发表机构
School of Mathematics and Statistics, Yunnan University（云南大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种更简单的奖赏收集旅行商问题近似算法，通过省略分裂预处理并将LP相对近似比从1.599改进至1.555761，主要贡献在于对奇偶校正步骤的更强分析。
AI 中文摘要
奖赏收集旅行商问题是度量旅行商问题的一个变体，其中顶点可以通过支付相关罚金而不被访问。目标是最小化旅行长度加上未访问顶点的总罚金。Blauth、Klein和Nägele给出了先前最佳的LP相对1.599近似算法。我们证明，通过省略树分解前的分裂预处理，他们的算法的更简单版本具有LP相对近似比1.555761。改进来自对奇偶校正步骤的更强分析。
英文摘要
The prize-collecting traveling salesperson problem is a variant of the metric traveling salesperson problem in which vertices may be left unvisited by paying their associated penalties. The objective is to minimize the length of the tour plus the total penalty of the unvisited vertices. Blauth, Klein, and Nägele gave the previously best-known LP-relative $1.599$-approximation. We show that a simpler version of their algorithm, obtained by omitting the splitting-off preprocessing before the tree decomposition, has an LP-relative approximation ratio of $1.555761$. The improvement comes entirely from a new analysis of the parity-correction step: a simple analysis already gives $1.56$, and the stated factor follows from a numerical parameter search with exact verification.
Comments25 pages, 2 figures
