In this paper we study a maximization version of the classical Edge Dominating Set (EDS) problem, namely, the Upper EDS problem, in the realm of Parameterized Complexity. In this problem, given an undirected graph $G$, a positive integer $k$, the question is to check whether $G$ has a minimal edge dominating set of size at least $k$. We obtain the following results for Upper EDS. We prove that Upper EDS admits a kernel with at most $4k^2-2$ vertices. We also design a fixed-parameter tractable (FPT) algorithm for Upper EDS running in time $2^{\mathcal{O}(k)} \cdot n^{\mathcal{O}(1)}$.
翻译：在本文中,我们研究了经典边际占位(EDS)问题的最大化版本,即在参数化复杂度范围内的上EDS问题。在这个问题中,考虑到一个未方向的图形$G$,正整数$k$,问题在于检查$G$是否拥有最小的边际占位数至少为$k$。我们获得了上EDS的以下结果。我们证明上EDS接纳了一个内核,最多为4k%2-2美元。我们还为时运行的上EDS设计了一个固定参数可移动的算法 $2\mathcal{O}(k)}\cdot n ⁇ mathcal{O}$2\k}。
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