权重图的等比式哈明嵌入式
Joseph Berleant1, Kristin Sheridan2, Anne Condon3
1Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States of America.
概括
本研究将权重图的汉明嵌入引入汉明图中. 它表明,一个图形可以是汉明嵌入的,如果,只有它的正规等比表示因子可以嵌入,简化了复杂的图形嵌入问题.
科学领域:
- 图形理论 图形理论
- 组合优化的优化.
- 离散的数学 离散的数学
背景情况:
- 同度嵌入式保留了图形顶点之间的最短路径距离.
- 汉明图是与编码理论和计算机科学相关的未加权图.
- 之前的工作重点是将未加权图嵌入Hamming嵌入到完整图中.
研究的目的:
- 为了研究权重图的异面嵌入在未权重的汉明图中 (汉明嵌入).
- 为了利用图形的正规等比表示来分析哈明嵌入.
- 为权重图形建立哈明格嵌入存在的条件.
主要方法:
- 对加权图的哈明嵌入定义在未加权的哈明图中.
- 使用图形的笛卡尔积分分解,称为其正规等比表示.
- 介绍哈明嵌入的正规分区的概念.
主要成果:
- 一个图的每一个哈明嵌入都可以分割成一个正规分区.
- 规范分区的部分为图形规范等比表示的每个因子提供了哈明嵌入.
- 一个图允许哈明嵌入,如果,只有在它的正规等比表示中的每个因子是哈明嵌入的.
结论:
- 这项研究将以前未加权图的结果扩展到加权图.
- 一个图的汉明嵌入存在是由其正规等比表示因子的嵌入性决定的.
- 对于具有非碎的等比表示的图形,通过分析较小的组件图形来简化确定哈明嵌入性.
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