{"title":"基于图形度量的车辆路径控制","authors":"Tobias Mömke, Hang Zhou","doi":"10.48550/arXiv.2210.09806","DOIUrl":null,"url":null,"abstract":"We study the capacitated vehicle routing problem in graphic metrics (graphic CVRP). Our main contribution is a new lower bound on the cost of an optimal solution. For graphic metrics, this lower bound is tight and significantly stronger than the well-known bound for general metrics. The proof of the new lower bound is simple and combinatorial. Using this lower bound, we analyze the approximation ratio of the classical iterated tour partitioning algorithm combined with the TSP algorithms for graphic metrics of Christofides [1976], of M\\\"omke-Svensson [JACM 2016], and of Seb\\H{o}-Vygen [Combinatorica 2014]. In particular, we obtain a 1.95-approximation for the graphic CVRP.","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"88 1","pages":"114-123"},"PeriodicalIF":0.0000,"publicationDate":"2022-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Capacitated Vehicle Routing in Graphic Metrics\",\"authors\":\"Tobias Mömke, Hang Zhou\",\"doi\":\"10.48550/arXiv.2210.09806\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the capacitated vehicle routing problem in graphic metrics (graphic CVRP). Our main contribution is a new lower bound on the cost of an optimal solution. For graphic metrics, this lower bound is tight and significantly stronger than the well-known bound for general metrics. The proof of the new lower bound is simple and combinatorial. Using this lower bound, we analyze the approximation ratio of the classical iterated tour partitioning algorithm combined with the TSP algorithms for graphic metrics of Christofides [1976], of M\\\\\\\"omke-Svensson [JACM 2016], and of Seb\\\\H{o}-Vygen [Combinatorica 2014]. In particular, we obtain a 1.95-approximation for the graphic CVRP.\",\"PeriodicalId\":93491,\"journal\":{\"name\":\"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)\",\"volume\":\"88 1\",\"pages\":\"114-123\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2210.09806\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2210.09806","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study the capacitated vehicle routing problem in graphic metrics (graphic CVRP). Our main contribution is a new lower bound on the cost of an optimal solution. For graphic metrics, this lower bound is tight and significantly stronger than the well-known bound for general metrics. The proof of the new lower bound is simple and combinatorial. Using this lower bound, we analyze the approximation ratio of the classical iterated tour partitioning algorithm combined with the TSP algorithms for graphic metrics of Christofides [1976], of M\"omke-Svensson [JACM 2016], and of Seb\H{o}-Vygen [Combinatorica 2014]. In particular, we obtain a 1.95-approximation for the graphic CVRP.
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