{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:26:52Z","timestamp":1761596812807},"reference-count":15,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[1992,8,1]],"date-time":"1992-08-01T00:00:00Z","timestamp":712627200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Operations Research Letters"],"published-print":{"date-parts":[[1992,8]]},"DOI":"10.1016\/0167-6377(92)90068-e","type":"journal-article","created":{"date-parts":[[2003,6,30]],"date-time":"2003-06-30T18:40:45Z","timestamp":1056998445000},"page":"83-88","source":"Crossref","is-referenced-by-count":5,"title":["Analysis of the Held-Karp lower bound for the asymmetric TSP"],"prefix":"10.1016","volume":"12","author":[{"given":"David P","family":"Williamson","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0167-6377(92)90068-E_BIB1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/BF01584228","article-title":"A restricted Lagrangean approach to the traveling salesman problem","volume":"21","author":"Balas","year":"1981","journal-title":"Math. Programming"},{"key":"10.1016\/0167-6377(92)90068-E_BIB2","series-title":"The Traveling Salesman Problem","article-title":"Branch and bound methods","author":"Balas","year":"1985"},{"key":"10.1016\/0167-6377(92)90068-E_BIB3","article-title":"Worst case analysis of a new heuristic for the traveling salesman problem","author":"Christofides","year":"1976"},{"key":"10.1016\/0167-6377(92)90068-E_BIB4","series-title":"Combinatorial Optimization","article-title":"The travelling salesman problem","author":"Christofides","year":"1979"},{"key":"10.1016\/0167-6377(92)90068-E_BIB5","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/BF01584082","article-title":"Matroids and the greedy algorithm","volume":"1","author":"Edmonds","year":"1971","journal-title":"Math. Programming"},{"key":"10.1016\/0167-6377(92)90068-E_BIB6","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/S0167-5060(08)70459-X","article-title":"On connectivity properties of Eulerian digraphs","volume":"41","author":"Frank","year":"1989","journal-title":"Annals of Disc. Math."},{"key":"10.1016\/0167-6377(92)90068-E_BIB7","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1002\/net.3230120103","article-title":"On the worst-case performance of some algorithms for the asymmetric traveling salesman problem","volume":"12","author":"Frieze","year":"1982","journal-title":"Networks"},{"key":"10.1016\/0167-6377(92)90068-E_BIB8","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1007\/BFb0120690","article-title":"Lagrangean relaxation for integer programming","volume":"2","author":"Geoffrion","year":"1974","journal-title":"Math. Programming Study"},{"key":"10.1016\/0167-6377(92)90068-E_BIB9","article-title":"Survivable networks, linear programming relaxations and the parsimonious property","author":"Goemans","year":"1990"},{"key":"10.1016\/0167-6377(92)90068-E_BIB10","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1287\/moor.16.1.72","article-title":"Probabilistic analysis of the Held and Karp lower bound for the Euclidean traveling salesman problem","volume":"16","author":"Goemans","year":"1991","journal-title":"Math. Oper. Res."},{"key":"10.1016\/0167-6377(92)90068-E_BIB11","doi-asserted-by":"crossref","first-page":"1138","DOI":"10.1287\/opre.18.6.1138","article-title":"The traveling-salesman problem and minimum spanning trees","volume":"18","author":"Held","year":"1970","journal-title":"Oper. Res."},{"key":"10.1016\/0167-6377(92)90068-E_BIB12","unstructured":"D.S. Johnson, personal communication, 1989."},{"key":"10.1016\/0167-6377(92)90068-E_BIB13","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/BF01585735","article-title":"Minimum-weight two-connected spanning networks","volume":"46","author":"Monma","year":"1990","journal-title":"Math. Programming"},{"key":"10.1016\/0167-6377(92)90068-E_BIB14","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/0020-0190(90)90028-V","article-title":"Analyzing the Held-Karp TSP bound: A monotonicity property with application","volume":"35","author":"Shmoys","year":"1990","journal-title":"Inform. Process. Lett."},{"key":"10.1016\/0167-6377(92)90068-E_BIB15","article-title":"Analysis of the Held-Karp heuristic for the traveling salesman problem","author":"Williamson","year":"1990"}],"container-title":["Operations Research Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:016763779290068E?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:016763779290068E?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,18]],"date-time":"2019-03-18T09:50:39Z","timestamp":1552902639000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/016763779290068E"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,8]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1992,8]]}},"alternative-id":["016763779290068E"],"URL":"https:\/\/doi.org\/10.1016\/0167-6377(92)90068-e","relation":{},"ISSN":["0167-6377"],"issn-type":[{"value":"0167-6377","type":"print"}],"subject":[],"published":{"date-parts":[[1992,8]]}}}