188824"},{"key":"13_CR21","doi-asserted-by":"publisher","unstructured":"Svensson, O., Tarnawski, J., V\u00e9gh, L.A.: A constant-factor approximation algorithm for the asymmetric traveling salesman problem. J. ACM 67(6) (2020). https:\/\/doi.org\/10.1145\/3424306","DOI":"10.1145\/3424306"},{"issue":"1","key":"13_CR22","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1137\/20M1339313","volume":"51","author":"V Traub","year":"2022","unstructured":"Traub, V., Vygen, J.: An improved approximation algorithm for the Asymmetric Traveling Salesman Problem. SIAM J. Comput. 51(1), 139\u2013173 (2022). https:\/\/doi.org\/10.1137\/20M1339313","journal-title":"SIAM J. Comput."},{"key":"13_CR23","doi-asserted-by":"publisher","DOI":"10.1017\/9781009445436","author":"V Traub","year":"2024","unstructured":"Traub, V., Vygen, J.: Approximation algorithms for traveling salesman problems. Camb. Univer. Press (2024). https:\/\/doi.org\/10.1017\/9781009445436","journal-title":"Camb. Univer. Press"}],"container-title":["Lecture Notes in Computer Science","Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-15791-1_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T22:54:39Z","timestamp":1774997679000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-15791-1_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032157904","9783032157911"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-15791-1_13","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":"1 April 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"OPTIMA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Optimization and Applications","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Petrovac","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Montenegro","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"optima2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/conf-optima.ru","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}