通过增加边改进度量图的膨胀
Improving the dilation of a metric graph by adding edges
摘要：
大多数关于spatial的文献都集中在从头开始构建图。本文的重点是添加边来改进现有的图。在这个领域的一个主要的开放问题是：给定一个图嵌入在度量空间，和预算的$k$边缘，其中$k$边缘，我们添加到产生一个最小膨胀图？$k=1$过去曾被研究过，但对$k > 1$没有重大突破的特殊情况。我们提供了第一个积极的结果，一个$O(k)$近似算法，运行在$O(n^3 \log n)$的时间。
英文摘要：
Most of the literature on spanners focuses on building the graph from scratch. This paper instead focuses on adding edges to improve an existing graph. A major open problem in this field is: given a graph embedded in a metric space, and a budget of $k$ edges, which $k$ edges do we add to produce a minimum-dilation graph? The special case where $k=1$ has been studied in the past, but no major breakthroughs have been made for $k > 1$. We provide the first positive result, an $O(k)$-approximation algorithm that runs in $O(n^3 \log n)$ time.
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。
