翻转Schelling过程中几何图形对单色区域的影响

IF 0.4 4区 计算机科学 Q4 MATHEMATICS
Thomas Bläsius , Tobias Friedrich , Martin S. Krejca , Louise Molitor
{"title":"翻转Schelling过程中几何图形对单色区域的影响","authors":"Thomas Bläsius ,&nbsp;Tobias Friedrich ,&nbsp;Martin S. Krejca ,&nbsp;Louise Molitor","doi":"10.1016/j.comgeo.2022.101902","DOIUrl":null,"url":null,"abstract":"<div><p>Schelling's classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We introduce an agent-based saturated open-city variant, the Flip Schelling Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to change their types; similar to a new agent arriving as soon as another agent leaves the vertex.</p><p><span>We investigate the probability that an edge </span><span><math><mo>{</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>}</mo></math></span> is monochrome, i.e., that both vertices <em>u</em> and <em>v</em><span><span> have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two </span>adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and, moreover, that large common neighborhoods are more decisive.</span></p><p><span><span>As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random </span>geometric graphs, we show that the existence of an edge </span><span><math><mo>{</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>}</mo></math></span> makes a highly decisive common neighborhood for <em>u</em> and <em>v</em> more likely. Based on this, we prove the existence of a constant <span><math><mi>c</mi><mo>&gt;</mo><mn>0</mn></math></span> such that the expected fraction of monochrome edges after the FSP is at least <span><math><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mi>c</mi></math></span>. (2) For Erdős–Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most <span><math><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mi>o</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math></span>. Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.</p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The impact of geometry on monochrome regions in the flip Schelling process\",\"authors\":\"Thomas Bläsius ,&nbsp;Tobias Friedrich ,&nbsp;Martin S. Krejca ,&nbsp;Louise Molitor\",\"doi\":\"10.1016/j.comgeo.2022.101902\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Schelling's classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We introduce an agent-based saturated open-city variant, the Flip Schelling Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to change their types; similar to a new agent arriving as soon as another agent leaves the vertex.</p><p><span>We investigate the probability that an edge </span><span><math><mo>{</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>}</mo></math></span> is monochrome, i.e., that both vertices <em>u</em> and <em>v</em><span><span> have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two </span>adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and, moreover, that large common neighborhoods are more decisive.</span></p><p><span><span>As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random </span>geometric graphs, we show that the existence of an edge </span><span><math><mo>{</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>}</mo></math></span> makes a highly decisive common neighborhood for <em>u</em> and <em>v</em> more likely. Based on this, we prove the existence of a constant <span><math><mi>c</mi><mo>&gt;</mo><mn>0</mn></math></span> such that the expected fraction of monochrome edges after the FSP is at least <span><math><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mi>c</mi></math></span>. (2) For Erdős–Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most <span><math><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mi>o</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math></span>. Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.</p></div>\",\"PeriodicalId\":51001,\"journal\":{\"name\":\"Computational Geometry-Theory and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Geometry-Theory and Applications\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0925772122000451\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Geometry-Theory and Applications","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0925772122000451","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

谢林的经典隔离模型对居住隔离现象的广泛传播给出了连贯的解释。我们引入了一种基于代理的饱和开放城市变体,即Flip-Schelling过程(FSP),在该变体中,放置在图上的代理具有两种类型中的一种,并根据其邻域中的主要类型来决定是否更改其类型;类似于新的代理在另一个代理离开顶点时立即到达。我们研究了边{u,v}是单色的概率,即顶点u和v在FSP中具有相同类型的概率,并为分析底层图拓扑结构对居住隔离的影响提供了一个通用框架。特别是,对于两个相邻的顶点,我们证明了一个高度决定性的公共邻域,即具有不同类型的顶点数量之差的绝对值较高的公共邻域支持分离,此外,大的公共邻域更具决定性。作为一个应用,我们研究了FSP在有和没有几何的两个常见随机图模型上的预期行为:(1)对于随机几何图,我们证明了边{u,v}的存在使u和v更有可能成为一个高度决定性的公共邻域。在此基础上,我们证明了一个常数c>;0,使得FSP之后单色边缘的预期分数为至少1/2+c。(2) 对于Erdõs–Rényi图,我们证明了大的公共邻域是不可能的,并且FSP之后单色边缘的预期分数最多为1/2+o(1)。我们的结果表明,基础图的簇结构对所获得的偏析强度有显著影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The impact of geometry on monochrome regions in the flip Schelling process

Schelling's classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We introduce an agent-based saturated open-city variant, the Flip Schelling Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to change their types; similar to a new agent arriving as soon as another agent leaves the vertex.

We investigate the probability that an edge {u,v} is monochrome, i.e., that both vertices u and v have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and, moreover, that large common neighborhoods are more decisive.

As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random geometric graphs, we show that the existence of an edge {u,v} makes a highly decisive common neighborhood for u and v more likely. Based on this, we prove the existence of a constant c>0 such that the expected fraction of monochrome edges after the FSP is at least 1/2+c. (2) For Erdős–Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most 1/2+o(1). Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.

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
CiteScore
1.60
自引率
16.70%
发文量
43
审稿时长
>12 weeks
期刊介绍: Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.
×
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