求解最小连通支配集的性能保证进化算法
Performance Guaranteed Evolutionary Algorithm for Minimum Connected Dominating Set
摘要：
连通支配集是无线传感器网络虚拟骨干网的一种广泛采用的模型。在本文中，我们设计了一个进化算法的最小连通支配集问题（MinCDS），其性能从理论上保证的计算时间和近似比。给定一个连通图$G=(V,E)$，连通支配集（CDS）是一个子集$C\subseteq V$，使得$V\setminus C$中的每个顶点在$C$中都有一个邻居，并且由$C$诱导的$G$的子图是连通的. MinCDS的目标是找到具有最小基数的$G$的CDS。我们表明，我们的进化算法可以找到一个CDS在预期的$O(n^3)$时间内接近最优值的因素$(2+\lnΔ)$，其中$n$和$Δ$的顶点数和最大程度的图$G$，分别。
英文摘要：
A connected dominating set is a widely adopted model for the virtual backbone of a wireless sensor network. In this paper, we design an evolutionary algorithm for the minimum connected dominating set problem (MinCDS), whose performance is theoretically guaranteed in terms of both computation time and approximation ratio. Given a connected graph $G=(V,E)$, a connected dominating set (CDS) is a subset $C\subseteq V$ such that every vertex in $V\setminus C$ has a neighbor in $C$, and the subgraph of $G$ induced by $C$ is connected. The goal of MinCDS is to find a CDS of $G$ with the minimum cardinality. We show that our evolutionary algorithm can find a CDS in expected $O(n^3)$ time which approximates the optimal value within factor $(2+\lnΔ)$, where $n$ and $Δ$ are the number of vertices and the maximum degree of graph $G$, respectively.
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。
