{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T14:40:03Z","timestamp":1723128003576},"reference-count":0,"publisher":"Informa UK Limited","issue":"2","license":[{"start":{"date-parts":[[1998,1,1]],"date-time":"1998-01-01T00:00:00Z","timestamp":883612800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics and Decision Sciences"],"published-print":{"date-parts":[[1998,1,1]]},"abstract":"<jats:p>Two instances of the traveling salesman problem, on the same node set <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mo>{<\/mml:mo><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><mml:mn>2<\/mml:mn><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:mi>n<\/mml:mi><\/mml:mrow><mml:mo>}<\/mml:mo><\/mml:mrow><\/mml:math>\nbut with different cost matrices <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>C<\/mml:mi><\/mml:math>\n and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>C<\/mml:mi><mml:mo>\u2032<\/mml:mo><\/mml:msup><\/mml:math>\n, are equivalent iff there exist <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mo>{<\/mml:mo><mml:mrow><mml:msub><mml:mi>a<\/mml:mi><mml:mi>i<\/mml:mi><\/mml:msub><mml:mo>,<\/mml:mo><mml:msub><mml:mi>b<\/mml:mi><mml:mi>i<\/mml:mi><\/mml:msub><mml:mo>:<\/mml:mo><mml:mtext>\u2009<\/mml:mtext><mml:mi>i<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:mtext>\u2009<\/mml:mtext><mml:mi>n<\/mml:mi><\/mml:mrow><mml:mo>}<\/mml:mo><\/mml:mrow><\/mml:math> such\nthat for any <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>1<\/mml:mn><mml:mo>\u2264<\/mml:mo><mml:mi>i<\/mml:mi><mml:mo>, <\/mml:mo><mml:mi>j<\/mml:mi><mml:mo>\u2264<\/mml:mo><mml:mi>n<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>i<\/mml:mi><mml:mo>\u2260<\/mml:mo><mml:mi>j<\/mml:mi><mml:mo>,<\/mml:mo><mml:msup><mml:mi>C<\/mml:mi><mml:mo>\u2032<\/mml:mo><\/mml:msup><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:mi>i<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>j<\/mml:mi><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mo>=<\/mml:mo><mml:mi>C<\/mml:mi><mml:mrow><mml:mo>(<\/mml:mo><mml:mrow><mml:mi>i<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>j<\/mml:mi><\/mml:mrow><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mo>+<\/mml:mo><mml:msub><mml:mi>a<\/mml:mi><mml:mi>i<\/mml:mi><\/mml:msub><mml:mo>+<\/mml:mo><mml:msub><mml:mi>b<\/mml:mi><mml:mi>j<\/mml:mi><\/mml:msub><\/mml:math> [7]. One of the well-solved special cases\nof the traveling salesman problem (TSP) is the convex-hull-and-line TSP. We extend the solution\nscheme for this class of TSP given in [9] to a more general class which is closed with respect to\nthe above equivalence relation. The cost matrix in our general class is a certain composition of\nKalmanson matrices. This gives a new, non-trivial solvable case of TSP.<\/jats:p>","DOI":"10.1155\/s1173912698000108","type":"journal-article","created":{"date-parts":[[2007,3,8]],"date-time":"2007-03-08T07:44:28Z","timestamp":1173339868000},"page":"177-191","source":"Crossref","is-referenced-by-count":1,"title":["A generalization of the convex-hull-and-line traveling salesman problem"],"prefix":"10.1080","volume":"2","author":[{"given":"Md. Fazle","family":"Baki","sequence":"first","affiliation":[{"name":"Department of Management Sciences, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. N.","family":"Kabadi","sequence":"additional","affiliation":[{"name":"Faculty of Administration, University of New Brunswick, PO Box 4400, Fredericton E3B 5A3, New Brunswick, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"301","container-title":["Journal of Applied Mathematics and Decision Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/1998\/847641.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/1998\/847641.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T14:22:56Z","timestamp":1723126976000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ads\/1998\/847641\/abs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1,1]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1998,1,1]]}},"alternative-id":["847641"],"URL":"https:\/\/doi.org\/10.1155\/s1173912698000108","relation":{},"ISSN":["1173-9126"],"issn-type":[{"type":"print","value":"1173-9126"}],"subject":[],"published":{"date-parts":[[1998,1,1]]}}}