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Algorithmic aspects of upper edge domination
Theoretical Computer Science ( IF 0.9 ) Pub Date : 2021-04-01 , DOI: 10.1016/j.tcs.2021.03.038
Jérôme Monnot , Henning Fernau , David Manlove

We study the problem of finding a minimal edge dominating set of maximum size in a given graph G=(V,E), called Upper EDS. We show that this problem is not approximable within a ratio of nε12, for any ε(0,12), assuming PNP, where n=|V|. On the other hand, for graphs of minimum degree at least 2, we give an approximation algorithm with ratio 1n, matching this lower bound. We further show that Upper EDS is APX-complete in bipartite graphs of maximum degree 4, and NP-hard in planar bipartite graphs of maximum degree 4.



中文翻译:

上边缘支配的算法方面

我们研究了在给定图中找到最大尺寸的最小边支配集的问题 G=(,),称为上 EDS。我们证明了这个问题在比例为nε-12,对于任何 ε(0,12), 假设 NP, 在哪里 n=||. 另一方面,对于最小度数至少为 2 的图,我们给出了一个近似算法1n,匹配这个下界。我们进一步表明,上 EDS悉尼证券交易所-在最大程度为 4 的二部图中完成,和 NP-hard 在最大度数为 4 的平面二部图中。

更新日期:2021-06-01
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