Adaptive stable marriage algorithms

ACM SE '10 Pub Date : 2010-04-15 DOI:10.1145/1900008.1900057
John Dabney, B. C. Dean
{"title":"Adaptive stable marriage algorithms","authors":"John Dabney, B. C. Dean","doi":"10.1145/1900008.1900057","DOIUrl":null,"url":null,"abstract":"Although it takes O(n2) worst-case time to solve a stable marriage problem instance with n men and n women, a trivial O(n) algorithm suffices if all men are known to have identical preference lists and all women also are known to have identical preference lists. Since real-world instances often involve men or women with similar but not necessarily identical preference lists, this motivates us to introduce the notion of an adaptive stable marriage algorithm --- an algorithm whose running time is of the form O(n + k), where k describes the aggregate amount of disagreement between the preference lists in our instance versus a pair of specified \"consensus\" preference lists, one for the men and one for women. The running time of an adaptive stable matching algorithm therefore gracefully scales from O(n2) in the worse case down to O(n) in the case where preference lists are all in close agreement. We show how the O(n+k) running time bound can be achieved if all women are known to have identical preference lists, leaving the case where both men and women can have non-identical but similar preference lists as an open question. We also show how this special case may serve as a good model for sports drafts.","PeriodicalId":333104,"journal":{"name":"ACM SE '10","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM SE '10","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1900008.1900057","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3

Abstract

Although it takes O(n2) worst-case time to solve a stable marriage problem instance with n men and n women, a trivial O(n) algorithm suffices if all men are known to have identical preference lists and all women also are known to have identical preference lists. Since real-world instances often involve men or women with similar but not necessarily identical preference lists, this motivates us to introduce the notion of an adaptive stable marriage algorithm --- an algorithm whose running time is of the form O(n + k), where k describes the aggregate amount of disagreement between the preference lists in our instance versus a pair of specified "consensus" preference lists, one for the men and one for women. The running time of an adaptive stable matching algorithm therefore gracefully scales from O(n2) in the worse case down to O(n) in the case where preference lists are all in close agreement. We show how the O(n+k) running time bound can be achieved if all women are known to have identical preference lists, leaving the case where both men and women can have non-identical but similar preference lists as an open question. We also show how this special case may serve as a good model for sports drafts.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
自适应稳定婚姻算法
虽然解决一个有n个男人和n个女人的稳定婚姻问题实例需要O(n2)的最坏情况时间,但如果已知所有的男人有相同的偏好列表,并且已知所有的女人也有相同的偏好列表,那么一个平凡的O(n)算法就足够了。由于现实世界的实例通常涉及具有相似但不一定相同偏好列表的男性或女性,这促使我们引入自适应稳定婚姻算法的概念——该算法的运行时间为O(n + k),其中k描述了我们实例中的偏好列表与一对指定的“共识”偏好列表之间的分歧总量,一个用于男性,一个用于女性。因此,自适应稳定匹配算法的运行时间从最坏情况下的O(n2)优雅地扩展到偏好列表都非常一致的情况下的O(n)。我们展示了如果已知所有女性都有相同的偏好列表,如何实现O(n+k)的运行时间限制,留下男性和女性都有不相同但相似的偏好列表的情况作为一个开放问题。我们还展示了这种特殊情况如何可以作为体育选秀的一个很好的模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Teaching software engineering using open source software Dynamic ontology version control Visualization of the CreSIS Greenland data sets Java nano patterns: a set of reusable objects Towards power efficient consolidation and distribution of virtual machines
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1