Arora-Rao-Vazirani结构定理的一个改进
A Reformulation of the Arora-Rao-Vazirani Structure Theorem
摘要：
在一篇著名的论文[ARV]中，Arora，Rao和Vazirani获得了平衡分离器问题和均匀稀疏割的O（sqrt（log n））近似。他们结果的核心是关于满足三角不等式的点集的几何陈述，这也是近似算法和几何嵌入的后续工作的基础。本文利用几何图中的大集在满足三角不等式的点集上的展开，给出了文献[ARV]中结构定理的一个等价形式。
英文摘要：
In a well-known paper[ARV], Arora, Rao and Vazirani obtained an O(sqrt(log n)) approximation to the Balanced Separator problem and Uniform Sparsest Cut. At the heart of their result is a geometric statement about sets of points that satisfy triangle inequalities, which also underlies subsequent work on approximation algorithms and geometric embeddings. In this note, we give an equivalent formulation of the Structure theorem in [ARV] in terms of the expansion of large sets in geometric graphs on sets of points satisfying triangle inequalities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
