{"title":"A Nearly Optimal Deterministic Algorithm for Online Transportation Problem","authors":"Tsubasa Harada, Toshiya Itoh","doi":"arxiv-2406.03778","DOIUrl":null,"url":null,"abstract":"We propose a new deterministic algorithm called Subtree-Decomposition for the\nonline transportation problem and show that the algorithm is\n$(8m-5)$-competitive, where $m$ is the number of server sites. It has long been known that the competitive ratio of any deterministic\nalgorithm is lower bounded by $2m-1$ for this problem. On the other hand, the\nconjecture proposed by Kalyanasundaram and Pruhs in 1998 asking whether a\ndeterministic $(2m-1)$-competitive algorithm exists for the online\ntransportation problem has remained open for over two decades. The upper bound on the competitive ratio, $8m-5$, which is the result of this\npaper, is the first to come close to this conjecture, and is the best possible\nwithin a constant factor.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.03778","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a new deterministic algorithm called Subtree-Decomposition for the
online transportation problem and show that the algorithm is
$(8m-5)$-competitive, where $m$ is the number of server sites. It has long been known that the competitive ratio of any deterministic
algorithm is lower bounded by $2m-1$ for this problem. On the other hand, the
conjecture proposed by Kalyanasundaram and Pruhs in 1998 asking whether a
deterministic $(2m-1)$-competitive algorithm exists for the online
transportation problem has remained open for over two decades. The upper bound on the competitive ratio, $8m-5$, which is the result of this
paper, is the first to come close to this conjecture, and is the best possible
within a constant factor.