Minmax Tree Cover in the Euclidean Space
J. Graph Algorithms Appl.(2011)
摘要
Let G = (V,E) be an edge-weighted graph, and let w(H) denote the sum of the weights of the edges in a subgraph H of G. Given a positive integer k, the balanced tree partitioning problem requires to cover all vertices in V by a set $\mathcal{T}$ of k trees of the graph so that the ratio α of $\max_{T\in \mathcal{T}}w(T)$ to w(T *)/k is minimized, where T * denotes a minimum spanning tree of G. The problem has been used as a core analysis in designing approximation algorithms for several types of graph partitioning problems over metric spaces, and the performance guarantees depend on the ratio α of the corresponding balanced tree partitioning problems. It is known that the best possible value of α is 2 for the general metric space. In this paper, we study the problem in the d-dimensional Euclidean space ℝ d , and break the bound 2 on α, showing that $\alpha
更多查看译文
关键词
minmax tree cover,edge-weighted graph,metric space,d-dimensional euclidean space,core analysis,balanced tree,approximation algorithm,corresponding balanced tree,k tree,general metric space,euclidean space,positive integer k,approximation algorithms,minimum spanning tree,graph partitioning
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络