扩张空间与(p，δ) -双曲空间中的交通拥堵

Q3 Mathematics

Internet Mathematics Pub Date : 2015-03-04 DOI:10.1080/15427951.2014.884513

Shi Li, G. Tucci

{"title":"扩张空间与(p，δ) -双曲空间中的交通拥堵","authors":"Shi Li, G. Tucci","doi":"10.1080/15427951.2014.884513","DOIUrl":null,"url":null,"abstract":"In this article we define the notion of (p, δ)–Gromov hyperbolic space where we relax the Gromov slimness condition to allow that not all, but a positive fraction of all triangles, are δ–slim. Furthermore, we study their traffic congestion under geodesic routing. We also construct a constant degree family of expanders with congestion Θ(n2) in contrast to random regular graphs that have congestion O(nlog3(n)).","PeriodicalId":38105,"journal":{"name":"Internet Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2015-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/15427951.2014.884513","citationCount":"9","resultStr":"{\"title\":\"Traffic Congestion in Expanders and (p,δ)–Hyperbolic Spaces\",\"authors\":\"Shi Li, G. Tucci\",\"doi\":\"10.1080/15427951.2014.884513\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article we define the notion of (p, δ)–Gromov hyperbolic space where we relax the Gromov slimness condition to allow that not all, but a positive fraction of all triangles, are δ–slim. Furthermore, we study their traffic congestion under geodesic routing. We also construct a constant degree family of expanders with congestion Θ(n2) in contrast to random regular graphs that have congestion O(nlog3(n)).\",\"PeriodicalId\":38105,\"journal\":{\"name\":\"Internet Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-03-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/15427951.2014.884513\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Internet Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/15427951.2014.884513\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Internet Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/15427951.2014.884513","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 9

摘要

在这篇文章中，我们定义了(p， δ) -Gromov双曲空间的概念，我们放宽了Gromov细度条件，以允许不是所有三角形，而是所有三角形的一个正分数，是δ细度的。此外，我们还研究了它们在测地线路由下的交通拥堵问题。我们还构造了一个具有拥塞Θ(n2)的常数度扩展器族，与具有拥塞O(nlog3(n))的随机正则图形成对比。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Traffic Congestion in Expanders and (p,δ)–Hyperbolic Spaces

In this article we define the notion of (p, δ)–Gromov hyperbolic space where we relax the Gromov slimness condition to allow that not all, but a positive fraction of all triangles, are δ–slim. Furthermore, we study their traffic congestion under geodesic routing. We also construct a constant degree family of expanders with congestion Θ(n2) in contrast to random regular graphs that have congestion O(nlog3(n)).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Internet Mathematics Mathematics-Applied Mathematics

自引率

0.00%

发文量