🤖 AI Summary
本文通过改进分析方法，简化了之前最佳算法，为带奖旅行商问题提供了一个LP相对近似比为1.555761的新解法。
📝 Abstract
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 from a stronger analysis of the parity-correction step.