An Approximation Algorithm for Random Generation of Capacities

Pub Date : 2022-06-09 DOI:10.48550/arXiv.2206.04774
M. Grabisch, C. Labreuche, Peiqi Sun
{"title":"An Approximation Algorithm for Random Generation of Capacities","authors":"M. Grabisch, C. Labreuche, Peiqi Sun","doi":"10.48550/arXiv.2206.04774","DOIUrl":null,"url":null,"abstract":"Capacities on a finite set are sets functions vanishing on the empty set and being monotonic w.r.t. inclusion. Since the set of capacities is an order polytope, the problem of randomly generating capacities amounts to generating all linear extensions of the Boolean lattice. This problem is known to be intractable even as soon as $$n>5$$ n > 5 , therefore approximate methods have been proposed, most notably one based on Markov chains. Although quite accurate, this method is time consuming. In this paper, we propose the 2-layer approximation method, which generates a subset of linear extensions, eliminating those with very low probability. We show that our method has similar performance compared to the Markov chain but is much less time consuming.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.48550/arXiv.2206.04774","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1

Abstract

Capacities on a finite set are sets functions vanishing on the empty set and being monotonic w.r.t. inclusion. Since the set of capacities is an order polytope, the problem of randomly generating capacities amounts to generating all linear extensions of the Boolean lattice. This problem is known to be intractable even as soon as $$n>5$$ n > 5 , therefore approximate methods have been proposed, most notably one based on Markov chains. Although quite accurate, this method is time consuming. In this paper, we propose the 2-layer approximation method, which generates a subset of linear extensions, eliminating those with very low probability. We show that our method has similar performance compared to the Markov chain but is much less time consuming.
分享
查看原文
容量随机生成的一种近似算法
有限集上的容量是在空集上消失的集函数,并且是单调的。由于容量集是阶多面体,因此随机生成容量的问题相当于生成布尔格的所有线性扩展。众所周知,即使$$n>5$$n>5,这个问题也很难解决,因此已经提出了近似方法,最显著的是基于马尔可夫链的方法。虽然这种方法很准确,但很耗时。在本文中,我们提出了两层近似方法,该方法生成线性扩展的子集,消除了那些概率很低的线性扩展。我们表明,与马尔可夫链相比,我们的方法具有类似的性能,但耗时要少得多。
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 求助全文
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信