稀疏生成子的出现与贪婪良好分离对分解
The Emergence of Sparse Spanners and Greedy Well-Separated Pair Decomposition
摘要：
在$R^d$中的一组点上的一个图包含任意两点之间的最短路径，其长度至多是它们的欧氏距离的常数因子。在本文中，我们研究新的模型，旨在解释为什么好的空间“出现”在现实中，当他们显然是内置的块与自己的利益和建设是不协调的代理。我们的主要结果是表明，如果边是内置的一个任意的顺序，但边是建立当且仅当它的端点不“接近”的端点现有的边缘，图是一个$(1 + \eps)$的线性数的边缘，常数的平均度，和总的边缘长度作为一个小的对数因子的成本的最小生成树。作为一个副产品，我们展示了一个简单的贪心算法，用于构建最佳大小以及分离对分解，可能是自己的兴趣。
英文摘要：
A spanner graph on a set of points in $R^d$ contains a shortest path between any pair of points with length at most a constant factor of their Euclidean distance. In this paper we investigate new models and aim to interpret why good spanners 'emerge' in reality, when they are clearly built in pieces by agents with their own interests and the construction is not coordinated. Our main result is to show that if edges are built in an arbitrary order but an edge is built if and only if its endpoints are not 'close' to the endpoints of an existing edge, the graph is a $(1 + \eps)$-spanner with a linear number of edges, constant average degree, and the total edge length as a small logarithmic factor of the cost of the minimum spanning tree. As a side product, we show a simple greedy algorithm for constructing optimal size well-separated pair decompositions that may be of interest on its own.
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。
