距离遗传图中配对支配问题的最优算法
Optimal Algorithm for Paired-Domination in Distance-Hereditary Graphs
AI总结：
针对距离遗传图中的配对支配问题，本文提出$O(n+m)$时间复杂度的最优算法，相比Lin等人$O(n^2)$的方案大幅提升效率，且在有分解树时可达$O(n)$复杂度。
摘要：
支配问题及其变体是算法图论中的经典领域。在这些变体中，配对支配问题因其在安全和监控领域的实际应用而尤为突出。给定输入图$G$，配对支配问题需要找到一个最小支配集$D$，使得$D$在$G$中诱导的子图具有完美匹配。Lin等人在2020年《Algorithmica》期刊的《距离遗传图上的配对支配问题》中提出了时间复杂度为$O(n^2)$的解决方案。本文通过引入$O(n+m)$时间复杂度的算法显著改进了他们的成果，且当提供图$G$的分解树时，该算法的时间复杂度可进一步降低至$O(n)$。
英文摘要：
The domination problem and its variants represent a classical domain within algorithmic graph theory. Among these variants, the paired-domination problem holds particular prominence due to its real-world implications in security and surveillance domains. Given an input graph $G$, the paired-domination problem involves identifying a minimum dominating set $D$ that induces a subgraph of $G$ with a perfect matching. Lin et al.~[\emph{Paired-domination problem on distance-hereditary graphs}, Algorithmica, 2020] previously presented a solution to this problem with a time complexity of $O(n^2)$. This paper significantly enhances their findings by introducing an $O(n+m)$-time algorithm. Furthermore, the time complexity of this algorithm can be reduced to $O(n)$ when provided with a decomposition tree for the graph $G$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
