增加图形以最小化半径

Joachim Gudmundsson, Y. Sha, Fan Yao
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引用次数: 1

摘要

研究了在增广图半径最小的情况下,通过增加k条边来增广度量图的问题。我们给出了一个简单的3-近似算法,并证明对于任何> 0的ε,除非P = NP,否则不存在多项式时间(5 / 3- ε)近似算法。对于输入图为树的特殊情况,给出了两种精确的算法,其中一种算法推广到处理树宽有界的度量图。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Augmenting Graphs to Minimize the Radius
We study the problem of augmenting a metric graph by adding k edges while minimizing the radius of the augmented graph. We give a simple 3-approximation algorithm and show that there is no polynomial-time (5 / 3 − ϵ )-approximation algorithm, for any ϵ > 0, unless P = NP . We also give two exact algorithms for the special case when the input graph is a tree, one of which is generalized to handle metric graphs with bounded treewidth.
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