For a graph G = (V, E) with no isolated vertices, a set \(D\subseteq V\) is called a semipaired dominating set of G if (i)D is a dominating set of G, and (ii)D can be partitioned into two element subsets such that the vertices in each two element set are at distance at most two. The minimum cardinality of a semipaired dominating set of G is called the semipaired domination number of G, and is denoted by γ_pr2(G). The Minimum Semipaired Domination problem is to find a semipaired dominating set of G of cardinality γ_pr2(G). In this paper, we initiate the algorithmic study of the Minimum Semipaired Domination problem. We show that the decision version of the Minimum Semipaired Domination problem is NP-complete for bipartite graphs and chordal graphs. On the positive side, we present a linear-time algorithm to compute a minimum cardinality semipaired dominating set of interval graphs. We also propose a \(1+\ln (2{\Delta }+2)\)-approximation algorithm for the Minimum Semipaired Domination problem, where Δ denotes the maximum degree of the graph and show that the Minimum Semipaired Domination problem cannot be approximated within \((1-\epsilon ) \ln |V|\) for any 𝜖 > 0 unless P=NP.

对于没有孤立顶点的图G =（V，E），如果（i）D是G的主导集，并且（i i），则将\（D \ subseteq V \）称为G的半对主导集。D可以划分为两个元素子集，以使每两个元素集中的顶点之间的距离最多为两个。一semipaired支配集的最小基数ģ被称为的semipaired控制数ģ，并且由表示γ _{p - [R 2}（g ^）。的最小Semipaired统治问题是要找到一个semipaired支配集的ģ基数的γ _{p - [R 2}（g ^）。在本文中，我们启动了最小半对支配问题的算法研究。我们证明了最小半配对控制问题的决策版本对于二部图和弦图都是NP完全的。在积极方面，我们提出了一种线性时间算法来计算最小基数半对支配间隔图集。我们还为最小半配对控制提出了\（1+ \ ln（2 {\ Delta} +2）\） -近似算法问题，其中Δ表示图的最大程度，并且表明对于任何𝜖 > 0，除非P = NP，否则最小半配对支配问题不能在\（（1- \ epsilon）\ ln | V | \）内近似。