{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T23:44:48Z","timestamp":1768088688112,"version":"3.49.0"},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2008,2,1]],"date-time":"2008-02-01T00:00:00Z","timestamp":1201824000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2008,2]]},"abstract":"<jats:p>The Symmetric Circulant Travelling Salesman Problem asks for the minimum cost tour in a symmetric circulant matrix. The computational complexity of this problem is not known \u2013 only upper and lower bounds have been determined. This paper provides a characterisation of the two-stripe case. Instances where the minimum cost of a tour is equal to either the upper or lower bound are recognised. A new construction providing a tour is proposed for the remaining instances, and this leads to a new upper bound that is closer than the previous one.<\/jats:p>","DOI":"10.1017\/s0960129508006609","type":"journal-article","created":{"date-parts":[[2008,3,5]],"date-time":"2008-03-05T14:42:14Z","timestamp":1204728134000},"page":"165-175","source":"Crossref","is-referenced-by-count":7,"title":["The Travelling Salesman Problem in symmetric circulant matrices with two stripes"],"prefix":"10.1017","volume":"18","author":[{"given":"IVAN","family":"GERACE","sequence":"first","affiliation":[]},{"given":"FEDERICO","family":"GRECO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,2,1]]},"reference":[{"key":"S0960129508006609_ref7","unstructured":"Gerace I. and Irving R. W. (1998) The traveling salesman problem in circulant graphs. Technical Report of Department of Computing Science, University of Glasgow, U.K., TR-1998-15."},{"key":"S0960129508006609_ref10","unstructured":"Van Der Veen J. A. A. (1992) Solvable Cases of the Traveling Salesman Problem with Various Objective Functions, Ph.D. Thesis, University of Groningen, Holland."},{"key":"S0960129508006609_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(96)00298-1"},{"key":"S0960129508006609_ref1","first-page":"213","article-title":"Hamiltonian Circuits in Sparse Circulant Digraphs","volume":"76","author":"Bogdanowicz","year":"2005","journal-title":"Ars Combinatoria"},{"key":"S0960129508006609_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(91)90024-Q"},{"key":"S0960129508006609_ref4","volume-title":"Circulant Matrices","author":"Davis","year":"1979"},{"key":"S0960129508006609_ref5","doi-asserted-by":"publisher","DOI":"10.1287\/opre.25.5.741"},{"key":"S0960129508006609_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(98)10126-X"},{"key":"S0960129508006609_ref6","unstructured":"Gerace I. and Greco F. (2006) Bounds for the Symmetric Circulant Traveling Salesman Problem. Rapporto Tecnico del Dip. di Matematica e Informatica dell'Universit\u00e0 di Perugia, Italy, TR 4-2006."},{"key":"S0960129508006609_ref9","doi-asserted-by":"publisher","DOI":"10.1112\/S0024611503014412"},{"key":"S0960129508006609_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(01)00136-4"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129508006609","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T19:28:46Z","timestamp":1554146926000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129508006609\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,2]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["S0960129508006609"],"URL":"https:\/\/doi.org\/10.1017\/s0960129508006609","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,2]]}}}