POWRE: Distance Graphs and Channel Assignment Problems

POWRE：距离图和通道分配问题

• 批准号: 9805945
• 负责人: Daphne Liu
• 金额: $ 7.37万
• 依托单位: California State L A University Auxiliary Services Inc.
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-01 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9805945&HistoricalAwards=false
• 关键词: POWRE; Distance; Graphs; Channel; Assignment

This project initiates further research on the fields of distancegraphs and the channel assignment (also named T-coloring). Bothfields have been active research areas for years.There are two major components in this project. The first oneextends research on problems on distance graphs and T-coloringand their connections. The first connection between distancegraphs and T-coloring was proved by the PI [1997] and was used toobtain extend solutions on a problem on distance graphs raisedand studied by Eggleton, Erdos and Skilton [1985]. A joint workwith Chang and Zhu [1997] completely solved the problem andproved the second connection which showed that the fractionalchromatic number of a distance graph is equal to its asymptoticT-coloring ratio. The latter parameter was shown, by Griggs andthe PI [1996], to be closely related to an earlier number theoryproblem, namely, density of sequences with missing differences,studied by Cantor and Gordon [1975] and by Haralambis [1977]. Theproject will follow this direction of research to explore otheruseful connections between distance graphs and T-coloring, toobtain further results on distance graphs including theirchromatic number, circular chromatic number and fractionalchromatic number, and to study a generalization of the problem ofEggleton, Erdos and Skilton.Motivated from practical situations in the channel assignmentproblem, several variations of T-coloring have been studied. Thesecond part of this project will extend the research of the PI'spast and current work and joint work on two variations ofT-coloring, namely, no-hole T-coloring and distance two labelingsof graphs. Research on the distance two labelings will alsobenefit the practical two-level-interference channel assignmentproblem.For update references and works of this project, readers arewelcome to visit the PI's web site at:www.calstatela.edu/faculty/dliu/dliu.htm or email to:[e-mail] POWRE project is supported by the MPS Office of Multidisciplinary Activities (OMA).

本计画将在距离图与通道分配（也称为T-着色）领域作进一步的研究。 这两个领域多年来一直是活跃的研究领域。 第一部分是对距离图和T-染色及其联系问题的研究。 距离图与T-染色的第一个联系是由PI [1997]证明的，并被用于Eggleton，Erdos和Skilton [1985]提出和研究的距离图问题的推广解。 Chang和Zhu [1997]的一个联合工作完全解决了这个问题，并证明了第二种联系，即距离图的分数色数等于它的渐近T-染色比。 后一个参数被Griggs和PI [1996]证明与一个早期的数论问题密切相关，即Cantor和Gordon [1975]和Haralambis [1977]研究的缺失差序列的密度。本项目将沿着这一研究方向探索距离图与T-着色之间的其他有用联系，进一步得到距离图的色数、圆色数和分数色数等结果，并研究Eggleton，Erdos和Skilton问题的推广。 本项目的第二部分是对PI的过去和现在的工作以及与PI的联合工作的扩展，主要研究了T-染色的两个变种，即图的无洞T-染色和距离二标号。 对距离两标记的研究也将有助于实际的两电平干扰信道分配问题。如需本项目的最新参考资料和工作，欢迎访问PI的网站：www.calstatela.edu/faculty/dliu/dliu.htm或电子邮件：[e-mail]。