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A 43-approximation algorithm for the Maximum Internal Spanning Tree Problem
Journal of Computer and System Sciences ( IF 1.1 ) Pub Date : 2021-01-12 , DOI: 10.1016/j.jcss.2021.01.001
Xingfu Li , Daming Zhu , Lusheng Wang

In this paper, we study the Maximum Internal Spanning Tree Problem (MIST). Given an undirected simple graph G, the task for the Maximum Internal Spanning Tree problem is to find a spanning tree of G with maximum number of internal vertices. We present an approximation algorithm with performance ratio 43, which improves upon the best known performance ratio 32. Our algorithm benefits from a new observation for bounding the number of internal vertices of a spanning tree. We can also give an example to show that the performance ratio 43 is actually tight for this algorithm. Finally, we show that MIST is Max-SNP-hard.



中文翻译:

一种 43内部生成树问题的最大近似算法

在本文中,我们研究了最大内部生成树问题(MIST)。给定一个无向的简单图G,最大内部生成树问题的任务是找到具有最大内部顶点数量的G的生成树。我们提出一种具有性能比的近似算法43,从而改善了最知名的性能比 32。我们的算法得益于对生成树内部顶点数量进行限制的新观察。我们还可以举一个例子来说明性能比43实际上对于该算法来说是严格的。最后,我们证明MIST是Max-SNP困难的。

更新日期:2021-01-18
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