{"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":"11 1","pages":"134 - 142"},"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\":\"11 1\",\"pages\":\"134 - 142\"},\"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}
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)).
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