Let \(G=(V,E)\) be a graph without isolated vertices. A set \(D\subseteq V\) is said to be a dominating set of G if for every vertex \(v\in V\setminus D\), there exists a vertex \(u\in D\) such that \(uv\in E\). A set \(D\subseteq V\) is called a semitotal dominating set of G if D is a dominating set and every vertex in D is within distance 2 from another vertex of D. For a given graph G, the semitotal domination problem is to find a semitotal dominating set of G with minimum cardinality. The decision version of the semitotal domination problem is shown to be NP-complete for chordal graphs and bipartite graphs. Henning and Pandey (Theor Comput Sci 766:46–57, 2019) proposed an \(O(n^2)\) time algorithm for computing a minimum semitotal dominating set in interval graphs. In this paper, we show that for a given interval graph \(G=(V,E)\), a minimum semitotal dominating set of G can be computed in \(O(n+m)\) time, where \(n=|V|\) and \(m=|E|\). This improves the complexity of the semitotal domination problem for interval graphs from \(O(n^2)\) to \(O(n+m)\).

令\（G =（V，E）\）是没有孤立顶点的图。一组\（d \ subseteq V \）被说成是一个主导组ģ如果对于每个顶点（以V v \ \ setminus d \）\，存在顶点\（U \在d \） ，使得\ （uv \ in E \）。一组\（d \ subseteq V \）被称为semitotal控制集的ģ如果d是一个控制集，并在每个顶点d是距离2内的另一顶点d。对于给定的图G，半总支配问题是找到G的半总支配集用最小的基数。对于和弦图和二部图，半总支配问题的决策版本显示为NP-完全。Henning和Pandey（Theor Comput Sci 766：46–57，2019）提出了一种\（O（n ^ 2）\）时间算法，用于计算区间图中的最小半总支配集。在本文中，我们表明对于给定的间隔图\（G =（V，E）\），可以在\（O（n + m）\）时间内计算出G的最小半总控制集，其中\（ n = | V | \）和\（m = | E | \）。这提高了从\（O（n ^ 2）\）到\（O（n + m）\）的区间图的半总控制问题的复杂性。