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ACM"],"published-print":{"date-parts":[[2016,3,30]]},"abstract":"<jats:p>We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a decreased cost.<\/jats:p>\n          <jats:p>\n            For the TSP on graphic metrics (graph-TSP), we show that the approach gives a 1.461-approximation algorithm with respect to the Held-Karp lower bound. For graph-TSP restricted either to half-integral solutions to the Held-Karp relaxation or to a class of graphs that contains subcubic and claw-free graphs, we show that the integrality gap of the Held-Karp relaxation matches the conjectured ratio 4\/3. The framework also allows for generalizations in a natural way and leads to analogous results for the\n            <jats:italic>s<\/jats:italic>\n            ,\n            <jats:italic>t<\/jats:italic>\n            -path traveling salesman problem on graphic metrics where the start and end vertices are prespecified.\n          <\/jats:p>","DOI":"10.1145\/2739008","type":"journal-article","created":{"date-parts":[[2016,2,22]],"date-time":"2016-02-22T13:07:16Z","timestamp":1456146436000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":35,"title":["Removing and Adding Edges for the Traveling Salesman Problem"],"prefix":"10.1145","volume":"63","author":[{"given":"Tobias","family":"M\u00f6mke","sequence":"first","affiliation":[{"name":"Saarland University, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ola","family":"Svensson","sequence":"additional","affiliation":[{"name":"EPFL, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2016,2,12]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2213977.2214055"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/290179.290180"},{"key":"e_1_2_1_3_1","volume-title":"Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA\u201998)","author":"Arora S."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480102409619"},{"key":"e_1_2_1_5_1","volume-title":"Integer Programming and Combinatorial Optimization. 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X.","year":"1995","journal-title":"Mathematics and Statistics"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580607"},{"key":"e_1_2_1_15_1","volume-title":"Proceedings of the 18th Conference on Integer Programming and Combinatorial Optimization (IPCO'16)","author":"Gottschalk C."},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the 36th Annual Symposium on Foundations of Computer Science (FOCS\u201995)","author":"Grigni M."},{"key":"e_1_2_1_17_1","volume-title":"Geometric Algorithms and Combinatorial Optimization. Algorithms and Combinatorics Series","volume":"2","author":"Gr\u00f6tschel M."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.18.6.1138"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6377(91)90016-I"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0118(200104)36:4%26lt;%26gt;1.0.CO;2-O"},{"key":"e_1_2_1_21_1","unstructured":"M. Karpinski M. Lampis and R. Schmied. 2013. New inapproximability bounds for TSP. CoRR abs\/1303.6437. http:\/\/arxiv.org\/abs\/1303.6437.  M. Karpinski M. Lampis and R. Schmied. 2013. New inapproximability bounds for TSP. 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