Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms最新文献

筛选

英文中文

An Optimal Truthful Mechanism for the Online Weighted Bipartite Matching Problem 在线加权二部匹配问题的最优真实机制

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms Pub Date : 2019-01-01 DOI: 10.1137/1.9781611975482.120

Rebecca Reiffenhauser

{"title":"An Optimal Truthful Mechanism for the Online Weighted Bipartite Matching Problem","authors":"Rebecca Reiffenhauser","doi":"10.1137/1.9781611975482.120","DOIUrl":"https://doi.org/10.1137/1.9781611975482.120","url":null,"abstract":"In the weighted bipartite matching problem, the goal is to find a maximum-weight matching in a bipartite graph with nonnegative edge weights. We consider its online version where the first vertex set is known beforehand, but vertices of the second set appear one after another. Vertices of the first set are interpreted as items, and those of the second set as bidders. On arrival, each bidder vertex reveals the weights of all adjacent edges and the algorithm has to decide which of those to add to the matching. We introduce an optimal, e-competitive truthful mechanism under the assumption that bidders arrive in random order (secretary model). It has been shown that the upper and lower bound of e for the original secretary problem extends to various other problems even with rich combinatorial structure, one of them being weighted bipartite matching. But truthful mechanisms so far fall short of reasonable competitive ratios once respective algorithms deviate from the original, simple threshold form. The best known mechanism for weighted bipartite matching by Krysta and Vöcking [19] offers only a ratio logarithmic in the number of online vertices. We close this gap, showing that truthfulness does not impose any additional bounds. The proof technique is new in this surrounding, and based on the observation of an independency inherent to the mechanism. The insights provided hereby are interesting in their own right and appear to offer promising tools for other problems, with or without truthfulness.","PeriodicalId":300081,"journal":{"name":"Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121425009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 14

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms 第三十届ACM-SIAM离散算法研讨会论文集

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms Pub Date : 1900-01-01 DOI: 10.5555/3310435

M. Crochemore, G. M. Landau, Michal Ziv-Ukelson

引用次数: 11